research article a multilayer improved rbm network based...

Research ArticleA Multilayer Improved RBM Network Based Image CompressionMethod in Wireless Sensor Networks

Chunling Cheng1 Shu Wang1 Xingguo Chen1 and Yanying Yang2

1College of Computer Nanjing University of Posts and Telecommunications Nanjing 213001 China2Department of Information and Technology Nanjing College of Forestry Police Nanjing 210023 China

Correspondence should be addressed to Shu Wang wangshu njuptfoxmailcom

Received 5 November 2015 Accepted 21 January 2016

Academic Editor Reza Malekian

Copyright copy 2016 Chunling Cheng et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The processing capacity and power of nodes in a Wireless Sensor Network (WSN) are limited And most image compressionalgorithms inWSNare subject to random image content changes or have low image qualities after the images are decodedThereforean image compression method based on multilayer Restricted Boltzmann Machine (RBM) network is proposed in this paper Thealternative iteration algorithm is also applied in RBM to optimize the training process The proposed image compression methodis compared with a region of interest (ROI) compression method in simulations Under the same compression ratio the qualitiesof reconstructed images are better than that of ROI When the number of hidden units in top RBM layer is 8 the peak signal-to-noise ratio (PSNR) of the multilayer RBM network compression method is 742141 and it is much higher than that of ROI whichis 602093 The multilayer RBM based image compression method has better compression performance and can effectively reducethe energy consumption during image transmission in WSN

1 Introduction

WSNs emerge as a new research hot spot in recent yearsIn a WSN the resources in each sensor node are limitedTherefore it is a huge challenge to reduce energy consump-tion and extend the lifetime of a sensor node The energycost of transmitting image in WSN remains to be a mainfactor that affects the lifetime of a sensor node To reduce thebandwidth and energy consumption in image transmissionit is necessary to propose a more effective image compressionmethod

Currently the image compression algorithms in WSNsare subject to the random changes in image contents It isunrealistic to describe various images in real world with onlyone kind of image model To address this issue the neuralnetwork is adopted in WSNs to compress images As animportant branch of neural network Deep Learning [1 2] hasmany computation models Restricted Boltzmann Machine(RBM) [3 4] is one of the prime models of Deep LearningWhen themultilayer RBMbased network is used to compressimages the quality of compressed images hasmuch to dowith

the likelihood of training data in each RBM layer Moreoverthe training complexity of RBM has a great effect on theenergy consumption of image compression coding

Most of the current RBM training algorithms are carriedout only with large quantities of sampling using MarkovChain Monte Carlo (MCMC) method The average jointprobability between visible units and hidden units is esti-mated based on these samples without calculating the nor-malizing parameter However the frequency of state transi-tions should be enough to ensure that the acquired samplessatisfy the target distribution when MCMC sampling isconducted Also large quantities of sampling are needed toimprove the accuracy of the estimated value which increasesthe difficulties of RBM training Aiming at the problemsencountered in the current RBM training process alternativealgorithm is used in the RBM training process

We have adopted the alternative iteration algorithm intothe process of RBM training In this algorithm the normaliz-ing parameter is considered as another unknown parameterTherefore the likelihood function can be transformed intotwo subfunctions One is about the normalizing parameter

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2016 Article ID 1851829 11 pageshttpdxdoiorg10115520161851829

2 International Journal of Distributed Sensor Networks

and the other is about the model distribution parameter Themodel distribution parameter which is about to be assessed iscalculated alternatively with the normalizing parameter andeventually can be obtained through a highly efficient trainingprocess This training process is of low complexity Thisalgorithm can improve the likelihood of RBM for trainingdata

Furthermore we have used the improved RBM train-ing process in image compression in WSNs A multilayerimproved RBM based image compression method is pre-sented in this paper This image compression method canextract more abstract data to coding based on the image fea-tures and has a better compression effect In the simulationsthe reconstructed image quality of multilayer RBM networksis superior to that of another image compression methodunder the same compression ratio which will be stated indetail in Section 5 At the same time the proposed imagecompression method can reduce the energy consumptionduring image data transmission process

The rest of the paper is organized as follows In Section 2related work on image compression and RBM training algo-rithms is discussed Section 3 presents the basic idea of themultilayer RBM network based image compression methodAnd the RBM model and the improved RBM algorithmbased on alternative iteration are depicted in Section 4 Theperformance of the proposed algorithm is compared withsome typical algorithms in Section 5 At last conclusions andfuture work are presented in Section 6

2 Related Work

Typical image compression algorithms include time-spacerelated data compression algorithm wavelet transform baseddata compression algorithm distributed data compressionalgorithm and improved traditional data compression algo-rithm

The space-time relativity based data compression algo-rithm mainly includes prediction coding and linear fittingmethod for time series A prediction coding method isproposed in [5] It can effectively evaluate the source databased on the time relativity of the source data However theprediction coding based data compression method does notinvolve large amount of image data transmission Reference[6] proposes a curve fitting technology based data flow com-pression method It compresses data collected on each nodeand restores the data in the base station But this method isvery complex and it does not consider the transmission delayin each sensor node Reference [7] presents a space-time datacompression technology based on simple linear regressionmodel This method can eliminate data redundancy in singlenode and collector node respectively But only the data thatsatisfies the error requirement is considered in this methodAbnormal data is not involved in this method

Wavelet transform is a time-frequency analysis methodwhich is superior to traditional signal analysis methodsReference [8] considers the existence of stream data in thedata transmission of sensor networks It compresses databy using wavelet transform based on the data aggregation

and the DC routing algorithm In [9 10] a ring modelbased distributed time-space data compression algorithmand a wavelet based self-fitting data compression algorithmare proposed Storage efficient two-dimension and three-dimension continuouswavelet data compressionmethods areproposed in [11] They are based on the ring model of fittingsensor networkwavelet transform and the overlapping clusterpartition model respectively They are storage efficient andcan save the transmission energy consumption in networks

The distributed data compression algorithm is based onthe fact that all the centralized and decentralized informationservices can be implementedThe feature of a distributed datacompression algorithm is that it can reduce the data amountby the cooperative work among different sensor nodes Achain model based distributed data compression algorithmis proposed in [12] based on the random lengths of waveletsThis algorithm designs a chain model that is suitable forwavelet transform It is suitable for random lengths of waveletfunctions

Traditional lossless data compression methods mainlyinclude Run Length Encoding technology Huffman codingcompression dictionary compression method and arith-metic compression method These methods are mainlyadopted in advanced computers or workstations In theapplication of sensor networks the processing capacity ofeach processor is limited Its memory is small Therefore it isessential to optimize the traditional compression algorithmIn [13] the difference between the two perceptual pieces ofdata is encoded based on the self-fitting Huffman codingalgorithm Reference [14] proposes a region of interest (ROI)based lossy-lossless image compression method It carriesout different coding compression methods on the small areathat is important to itself and the other large area In thisway compression ratio is improved under the condition thatsensitive information is reserved

In recent years Deep Learning (DL) is widely usedin WSNs to carry out image compression Deep Learningextracts the characteristics of data from low to high layersby modeling the layer model of analyzing in human brainsHowever the effect of image compression using DL issubject to the likelihood of RBM for training data and thetraining complexity of RBMTherefore an improved trainingalgorithm based on RBM training is also proposed in thispaper

Currently researchers have made lots of researches onRBM training algorithms In 2002 Hinton proposed a fastlearning algorithm of RBM Contrastive Divergence (CD)[15]This algorithm is a RBMapproximate learning algorithmof high efficiency However the RBM model acquired by theCD algorithm is not a maximum entropymodel and does nothave high likelihood when training data [16]

In 2008 Tijmen Tieleman proposed a Persistent Con-trastive Divergence (PCD) algorithm [17]This algorithm hasremedied the deficiency in CD algorithm It has the sameefficiency of CDalgorithm and does not violate themaximumlikelihood learning In addition the RBM obtained by PCDtraining has more powerful pattern generation capacity In2009 Tieleman and Hinton made further improvement ofPCD algorithm [18] and proposed Fast Persistent Contrastive

International Journal of Distributed Sensor Networks 3

Divergence (FPCD) algorithm A group of auxiliary param-eters are involved in improving the Markov chain compositerate in PCD Another group of parameters which are calledFast Weight and denoted by1198821015840 are learned at the same timewhen carrying out RBM learning

Some RBM learning algorithms of MCMC samplingmethods based on tempering also appear during these yearsA parallel tempering algorithm based on RBM is introducedin [19]This algorithmmaintains a state for every distributionunder a certain temperature During state transition thelow temperature distribution state can be transmitted tohigh temperature distribution state by exchanging the twodistribution states In this way there is a high chance thatthe low temperature distribution state can be transmitted toa remote peak value therefore the whole distribution canbe sampled In 2014 Xu et al proposed a tempered basedMCMC method Tempered Transition in [20] to learn RBMmodel The main idea of Tempered Transition is to maintainthe current state in the target distribution When a new stateappears the state transition is carried out step by step fromlow to high temperature by which the state gravity fromthe current peak value can be decreased At last a group ofstate transitions from high to low temperature are conducteduntil the temperature gets normal The essence of the abovetwo algorithms can improve the RBM training efficiency byadopting the MCMC sampling method based on tempering[21]

3 Image Compression UsingMultilayer RBM Network

In a WSN the data transmission process can be dividedinto two parts data compression encoding process and datadecoding process The image sending and receiving processin WSNs can be shown in Figure 1

The basic idea of the multilayer based RBM network datacompression encoding method is as follows firstly an imagewhose pixel is 119872 times 119873 is changed into 119872 times 119873 pixel matrixthen normalization processing is carried out on each elementin this matrix based on the mean distribution preprocessingmethod and each element in the original matrix is changedin the range [0 1] We denote the changed matrix by 119892

119892 = (1198920row 1198921row 119892(119873minus1)row)

119879

=

[[[[[[

[

11989200

11989201

sdot sdot sdot 1198920119873minus1

11989210

11989211


d

119892119872minus10

119892119872minus11

sdot sdot sdot 119892119872minus1119873minus1

]]]]]]

]

(1)

where 119892119894row denotes a row in the matrix and 0 le 119894row lt 119872

119873 is the number of elements in each rowThen the image matrix 119892 is inputted into the multilayer

RBM network The network contains an input layer andmultiple hidden layers The connection weights and biasbetween input layer units and hidden layer units can beadjusted so as to make the hidden layer output equal to

PreprocessingThe

wirelesssender

Imagecompression

encodingtechnology

Communicationchannel

Imagedecoding

technology

Wirelessreceiving

end

Original image

data

Receiving image data

Figure 1 The image sending and receiving process

Input

Outputlayer

layer

RBM

RBM

RBM

Encoding

Encoding

Encoding

Decoding

Decoding

Decoding

Output the compressedimage data

Input original imagematrix

middot middot middot




Figure 2 Basic idea of image compression using multilayer RBM

the input of input layer as much as possible The output ofRBM hidden layer in the first layer is inputted into the RBMin the second layer When the number of hidden layer unitsis smaller than that of the input layer units it means thatthe hidden layer can effectively express the input of the inputlayerThe transformation from input layer to hidden layer canbe seen as the process of compression encoding The processof multilayer RBM network image compression is shown inFigure 2

The bottom input layer consists of 119872 times 119873 neural unitsEach neural unit represents a pixel in 119872 times 119873 image Thenumber of hidden units can be determined based on theimage compression ratio

Image decoding is the inverse process of image compres-sion coding process The compressed image is inputted intothe topmost layer and then is decoded from layer to layer Atlast the bottom level outputs the original image

Themain part of the improved image compression codingmethod is RBM It is essential to improve the likelihood ofRBM for image data so as to ensure high similarity betweenthe original image and the image after decoding Thereforewe have improved the training method of RBM


W

Hidden layer h

Visible layer v



Figure 3 Graph of RBMmodel

4 An Improved RBM Algorithm Based onAlternative Iteration Algorithm

41 The RBMModel RBM can be assumed as an undirectedgraph model [22] As is shown in Figure 3 V is the visiblelayer and ℎ is the hidden layer 119882 denotes the connectingweights of the edges that connect the two layers

Assume that there are 119899 visible units and119898 hidden unitsAnd the states of the visible and hidden units are referred toas vectors V and ℎ accordingly Then for a certain combinedstate (V ℎ) the energy of the RBM system can be defined as

119864 (V ℎ | 120579) = minus

119899

sum

119894=1

119886119894V119894minus

119898

sum

119895=1

119887119895ℎ119895minus

119899

sum

119894=1

119898

sum

119895=1

ℎ119895119908119894119895V119894 (2)

where 120579 = 119908119894119895 119886119894 119887119895 119908119894119895denotes the connecting weight

between visible unit 119894 and hidden unit 119895 119886119894is the bias of the

visible unit 119894 and 119887119895is the bias of the hidden units All the

parameters are real numbers And when these parameters aredecided we can get the joint probability distribution of (V ℎ)based on this energy function (2)

119875 (V ℎ | 120579) =119890minus119864(Vℎ|120579)

119885 (120579) (3)

where 119885(120579) = sumVℎ 119890minus119864(Vℎ|120579) is the normalizing parameter

The object of RBM learning process is to determine 120579 theparameter fitting training data Traditional way of getting thevalue of 120579 is to maximize the log-likelihood function basedon RBM

120579lowast= argmax

120579

119871 (120579) = argmax120579

119899119904

sum

119894=1

log119875 (V119894 | 120579) (4)

The stochastic gradient ascent is usually used to get theoptimum parameter 120579

lowast [23] The critical part during thisprocess is to calculate partial derivatives of log119875(V119894 | 120579)

with respect to every model distribution parameterThe jointdistribution of the visible and hidden units is involved andthis distribution will be determined only if 119885(120579) is obtainedwhich will need 2

119898+119899 times of calculationFrom the current researches the approximate value of

joint distribution can be obtained by some samplingmethodslike Gibbs Sampling [24] CD and so on However mostof these methods have the defect that the RBM training isvery complex because of the frequent state transitions andlarge quantities of sampling We propose applying alternative

iteration algorithm toRBMtrainingWhen themodel param-eter cannot be calculated because of some other uncertainparameters alternative iteration algorithm can be applied toget the maximum estimated value of these parameters usingiteration strategy

42 The Alternative Iteration The alternative iteration algo-rithm is a common method to solve optimization problemsFor instance there is a maximization problem max119891(119909 119910)Firstly 119909 keeps unchangeable and 119910 is changed to increasefunction 119891 Then 119910 keeps unchangeable and 119909 is changed toincrease 119891 The two operations are carried out alternativelyuntil 119891 cannot increase any more

The alternative iteration algorithm is adopted in thispaper to solve the problem of RBM training The likelihoodfunction 119897 in RBM training is defined as

max 119897 (120579 119911) (5)

where 119909 is the formalizing parameter 119911 and 119910 denotes themodel parameter 120579

The traditional way of getting the value of 120579 is tomaximize119897(120579) by using maximum likelihood estimation Generally weintend to get the maximum model distribution parameter120579 which can maximize the likelihood function But thenormalizing parameter 119911 is involved in this process whichmakes it quite difficult to calculate the likelihood functionHowever it will be easier to get the model parameter when119911 is already known The alternative iteration algorithm isfirstly adopted in RBM in this paperThe problem of trainingRBM can be considered as the double parameters solvingproblem For the two groups of unknown parameters 119911 and120579 we firstly keep 120579 unchangeable to get the expression of 119911With 120579 in this expression the likelihood function of 119911 can beobtained And then we keep estimated 119911 unchangeable anddeduce themaximization function of 120579 based on themarginaldistribution of the joint distribution of visible and hiddenlayers in RBM The improved algorithm will carry out thetwo operations alternatively until it satisfies the terminationconditions

43The Process of Calculating RBM Parameters by AlternativeIteration Assume that there is a group of training samples119881 = V1 V2 V3 V119894 V119894 = (V119894

1 V1198942 V119894

119899V) 119894 = 1 2

119899119904 where 119899V is the dimension of input sample whose value

is equal to the number of units in the visible layer and 119899119904is

the number of samples All of these samples are independentof each other After the input of sample V119894 and 119905 times ofiterations the value of the model parameter is denoted by 120579

119894

119905

and 119911119905denotes the value of the normalizing parameter where

119905 isin (0 119879) and 119879 is the maximum number of iterations 120579119894denotes the final value of themodel parameter when finishingthe training with the input of sample V119894 And 120579

0 is the initialinput value of the model parameter

When the algorithmbegins themodel parameter is firstlyinitialized by 1205790Then we take the first sample V1 as the inputof RBM and we set 1205791

0= 1205790 The normalized parameter is

then estimated and we get an initial value 1199111based on 120579

1

0


The model distributed parameter is estimated and changedto 1205791

1based on 119911

1 Continue to estimate the above two

parameters alternatively until the convergence condition issatisfied or it reaches the maximum iteration times 119879 Thefinal value of the model parameter which is obtained bysample V119894 is denoted by 120579

119894 After that the model parameteris denoted by 1205791 It is the initial value of the model parameterwhen inputting the second sample V2 which means 1205792

0= 1205791

When sample V119894 and model parameter 120579119894119905are inputted we

need to consider the objective function of 119911119905+1

Assume that119911119905= 119885(119911

119894| 120579119894

119905) is the distribution of the normalized parameter

of the sample when 120579119894

119905keeps unchanged where 119911

119894 is thenormalized parameter of sample V119894 The satisfied conditionsof 119885(119911

119894| 120579119894

119905) aresum

119911119894 119885(119911119894| 120579119894

119905) = 1 and119885(119911

119894| 120579119894

119905) ge 0 Because

the log function is concave we can calculate the approximateexpression of 119911 by using the Jensen inequality Then we canderive the following equation

119899V

sum

119899=1

log119901 (V119894119899 120579119894

119905) =

119899V

sum

119899=1

logsum119911119894

119901 (V119894119899 119911119894 120579119894

119905) (6)

Multiply the denominator and numerator of the rightfraction in (6) by 119885(119911

119894| 120579119894

119905)

119899V

sum

119899=1

log119901 (V119894119899 120579119894

119905) =

119899V

sum

119899=1

logsum119911119894

119885(119911119894| 120579119894

119905)

119901 (V119894 119911119894 120579119894119905)

119885 (119911119894 | 120579119894

119905) (7)

We can deduce from the Jensen inequality and theproperty concave function the following equation

119899V

sum

119899=1

logsum119911119894

119885(119911119894| 120579119894

119905)

119901 (V119894119899 119911119894 120579119894

119905)

119885 (119911119894 | 120579119894

119905)

ge

119899V

sum

119899=1

sum

119911119894

119885(119911119894| 120579119894

119905) log

119901 (V119894119899 119911119894 120579119894

119905)

119885 (119911119894 | 120579119894

119905)

(8)

Equation (8) is true if and only if 119901(V119894119899 119911119894 120579119894

119905)119885(119911

119894| 120579119894

119905) =

119888 where 119888 is a constant which is independent of 119911119894According to sum

119911119894 119885(119911119894

| 120579119894

119905) = 1 we can draw the

following equation

119885(119911119894| 120579119894

119905) =

119901 (V119894119899 119911119894 120579119894

119905)

sum119911119894 119901 (V119894119899 119911119894 120579119894

119905)=

119901 (V119894119899 119911119894 120579119894

119905)

119901 (V119894119899 120579119894

119905)

= 119901 (119911119894| V119894119899 120579119894

119905)

(9)

When 120579119894

119905keeps unchangeable we maximize 119901(V119894 | 119911

119905)

which is the same as maximizing ln119901(V119894 | 119911119905) Hence

119911119905+1

= arg max119911119905

119897 (119911119905) = arg max

119911119905

119899V

sum

119899=1

ln119901 (V119894119899| 119911119905) (10)

The normalized parameter can be estimated and we get avalue 119911

119905+1

At this time we need to choose the equation to calculate120579119894

119905+1 When 119911

119905+1and 120579

119894

119905are all already known we can get the

joint probability distribution of (V119894 ℎ) based on (1)

119901 (V119894 ℎ | 120579119894

119905) =

119890minus119864(V119894 ℎ|120579119894

119905)

119885 (120579119894

119905)

(11)

where 119885(120579119894

119905) is the normalized parameter 119911

119905+1which is

obtained aboveWe can get themarginal distribution of the joint probabil-

ity distribution 119901(V119894 ℎ | 120579119894

119905) based on the derivation equation

of the original RBM

119901 (V119894 | 120579119894119905) =

1

119911119905+1

sum

ℎ

119890minus119864(V119894 ℎ|120579119894

119905) (12)

Then we keep 119911119905+1

unchanged and get a value 120579119894119905+1

of themodel parameter

120579119894

119905+1= arg max

120579119894

119905

119897 (120579119894

119905) = arg max

120579119894

119905

119899V

sum

119899=1

ln119901 (V119894119899| 120579119894

119905) (13)

However the initial value 1205790 we assigned to the model

parameter may not be suitable for the model In that casewe can update the value of the model parameter by iterativeoptimization based on the alternative iteration algorithmThus sample V119894 can be used to estimate a value of 120579119894 120579119894 whichis obtained by the training of former sample can be used asthe initial value of 120579119894+1 120579119894+1 is the model parameter whichis about to be estimated based on the next sample Repeatthe optimization operations until termination conditions aresatisfied

The improved RBM algorithm is described inAlgorithm 1

5 Simulation Experiments andResults Analysis

The experiment consists of three parts the performanceanalysis of RBM the analysis of the compression performanceof the proposed image compression method and the evalu-ation of reconstructed image quality the analysis of energyconsumption inWSNs when multilayer RBM network imagecompressionmethod is usedMATLAB 2013a is used to carryout the simulations

51 Performance Analysis of the Improved RBM The datasetsof our experiment are the famous handwritten digitaldatabase of MNIST [25] and the toy dataset The MNISTdataset consists of 50000 groups of training samples and10000 groups of testing samples Each group of samplesconsists of a grayscale imagewhose resolution is 28lowast28Thereare handwritten Arabic numerals in the image These Arabicnumerals have their indexes so as to conduct the experimentwith supervised learning Part of the data samples in theMNIST dataset is shown in Figure 4

Compared withMINST dataset the toy dataset is simplerand lower dimensional It consists of 10000 images Each


Setting the convergence threshold 120590 the terminal threshold 120576

Input the value of the model parameter by pre training 1205790 maximum

iteration times 119879 number of hidden units 119899ℎ

Output the final value of the model parameter 120579119894For 119894 = 1 2 119899

119904(for all samples)

For 119905 = 1 2 119879

Computing 119911119905+1

119911119905+1

= argmax119911119905

119897(119911119905) = argmax

119911119905

sum119899V119899=1

ln119901(V119894119899| 119911119905)

Computing 120579119894

119905+1 120579119894119905+1

= argmax120579119894

119905

119897(120579119894

119905) = argmax

120579119894

119905

sum119899V119899=1

ln119901(V119894119899| 120579119894

119905)

Judging the reconstruction error of the model reaches 120590End forJudging the difference of the likelihoods of the two RBMs defined

by the adjacent parameters is within (0 120576)

End for

Algorithm 1 The RBM algorithm based on alternative iteration algorithm

Figure 4 Part of samples of MNIST database

image has 4 times 4 binary pixels The dataset is generated in thesame way as that mentioned in [26]

We compare the proposed algorithm with PCD algo-rithm parallel tempering algorithm (PT-K) [27] and paralleltempering with equienergy moves (PTEE) [28] in the experi-ments In PT-K119870 is the number of auxiliary distributions ofparallel tempering under different temperaturesThe value ofeach temperature is usually between 09 and 1The parameterin PT-K can be easily controlled and in our experiments 119870is set to 5 and 10 respectively Based on some preliminaryexperiments we find that PT can achieve better likelihoodscores than that of using 5 chains when using 10 chains Resultyielded by PTEE when using 5 chains is similar to that whenusing 10 chains which means that PTEE cannot be affectedby the number of Markov chains to some extent [28] Sowe show the results obtained by using PTEE and PT with 10chains

We evaluate their qualities by the likelihood of the RBMfor training data with two methods the reconstruction errorand enumerating states of hidden units

Firstly we compare the reconstruction errors of fouralgorithms with different numbers of hidden nodes on theMNIST dataset and toy dataset The first 30000 groups ofsamples in MINIST are divided into three parts Each partincludes 10000 groups of samples The number of hiddenunits is set to 10 15 20 25 30 50 100 200 250 300 and 350The number of iterations on each part ranges from 1 to 45And the average reconstruction errors of the three parts after15 and 30 times of iterations are shown respectively belowThen the experiments on the toy dataset are also executed

20

30

40

50

60

70

80

90

0 50 100 150 200 250 300 350

The a

vera

ge re

cons

truc

tion

erro

r (2-

norm

)

The number of hidden units

PCDOur proposed algorithm

PT-10PTEE-10

Figure 5 The reconstruction errors of the four algorithms after 15times of iterations on the MNIST dataset

We set the number of hidden units to 10 15 20 25 30 50100 150 200 250 and 300 Results obtained by using PT-10 PTEE-10 PCD and the proposed algorithm are shown inFigures 5ndash8

From Figures 5 and 6 we can see that the averagereconstruction error of the proposed algorithm is alwayssmaller than the other three algorithms on the MNISTdataset And we can get similar results from Figures 7 and8

Figures 5ndash8 show that all of the reconstruction errors offour algorithms decrease when the number of hidden unitsincreases When there are a small number of hidden unitsthe reconstruction error obtained by the proposed algorithmis close to that of the other three algorithms However whenthe number of hidden units increases the superiority ofthe proposed algorithm appears gradually And we can seedecreasing ratios of the average reconstruction errors of PT-10 PTEE-10 and our proposed algorithm compared with


20

30

40

50

60

70

80

90

0 50 100 150 200 250 300 350

The a

vera

ge re

cons

truc

tion

erro

r (2-

norm

)



PT-10PTEE-10


40

50

60

70

80

90

100

110

120

0 50 100 150 200 250 300

The a

vera

ge re

cons

truc

tion

erro

r (2-

norm

)



PT-10PTEE-10

Figure 7 The reconstruction errors of the four algorithms after 15times of iterations on the toy dataset

PCD on the MNIST and the toy dataset when there are thesame numbers of hidden units When the number of hiddenunits is 350 after 30 times of iterations the reconstructionerror of the proposed algorithm is 2660 lower than thatof PCD on MNIST dataset Under the same conditions andcompared with PCD PT-10 is 820 lower and PTEE-10 is1664 lower

Next a small scale of experiment with 15 hidden units isconducted on the MNIST dataset The log-likelihood can beobtained by enumerating states of hidden units Thereforehigh accuracy can be achieved Figure 9 shows the averagedlog-likelihood by training each model 5 times

Figure 9 shows that the likelihood of the proposed algo-rithm is not as good as the other three algorithms within

40

50

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80

90

100

110

120

0 50 100 150 200 250 300

The a

vera

ge re

cons

truc

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r (2-

norm

)



PT-10PTEE-10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The a

vera

ge lo

g-lik

eliho

od o

f tra

inin

g da

ta


PT-10PTEE-10

minus100

minus150

minus200

minus250

The number of parameter updating times (lowast5000)

Figure 9 The average likelihood of the four algorithms when thereare 15 hidden units on the MNIST dataset

10000 times of parameter updates However as the numberof updates gradually increases the likelihood for data of theproposed algorithm also increases which can be better thanthat of PTEE-10 When the number of updates is 30000 thelikelihood of PCD reaches the peak And it decreases becausethe number of Gibbs transitions increases and the modeldistribution also gets steeper and steeper PT-10 algorithmis a Monte Carlo method based on tempering It has moreeven distribution when the temperature gets higher so that itcan overcome the steep distribution difficulties by conductingstate transitions from low to high temperatures So it has abetter effect than that of PCD PTEE-10 proposes a new typeof move called equienergy move which improves the swaprates between neighboring chains to some extent But after


0 05 1 15 2 25 3

The a

vera

ge lo

g-lik

eliho

od o

f tra

inin

g da

ta

PTEE-10Our proposed algorithm

minus1

minus2

minus3

minus4

minus5

minus6

minus7

minus8

minus9

minus10


Figure 10The average likelihood of the two algorithms when thereare 10 hidden units on the toy dataset

Table 1The running time (in seconds) of different algorithmswhenthey are applied to toy dataset and MNIST dataset

Dataset PCD PT-10 PTEE-10 Our proposed algorithmMNIST 17497 18323 16535 40273Toy 0937 10562 8419 3017

18lowast5000 times of parameter updates the likelihood of PTEE-10 decreases gradually However the proposed algorithm willalways try to skip the steep distributions by increasing thenumber of samples constantly It has an overall effect whichis comparable with PTEE-10 at the beginning After 4 lowast 5000

times of parameter updates it has a better effect than the otherthree algorithms To validate the efficiency of the proposedalgorithm experiments are conducted on the toy datasetOnly the PTEE-10 and our proposed algorithm are comparedon the toy dataset since PTEE-10 is the most competitivemodel to our proposed algorithm The number of hiddenunits is set to 10 RBMs are trained five times via the proposedalgorithm and PTEE-10 The average likelihood scores areshown in Figure 10 We can conclude that the proposedalgorithm works better than PTEE-10 from Figure 10

Moreover we also recorded the running time of differentalgorithms on one epoch and on one training sample whenthey are applied to the toy dataset and the MNIST datasetAll experiments were conducted on a Windows operatingsystem machine with Intelreg CoreTM i5-3210M 250GHzCPUand 8GBRAM Table 1 displays the results

Based on the results in Table 1 we can see that the runningtime of our proposed algorithm is less than PT-10 and PTEE-10

From all the simulation results above we can see thatthe reconstruction error of the proposed algorithm is betterthan that of PCD PT-10 and PTEE-10 Under the sameconditions PT-10 and PTEE-10 perform better than PCD butPT-10 and PTEE-10 will spend tenfold time However theexperiment results obtained onMINST dataset show that the

proposed algorithm has better performance over the threeother algorithms which is also validated on the toy datasetMoreover the proposed algorithm only takes 2 or 3 times thetime that PCD will take

52 Performance Analysis of the Multilayer RBM NetworkImage Compression Method In this section the 256 times 256

Lena image is used Compression ratio is used to evaluate thecompression performance It is the data size ratio betweenthe compressed image and the original image It can reflectthe storage size and transmission efficiency of an image Peaksignal-to-noise ratio (PSNR) and signal-to-noise ratio (SNR)are the two main criteria to evaluate the performance of thereconstructed image quality For an image that has 119872 times 119873

pixels

SNR = 10 logsum119872

119894=1sum119873

119895[119909 (119894 119895)]

2

sum119872

119894=1sum119873

119895[119909 (119894 119895) minus (119894 119895)]

2

PSNR = 10 log 2552

(1119872119873)sum119872

1sum119873

1[119909 (119894 119895) minus (119894 119895)]

2

(14)

where 119909(119894 119895) and (119894 119895) respectively denote the gray valuesof the original image and the reconstructed image

In this experiment ROI image compression method [14]is compared with the proposed algorithm The compressionratio of the ROI compression method is calculated based onthe region of interest

119877ROI =119878119894+ 119878119887

119878 (15)

where 119878119894denotes the size of interest region 119878

119887is the

background region size of the reconstructed image and 119878

represents the original image sizeIn the proposed algorithm the compression ratio is

determined by the number of neural units in hidden layer

119877RBM =1198671lowast 1198672lowast sdot sdot sdot lowast 119867

119899minus1lowast 119880

119872 times 119873 (16)

where119872times119873 is the number of units in the bottom input layerand it is the number of pixels of an image119867

119894is the number of

nodes in the hidden layer 119894 of RBM 119880 is the number of unitsin the output layer of network 119899 is the number of layers

During the experiment the number of hidden layerunits 119880 of RBM is set to 2 4 and 8 respectively Wecompare the reconstructed image quality of ROI compressionalgorithm with that of the proposed algorithm under thecondition that the compression ratio is unchangeable Ina multilayer RBM network the middle data quantificationprocess will bring about some damage to image compressionTherefore the increasing number of hidden layers will makethe reconstructed image decline in quality So we set thenumber of layers in RBM to 3 The experiment results areshown in Table 2

The compression ratio is in inverse proportion to thenumber of hidden units 119880 From the objective qualityassessments of the reconstructed Lena image in Table 2 we


Table 2 The SNR and PSNR of Lena image when using multilayerRBM network compression algorithm and interest based compres-sion algorithm

Methods SNR (dB) PSNR (dB)119880 = 2

Multilayer RBM network 343152 499201ROI 304617 471041

119880 = 4


119880 = 8


can conclude that the quality of low compression ratio imageis better than that of the high compression ratio imageWhen the compression ratio is high although much storagespace is saved the reconstructed image cannot describe theimage texture details From Table 2 when the number ofhidden units is 8 the PSNR of the multilayer RBM networkcompressionmethod is 742141 At this time the visual effectsof the reconstructed Lena image are very close to that of theoriginal image

FromTable 2 we can also conclude that the reconstructedimage quality of multilayer RBM networks is superior to thatof ROI compression method under the same compressionratio The ROI compression algorithm can compress theinterest region and the background region respectively andtherefore it can get high compression ratio But the overallreconstructed image quality is not good because of the highcompression ratio of background region In multilayer RBMnetworks the compression ratio can be improved by settingthe number of neural units in each layer of RBM In additionthe training process in a multilayer RBM network is layeredThe data from the bottom input layer to the bottom hiddenlayer is the first compression The data from the first hiddenlayer to the second hidden layer is the second compressionThe second compression is based on the first compressionRBM in each layer will compress the image and greatlyremove the redundancy of the original image

53 The Energy Consumption Analysis of Wireless SensorNetwork In this section the energy consumption of a WSNis analyzed in the aspect of image transmitting The energyconsumed during the transmitting process can be calculatedusing the formula below

119864119879119909

=

119896

sum

119894

(2119864elec + 120576amp1198922

119894)119872 (17)

where 119864elec is the line loss in the electrical circuit 120576amprepresents the amplifier parameter 119896 is the number of nodes119892119894is the distance between transmitting nodes and 119872 is the

bit number of an image to be transmittedIn the process of simulation when cluster head nodes

receive images they transmit these images to coding nodes to

50

100

150

200

250

300

350

400

450

500

550

0 50 100 150 200 250Ener

gy co

nsum

ptio

n of

the t

rans

mitt

ing

node

(EJb

it)

Distance (m)

No compressionMultilayer RBM networkROI

Figure 11 The energy consumption of transmitting nodes

carry out compression coding Then the compressed imageis assigned to the transmitting node In the experiment wecalculate the energy consumption of every transmitting nodeWe compare the proposed algorithm with the ROI lossy-lossless image compression method under three conditions(1) no image compression methods are used (2) only themultilayer RBM network compression method is used (3)only the ROI compression method is used We compare theenergy consumption of transmitting nodes under the threeconditions In conditions (2) and (3) we compare the energyconsumption of the two algorithms under the same SNR

The parameter settings are as follows 119864elec = 05 times

10minus6 EJbit 120576amp = 1 times 10

minus9 EJbitm2 When the energyconsumption values of transmitting nodes are compared thedistance between transmitting nodes is between 0 and 250meters and the step size is 10 meters The experiment resultsare shown in Figure 11

Figure 11 shows that more energy is consumed whenthe transmitting distance increases When the transmittingdistances are the same the energy consumption of trans-mitting nodes using multilayer RBM network is obviouslysmaller than that using ROI compression method AlthoughROI compression method can code the interest region andbackground region respectively and get high compressionratio it cannot ensure high quality of the reconstructedimageHowever in themultilayer RBMnetwork compressionmethod data redundancy is reduced in every layer andtherefore it has high compression ratio

We continue to find out the relationship between imagecompression performance and compression energy con-sumption The image compression energy consumption canbe calculated using the formula below

119864119862= 119873119862lowast 119862 lowast 119881

2

119889119889 (18)


0

200

400

600

800

1000

1200

0 50 100 150 200 250

Tota

l ene

rgy

cons

umpt

ion

(EJb

it)

Distance (m)


Figure 12 Total energy consumption in WSN

where 119873119862is the time spent during the image compression

process119862 is the capacitance and119881119889119889

is the voltageThereforeunder the same compression environment the compressionenergy consumption 119864

119862is only subject to 119873

119862 The proposed

image compression method includes additional RBM train-ing process And the RBM is multilayered which will extendthe training processHowever theRBMtraining process neednot be carried out every time when images are compressedWhen the RBM training process is finished it can be used forall coding nodes

We continue to test the total energy consumption inWSNwhen the three image compression algorithms are usedrespectively and Figure 12 shows the results

Figure 12 shows that although RBM training processextends 119873

119862 the total energy consumption of the proposed

method is superior to the other two methods when thetransmitting distance increases Based on Table 2 the pro-posed image compression method has better reconstructedimage quality than ROI under the same compression ratioTherefore we can conclude that the proposed method canensure a better compression performance and smaller energyconsumption at the same time

6 Conclusions and Future Work

Image compression is an important research field in WSNsIt is difficult to find a comprehensive method of imagecompression because of the complex features in sensor net-works A multilayer RBM network based image compressionmethod is proposed in this paper And an improved RBMtraining algorithm based on alternative iteration is presentedto improve the likelihood of RBM However there remainmany problems to be solved when using multilayer RBMnetwork to compress imageThemultilayerRBMnetwork can

affect the delay in the sensor network We should find moresuitable normalizing parameter function during the RBMtraining process Besides the problem of finding routing pathshould also be considered Therefore we endeavor to findout more integrated image compression method so as toaccelerate the application of WSNs in real life

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is sponsored by the Fundamental Research Fundsfor the Central Universities (no LGZD201502) the NaturalScience Foundation of China (nos 61403208 and 61373139)and the Research and Innovation Projects for Graduates ofJiangsu Graduates of Jiangsu Province (no CXZZ12 0483)

References

[1] P J Sadowski D Whiteson and P Baldi ldquoSearching for HiggsBoson decay modes with deep learningrdquo in Proceedings of the28th Annual Conference on Neural Information Processing Sys-tems (NIPS rsquo14) pp 2393ndash2401 Montreal Canada December2014

[2] X Ding Y Zhang T Liu and J Duan ldquoDeep learning for event-driven stock predictionrdquo in Proceedings of the 24th InternationalJoint Conference on Artificial Intelligence (ICJAI rsquo15) pp 2327ndash2333 ACM Buenos Aires Argentina July 2015

[3] S Chatzis ldquoEcho-state conditional restricted boltzmannmachinesrdquo in Proceedings of the 28th AAAI Conference onArtificial Intelligence pp 1738ndash1744 2014

[4] T Osogami and M Otsuka ldquoRestricted Boltzmann machinesmodeling human choicerdquo in Proceedings of the 28th AnnualConference on Neural Information Processing Systems (NIPS rsquo14)pp 73ndash81 Montreal Canada December 2014

[5] C Zhang G-L Sun W-X Li Y Gao and L Lv ldquoResearchon data compression algorithm based on prediction codingfor wireless sensor network nodesrdquo in Proceedings of the Inter-national Forum on Information Technology and Applications(IFITA rsquo09) vol 1 pp 283ndash286 IEEE Chengdu China May2009

[6] L Xiang-YuW Ya-Zhe and Y Xiao-Chun ldquoFacing the wirelesssensor network streaming data compression technologyrdquo Com-puter Science vol 34 no 2 pp 141ndash143 2007

[7] L-C Wang and C-X Ma ldquoBased on a linear model of thespace-time data compression algorithm in sensor networksrdquoElectronics and Information Technology vol 32 no 3 pp 755ndash758 2010

[8] L Wang and S-W Zhou ldquoBased on interval wavelet transformin hybrid entropy data compression algorithm in sensor net-workrdquo Computer Applications vol 25 no 11 pp 1676ndash16782005

[9] Z Si-wang L Ya-ping and Z Jian-ming ldquoBased on ring modelof wavelet compression algorithm in sensor networksrdquo Journalof Software vol 18 no 3 pp 669ndash680 2007

[10] Z Tie-jun L Ya-ping and Z Si-wang ldquoBased on adaptivemultiple modules data compression algorithm of wavelet in


wireless sensor networksrdquo Journal of Communication vol 30no 3 pp 48ndash53 2008

[11] S-W Zhou Y-P Lin and S-T Ye ldquoA kind of sensor networkstorage effective wavelet incremental data compression algo-rithmrdquo Journal of Computer Research and Development vol 46no 12 pp 2085ndash2092 2009

[12] W-H Luo and J-LWang ldquoBased on chainmodel of distributedwavelet compression algorithmrdquoComputer Engineering vol 36no 16 pp 74ndash76 2010

[13] F Xiang-Hui L Shi-Ning and D Peng-Lei ldquoAdaptive nonde-structive data compression system of WSNrdquo Computer Mea-surement and Control vol 18 no 2 pp 463ndash465 2010

[14] N Cai-xiang Study on Image Data Compression Processingin Wireless Multimedia Sensor Network Changrsquoan UniversityXirsquoan China 2014

[15] G E Hinton ldquoTraining products of experts by minimizingcontrastive divergencerdquo Neural Computation vol 14 no 8 pp1771ndash1800 2002

[16] I Sutskever and T Tieleman ldquoOn the convergence properties ofcontrastive divergencerdquo Journal ofMachine Learning ResearchmdashProceedings Track vol 9 pp 789ndash795 2010

[17] T Tieleman ldquoTraining restricted Boltzmann machines usingapproximations to the likelihood gradientrdquo in Proceedings of the25th International Conference on Machine Learning pp 1064ndash1071 ACM Helsinki Finland July 2008

[18] T Tieleman and G E Hinton ldquoUsing fast weights to improvepersistent contrastive divergencerdquo in Proceedings of the 26thAnnual International Conference on Machine Learning (ICMLrsquo09) pp 1033ndash1040 ACM June 2009

[19] G Desjardins A Courville and Y Bengio ldquoAdaptive paralleltempering for stochastic maximum likelihood learning ofRBMsrdquo in Neural Information Processing Systems (NIPS) MITPress 2010

[20] J Xu H Li and S Zhou ldquoImprovingmixing rate with temperedtransition for learning restricted Boltzmann machinesrdquo Neuro-computing vol 139 pp 328ndash335 2014

[21] Y Hu Markov chain Monte Carlo based improvements tothe learning algorithm of restricted Boltzmann machines [MSthesis] Shanghai Jiao Tong University Shanghai China 2012

[22] Y Bengio A C Courville and P VincentUnsupervised FeatureLearning and Deep Learning A Review and New PerspectivesDepartment of Computer Science and Operations ResearchUniversity of Montreal Montreal Canada 2012

[23] A Fischer and C Igel ldquoTraining restricted Boltzmannmachines an introductionrdquo Pattern Recognition vol 47 no 1pp 25ndash39 2014

[24] A Fischer andC Igel ldquoAnMpirical analysis of the divergence ofGibbs sampling based learning algorithms for restricted Boltz-mann machinesrdquo in Artificial Neural Networks-ICANN 201020th International Conference Thessaloniki Greece September15ndash18 2010 Proceedings Part III vol 6354 of Lecture Notes inComputer Science pp 208ndash217 Springer Berlin Germany 2010

[25] Y LeCun L Bottou Y Bengio and P Haffner ldquoGradient-basedlearning applied to document recognitionrdquo Proceedings of theIEEE vol 86 no 11 pp 2278ndash2324 1998

[26] G Desjardins A Courville and Y Bengio ldquoParallel temperingfor training of restricted Boltzmann machinesrdquo Journal ofMachine Learning Research Workshop amp Conference Proceed-ings vol 9 pp 145ndash152 2010

[27] K H Cho T Raiko and A Ilin ldquoParallel tempering is efficientfor learning restricted Boltzmann machinesrdquo in Proceedings of

the International Joint Conference on Neural Networks (IJCNNrsquo10) pp 1ndash8 Barcelona Spain July 2010

[28] N Ji and J Zhang ldquoParallel tempering with equi-energy movesfor training of restricted boltzmann machinesrdquo in Proceedingsof the International Joint Conference onNeural Networks (IJCNNrsquo14) pp 120ndash127 Beijing China July 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



and the other is about the model distribution parameter Themodel distribution parameter which is about to be assessed iscalculated alternatively with the normalizing parameter andeventually can be obtained through a highly efficient trainingprocess This training process is of low complexity Thisalgorithm can improve the likelihood of RBM for trainingdata

Furthermore we have used the improved RBM train-ing process in image compression in WSNs A multilayerimproved RBM based image compression method is pre-sented in this paper This image compression method canextract more abstract data to coding based on the image fea-tures and has a better compression effect In the simulationsthe reconstructed image quality of multilayer RBM networksis superior to that of another image compression methodunder the same compression ratio which will be stated indetail in Section 5 At the same time the proposed imagecompression method can reduce the energy consumptionduring image data transmission process

The rest of the paper is organized as follows In Section 2related work on image compression and RBM training algo-rithms is discussed Section 3 presents the basic idea of themultilayer RBM network based image compression methodAnd the RBM model and the improved RBM algorithmbased on alternative iteration are depicted in Section 4 Theperformance of the proposed algorithm is compared withsome typical algorithms in Section 5 At last conclusions andfuture work are presented in Section 6

2 Related Work

Typical image compression algorithms include time-spacerelated data compression algorithm wavelet transform baseddata compression algorithm distributed data compressionalgorithm and improved traditional data compression algo-rithm

The space-time relativity based data compression algo-rithm mainly includes prediction coding and linear fittingmethod for time series A prediction coding method isproposed in [5] It can effectively evaluate the source databased on the time relativity of the source data However theprediction coding based data compression method does notinvolve large amount of image data transmission Reference[6] proposes a curve fitting technology based data flow com-pression method It compresses data collected on each nodeand restores the data in the base station But this method isvery complex and it does not consider the transmission delayin each sensor node Reference [7] presents a space-time datacompression technology based on simple linear regressionmodel This method can eliminate data redundancy in singlenode and collector node respectively But only the data thatsatisfies the error requirement is considered in this methodAbnormal data is not involved in this method

Wavelet transform is a time-frequency analysis methodwhich is superior to traditional signal analysis methodsReference [8] considers the existence of stream data in thedata transmission of sensor networks It compresses databy using wavelet transform based on the data aggregation

and the DC routing algorithm In [9 10] a ring modelbased distributed time-space data compression algorithmand a wavelet based self-fitting data compression algorithmare proposed Storage efficient two-dimension and three-dimension continuouswavelet data compressionmethods areproposed in [11] They are based on the ring model of fittingsensor networkwavelet transform and the overlapping clusterpartition model respectively They are storage efficient andcan save the transmission energy consumption in networks

The distributed data compression algorithm is based onthe fact that all the centralized and decentralized informationservices can be implementedThe feature of a distributed datacompression algorithm is that it can reduce the data amountby the cooperative work among different sensor nodes Achain model based distributed data compression algorithmis proposed in [12] based on the random lengths of waveletsThis algorithm designs a chain model that is suitable forwavelet transform It is suitable for random lengths of waveletfunctions

Traditional lossless data compression methods mainlyinclude Run Length Encoding technology Huffman codingcompression dictionary compression method and arith-metic compression method These methods are mainlyadopted in advanced computers or workstations In theapplication of sensor networks the processing capacity ofeach processor is limited Its memory is small Therefore it isessential to optimize the traditional compression algorithmIn [13] the difference between the two perceptual pieces ofdata is encoded based on the self-fitting Huffman codingalgorithm Reference [14] proposes a region of interest (ROI)based lossy-lossless image compression method It carriesout different coding compression methods on the small areathat is important to itself and the other large area In thisway compression ratio is improved under the condition thatsensitive information is reserved

In recent years Deep Learning (DL) is widely usedin WSNs to carry out image compression Deep Learningextracts the characteristics of data from low to high layersby modeling the layer model of analyzing in human brainsHowever the effect of image compression using DL issubject to the likelihood of RBM for training data and thetraining complexity of RBMTherefore an improved trainingalgorithm based on RBM training is also proposed in thispaper

Currently researchers have made lots of researches onRBM training algorithms In 2002 Hinton proposed a fastlearning algorithm of RBM Contrastive Divergence (CD)[15]This algorithm is a RBMapproximate learning algorithmof high efficiency However the RBM model acquired by theCD algorithm is not a maximum entropymodel and does nothave high likelihood when training data [16]

In 2008 Tijmen Tieleman proposed a Persistent Con-trastive Divergence (PCD) algorithm [17]This algorithm hasremedied the deficiency in CD algorithm It has the sameefficiency of CDalgorithm and does not violate themaximumlikelihood learning In addition the RBM obtained by PCDtraining has more powerful pattern generation capacity In2009 Tieleman and Hinton made further improvement ofPCD algorithm [18] and proposed Fast Persistent Contrastive







119892 = (1198920row 1198921row 119892(119873minus1)row)

119879

=

[[[[[[

[

11989200

11989201


11989210

11989211


d

119892119872minus10

119892119872minus11


]]]]]]

]

(1)




PreprocessingThe

wirelesssender

Imagecompression

encodingtechnology


Imagedecoding

technology

Wirelessreceiving

end

Original image

data



Input

Outputlayer

layer

RBM

RBM

RBM

Encoding

Encoding

Encoding

Decoding

Decoding

Decoding













W

Hidden layer h

Visible layer v







119864 (V ℎ | 120579) = minus

119899

sum

119894=1

119886119894V119894minus

119898

sum

119895=1

119887119895ℎ119895minus

119899

sum

119894=1

119898

sum

119895=1

ℎ119895119908119894119895V119894 (2)





119875 (V ℎ | 120579) =119890minus119864(Vℎ|120579)

119885 (120579) (3)




120579

119871 (120579) = argmax120579

119899119904

sum

119894=1

log119875 (V119894 | 120579) (4)









max 119897 (120579 119911) (5)




1 V1198942 V119894

119899V) 119894 = 1 2




119894

119905







1

0



1based on 119911




0= 1205791



Assume that119911119905= 119885(119911

119894| 120579119894





119894| 120579119894

119905) aresum

119911119894 119885(119911119894| 120579119894

119905) = 1 and119885(119911

119894| 120579119894



119899V

sum

119899=1

log119901 (V119894119899 120579119894

119905) =

119899V

sum

119899=1

logsum119911119894

119901 (V119894119899 119911119894 120579119894

119905) (6)


119894| 120579119894

119905)

119899V

sum

119899=1

log119901 (V119894119899 120579119894

119905) =

119899V

sum

119899=1

logsum119911119894

119885(119911119894| 120579119894

119905)

119901 (V119894 119911119894 120579119894119905)

119885 (119911119894 | 120579119894

119905) (7)


119899V

sum

119899=1

logsum119911119894

119885(119911119894| 120579119894

119905)

119901 (V119894119899 119911119894 120579119894

119905)

119885 (119911119894 | 120579119894

119905)

ge

119899V

sum

119899=1

sum

119911119894

119885(119911119894| 120579119894

119905) log

119901 (V119894119899 119911119894 120579119894

119905)

119885 (119911119894 | 120579119894

119905)

(8)


119905)119885(119911

119894| 120579119894

119905) =


119911119894 119885(119911119894

| 120579119894


following equation

119885(119911119894| 120579119894

119905) =

119901 (V119894119899 119911119894 120579119894

119905)

sum119911119894 119901 (V119894119899 119911119894 120579119894

119905)=

119901 (V119894119899 119911119894 120579119894

119905)

119901 (V119894119899 120579119894

119905)

= 119901 (119911119894| V119894119899 120579119894

119905)

(9)

When 120579119894


119905)


119911119905+1

= arg max119911119905

119897 (119911119905) = arg max

119911119905

119899V

sum

119899=1

ln119901 (V119894119899| 119911119905) (10)


119905+1


119905+1 When 119911

119905+1and 120579

119894



119901 (V119894 ℎ | 120579119894

119905) =

119890minus119864(V119894 ℎ|120579119894

119905)

119885 (120579119894

119905)

(11)

where 119885(120579119894


119905+1which is




of the original RBM

119901 (V119894 | 120579119894119905) =

1

119911119905+1

sum

ℎ

119890minus119864(V119894 ℎ|120579119894

119905) (12)

Then we keep 119911119905+1



120579119894

119905+1= arg max

120579119894

119905

119897 (120579119894

119905) = arg max

120579119894

119905

119899V

sum

119899=1

ln119901 (V119894119899| 120579119894

119905) (13)














For 119905 = 1 2 119879

Computing 119911119905+1

119911119905+1

= argmax119911119905

119897(119911119905) = argmax

119911119905

sum119899V119899=1

ln119901(V119894119899| 119911119905)


119905+1 120579119894119905+1

= argmax120579119894

119905

119897(120579119894

119905) = argmax

120579119894

119905

sum119899V119899=1

ln119901(V119894119899| 120579119894

119905)



End for







20

30

40

50

60

70

80

90

0 50 100 150 200 250 300 350

The a

vera

ge re

cons

truc

tion

erro

r (2-

norm

)



PT-10PTEE-10






20

30

40

50

60

70

80

90

0 50 100 150 200 250 300 350

The a

vera

ge re

cons

truc

tion

erro

r (2-

norm

)



PT-10PTEE-10


40

50

60

70

80

90

100

110

120

0 50 100 150 200 250 300

The a

vera

ge re

cons

truc

tion

erro

r (2-

norm

)



PT-10PTEE-10





40

50

60

70

80

90

100

110

120

0 50 100 150 200 250 300

The a

vera

ge re

cons

truc

tion

erro

r (2-

norm

)



PT-10PTEE-10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The a

vera

ge lo

g-lik

eliho

od o

f tra

inin

g da

ta


PT-10PTEE-10

minus100

minus150

minus200

minus250





0 05 1 15 2 25 3

The a

vera

ge lo

g-lik

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pixels


119894=1sum119873

119895[119909 (119894 119895)]

2

sum119872

119894=1sum119873

119895[119909 (119894 119895) minus (119894 119895)]

2

PSNR = 10 log 2552

(1119872119873)sum119872

1sum119873

1[119909 (119894 119895) minus (119894 119895)]

2

(14)



119877ROI =119878119894+ 119878119887

119878 (15)


119887is the






119872 times 119873 (16)










119880 = 4


119880 = 8





119864119879119909

=

119896

sum

119894

(2119864elec + 120576amp1198922

119894)119872 (17)




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119864119862= 119873119862lowast 119862 lowast 119881

2

119889119889 (18)


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119862 The proposed











Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















119892 = (1198920row 1198921row 119892(119873minus1)row)

119879

=

[[[[[[

[

11989200

11989201


11989210

11989211


d

119892119872minus10

119892119872minus11


]]]]]]

]

(1)




PreprocessingThe

wirelesssender

Imagecompression

encodingtechnology


Imagedecoding

technology

Wirelessreceiving

end

Original image

data



Input

Outputlayer

layer

RBM

RBM

RBM

Encoding

Encoding

Encoding

Decoding

Decoding

Decoding













W

Hidden layer h

Visible layer v







119864 (V ℎ | 120579) = minus

119899

sum

119894=1

119886119894V119894minus

119898

sum

119895=1

119887119895ℎ119895minus

119899

sum

119894=1

119898

sum

119895=1

ℎ119895119908119894119895V119894 (2)





119875 (V ℎ | 120579) =119890minus119864(Vℎ|120579)

119885 (120579) (3)




120579

119871 (120579) = argmax120579

119899119904

sum

119894=1

log119875 (V119894 | 120579) (4)









max 119897 (120579 119911) (5)




1 V1198942 V119894

119899V) 119894 = 1 2




119894

119905







1

0



1based on 119911




0= 1205791



Assume that119911119905= 119885(119911

119894| 120579119894





119894| 120579119894

119905) aresum

119911119894 119885(119911119894| 120579119894

119905) = 1 and119885(119911

119894| 120579119894



119899V

sum

119899=1

log119901 (V119894119899 120579119894

119905) =

119899V

sum

119899=1

logsum119911119894

119901 (V119894119899 119911119894 120579119894

119905) (6)


119894| 120579119894

119905)

119899V

sum

119899=1

log119901 (V119894119899 120579119894

119905) =

119899V

sum

119899=1

logsum119911119894

119885(119911119894| 120579119894

119905)

119901 (V119894 119911119894 120579119894119905)

119885 (119911119894 | 120579119894

119905) (7)


119899V

sum

119899=1

logsum119911119894

119885(119911119894| 120579119894

119905)

119901 (V119894119899 119911119894 120579119894

119905)

119885 (119911119894 | 120579119894

119905)

ge

119899V

sum

119899=1

sum

119911119894

119885(119911119894| 120579119894

119905) log

119901 (V119894119899 119911119894 120579119894

119905)

119885 (119911119894 | 120579119894

119905)

(8)


119905)119885(119911

119894| 120579119894

119905) =


119911119894 119885(119911119894

| 120579119894


following equation

119885(119911119894| 120579119894

119905) =

119901 (V119894119899 119911119894 120579119894

119905)

sum119911119894 119901 (V119894119899 119911119894 120579119894

119905)=

119901 (V119894119899 119911119894 120579119894

119905)

119901 (V119894119899 120579119894

119905)

= 119901 (119911119894| V119894119899 120579119894

119905)

(9)

When 120579119894


119905)


119911119905+1

= arg max119911119905

119897 (119911119905) = arg max

119911119905

119899V

sum

119899=1

ln119901 (V119894119899| 119911119905) (10)


119905+1


119905+1 When 119911

119905+1and 120579

119894



119901 (V119894 ℎ | 120579119894

119905) =

119890minus119864(V119894 ℎ|120579119894

119905)

119885 (120579119894

119905)

(11)

where 119885(120579119894


119905+1which is




of the original RBM

119901 (V119894 | 120579119894119905) =

1

119911119905+1

sum

ℎ

119890minus119864(V119894 ℎ|120579119894

119905) (12)

Then we keep 119911119905+1



120579119894

119905+1= arg max

120579119894

119905

119897 (120579119894

119905) = arg max

120579119894

119905

119899V

sum

119899=1

ln119901 (V119894119899| 120579119894

119905) (13)














For 119905 = 1 2 119879

Computing 119911119905+1

119911119905+1

= argmax119911119905

119897(119911119905) = argmax

119911119905

sum119899V119899=1

ln119901(V119894119899| 119911119905)


119905+1 120579119894119905+1

= argmax120579119894

119905

119897(120579119894

119905) = argmax

120579119894

119905

sum119899V119899=1

ln119901(V119894119899| 120579119894

119905)



End for







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119894=1sum119873

119895[119909 (119894 119895)]

2

sum119872

119894=1sum119873

119895[119909 (119894 119895) minus (119894 119895)]

2

PSNR = 10 log 2552

(1119872119873)sum119872

1sum119873

1[119909 (119894 119895) minus (119894 119895)]

2

(14)



119877ROI =119878119894+ 119878119887

119878 (15)


119887is the






119872 times 119873 (16)










119880 = 4


119880 = 8





119864119879119909

=

119896

sum

119894

(2119864elec + 120576amp1198922

119894)119872 (17)




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0 50 100 150 200 250Ener

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nsum

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node

(EJb

it)

Distance (m)









119864119862= 119873119862lowast 119862 lowast 119881

2

119889119889 (18)


0

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0 50 100 150 200 250

Tota

l ene

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119862 The proposed











Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










W

Hidden layer h

Visible layer v







119864 (V ℎ | 120579) = minus

119899

sum

119894=1

119886119894V119894minus

119898

sum

119895=1

119887119895ℎ119895minus

119899

sum

119894=1

119898

sum

119895=1

ℎ119895119908119894119895V119894 (2)





119875 (V ℎ | 120579) =119890minus119864(Vℎ|120579)

119885 (120579) (3)




120579

119871 (120579) = argmax120579

119899119904

sum

119894=1

log119875 (V119894 | 120579) (4)









max 119897 (120579 119911) (5)




1 V1198942 V119894

119899V) 119894 = 1 2




119894

119905







1

0



1based on 119911




0= 1205791



Assume that119911119905= 119885(119911

119894| 120579119894





119894| 120579119894

119905) aresum

119911119894 119885(119911119894| 120579119894

119905) = 1 and119885(119911

119894| 120579119894



119899V

sum

119899=1

log119901 (V119894119899 120579119894

119905) =

119899V

sum

119899=1

logsum119911119894

119901 (V119894119899 119911119894 120579119894

119905) (6)


119894| 120579119894

119905)

119899V

sum

119899=1

log119901 (V119894119899 120579119894

119905) =

119899V

sum

119899=1

logsum119911119894

119885(119911119894| 120579119894

119905)

119901 (V119894 119911119894 120579119894119905)

119885 (119911119894 | 120579119894

119905) (7)


119899V

sum

119899=1

logsum119911119894

119885(119911119894| 120579119894

119905)

119901 (V119894119899 119911119894 120579119894

119905)

119885 (119911119894 | 120579119894

119905)

ge

119899V

sum

119899=1

sum

119911119894

119885(119911119894| 120579119894

119905) log

119901 (V119894119899 119911119894 120579119894

119905)

119885 (119911119894 | 120579119894

119905)

(8)


119905)119885(119911

119894| 120579119894

119905) =


119911119894 119885(119911119894

| 120579119894


following equation

119885(119911119894| 120579119894

119905) =

119901 (V119894119899 119911119894 120579119894

119905)

sum119911119894 119901 (V119894119899 119911119894 120579119894

119905)=

119901 (V119894119899 119911119894 120579119894

119905)

119901 (V119894119899 120579119894

119905)

= 119901 (119911119894| V119894119899 120579119894

119905)

(9)

When 120579119894


119905)


119911119905+1

= arg max119911119905

119897 (119911119905) = arg max

119911119905

119899V

sum

119899=1

ln119901 (V119894119899| 119911119905) (10)


119905+1


119905+1 When 119911

119905+1and 120579

119894



119901 (V119894 ℎ | 120579119894

119905) =

119890minus119864(V119894 ℎ|120579119894

119905)

119885 (120579119894

119905)

(11)

where 119885(120579119894


119905+1which is




of the original RBM

119901 (V119894 | 120579119894119905) =

1

119911119905+1

sum

ℎ

119890minus119864(V119894 ℎ|120579119894

119905) (12)

Then we keep 119911119905+1



120579119894

119905+1= arg max

120579119894

119905

119897 (120579119894

119905) = arg max

120579119894

119905

119899V

sum

119899=1

ln119901 (V119894119899| 120579119894

119905) (13)














For 119905 = 1 2 119879

Computing 119911119905+1

119911119905+1

= argmax119911119905

119897(119911119905) = argmax

119911119905

sum119899V119899=1

ln119901(V119894119899| 119911119905)


119905+1 120579119894119905+1

= argmax120579119894

119905

119897(120579119894

119905) = argmax

120579119894

119905

sum119899V119899=1

ln119901(V119894119899| 120579119894

119905)



End for







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119894=1sum119873

119895[119909 (119894 119895)]

2

sum119872

119894=1sum119873

119895[119909 (119894 119895) minus (119894 119895)]

2

PSNR = 10 log 2552

(1119872119873)sum119872

1sum119873

1[119909 (119894 119895) minus (119894 119895)]

2

(14)



119877ROI =119878119894+ 119878119887

119878 (15)


119887is the






119872 times 119873 (16)










119880 = 4


119880 = 8





119864119879119909

=

119896

sum

119894

(2119864elec + 120576amp1198922

119894)119872 (17)




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0 50 100 150 200 250Ener

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it)

Distance (m)









119864119862= 119873119862lowast 119862 lowast 119881

2

119889119889 (18)


0

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0 50 100 150 200 250

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l ene

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Distance (m)







119862 The proposed











Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1based on 119911




0= 1205791



Assume that119911119905= 119885(119911

119894| 120579119894





119894| 120579119894

119905) aresum

119911119894 119885(119911119894| 120579119894

119905) = 1 and119885(119911

119894| 120579119894



119899V

sum

119899=1

log119901 (V119894119899 120579119894

119905) =

119899V

sum

119899=1

logsum119911119894

119901 (V119894119899 119911119894 120579119894

119905) (6)


119894| 120579119894

119905)

119899V

sum

119899=1

log119901 (V119894119899 120579119894

119905) =

119899V

sum

119899=1

logsum119911119894

119885(119911119894| 120579119894

119905)

119901 (V119894 119911119894 120579119894119905)

119885 (119911119894 | 120579119894

119905) (7)


119899V

sum

119899=1

logsum119911119894

119885(119911119894| 120579119894

119905)

119901 (V119894119899 119911119894 120579119894

119905)

119885 (119911119894 | 120579119894

119905)

ge

119899V

sum

119899=1

sum

119911119894

119885(119911119894| 120579119894

119905) log

119901 (V119894119899 119911119894 120579119894

119905)

119885 (119911119894 | 120579119894

119905)

(8)


119905)119885(119911

119894| 120579119894

119905) =


119911119894 119885(119911119894

| 120579119894


following equation

119885(119911119894| 120579119894

119905) =

119901 (V119894119899 119911119894 120579119894

119905)

sum119911119894 119901 (V119894119899 119911119894 120579119894

119905)=

119901 (V119894119899 119911119894 120579119894

119905)

119901 (V119894119899 120579119894

119905)

= 119901 (119911119894| V119894119899 120579119894

119905)

(9)

When 120579119894


119905)


119911119905+1

= arg max119911119905

119897 (119911119905) = arg max

119911119905

119899V

sum

119899=1

ln119901 (V119894119899| 119911119905) (10)


119905+1


119905+1 When 119911

119905+1and 120579

119894



119901 (V119894 ℎ | 120579119894

119905) =

119890minus119864(V119894 ℎ|120579119894

119905)

119885 (120579119894

119905)

(11)

where 119885(120579119894


119905+1which is




of the original RBM

119901 (V119894 | 120579119894119905) =

1

119911119905+1

sum

ℎ

119890minus119864(V119894 ℎ|120579119894

119905) (12)

Then we keep 119911119905+1



120579119894

119905+1= arg max

120579119894

119905

119897 (120579119894

119905) = arg max

120579119894

119905

119899V

sum

119899=1

ln119901 (V119894119899| 120579119894

119905) (13)














For 119905 = 1 2 119879

Computing 119911119905+1

119911119905+1

= argmax119911119905

119897(119911119905) = argmax

119911119905

sum119899V119899=1

ln119901(V119894119899| 119911119905)


119905+1 120579119894119905+1

= argmax120579119894

119905

119897(120579119894

119905) = argmax

120579119894

119905

sum119899V119899=1

ln119901(V119894119899| 120579119894

119905)



End for







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pixels


119894=1sum119873

119895[119909 (119894 119895)]

2

sum119872

119894=1sum119873

119895[119909 (119894 119895) minus (119894 119895)]

2

PSNR = 10 log 2552

(1119872119873)sum119872

1sum119873

1[119909 (119894 119895) minus (119894 119895)]

2

(14)



119877ROI =119878119894+ 119878119887

119878 (15)


119887is the






119872 times 119873 (16)










119880 = 4


119880 = 8





119864119879119909

=

119896

sum

119894

(2119864elec + 120576amp1198922

119894)119872 (17)




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(EJb

it)

Distance (m)









119864119862= 119873119862lowast 119862 lowast 119881

2

119889119889 (18)


0

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0 50 100 150 200 250

Tota

l ene

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(EJb

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Distance (m)







119862 The proposed











Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















For 119905 = 1 2 119879

Computing 119911119905+1

119911119905+1

= argmax119911119905

119897(119911119905) = argmax

119911119905

sum119899V119899=1

ln119901(V119894119899| 119911119905)


119905+1 120579119894119905+1

= argmax120579119894

119905

119897(120579119894

119905) = argmax

120579119894

119905

sum119899V119899=1

ln119901(V119894119899| 120579119894

119905)



End for







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PT-10PTEE-10

minus100

minus150

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minus250





0 05 1 15 2 25 3

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pixels


119894=1sum119873

119895[119909 (119894 119895)]

2

sum119872

119894=1sum119873

119895[119909 (119894 119895) minus (119894 119895)]

2

PSNR = 10 log 2552

(1119872119873)sum119872

1sum119873

1[119909 (119894 119895) minus (119894 119895)]

2

(14)



119877ROI =119878119894+ 119878119887

119878 (15)


119887is the






119872 times 119873 (16)










119880 = 4


119880 = 8





119864119879119909

=

119896

sum

119894

(2119864elec + 120576amp1198922

119894)119872 (17)




50

100

150

200

250

300

350

400

450

500

550

0 50 100 150 200 250Ener

gy co

nsum

ptio

n of

the t

rans

mitt

ing

node

(EJb

it)

Distance (m)









119864119862= 119873119862lowast 119862 lowast 119881

2

119889119889 (18)


0

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400

600

800

1000

1200

0 50 100 150 200 250

Tota

l ene

rgy

cons

umpt

ion

(EJb

it)

Distance (m)







119862 The proposed











Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










20

30

40

50

60

70

80

90

0 50 100 150 200 250 300 350

The a

vera

ge re

cons

truc

tion

erro

r (2-

norm

)



PT-10PTEE-10


40

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60

70

80

90

100

110

120

0 50 100 150 200 250 300

The a

vera

ge re

cons

truc

tion

erro

r (2-

norm

)



PT-10PTEE-10





40

50

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100

110

120

0 50 100 150 200 250 300

The a

vera

ge re

cons

truc

tion

erro

r (2-

norm

)



PT-10PTEE-10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The a

vera

ge lo

g-lik

eliho

od o

f tra

inin

g da

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PT-10PTEE-10

minus100

minus150

minus200

minus250





0 05 1 15 2 25 3

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f tra

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minus1

minus2

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minus7

minus8

minus9

minus10













pixels


119894=1sum119873

119895[119909 (119894 119895)]

2

sum119872

119894=1sum119873

119895[119909 (119894 119895) minus (119894 119895)]

2

PSNR = 10 log 2552

(1119872119873)sum119872

1sum119873

1[119909 (119894 119895) minus (119894 119895)]

2

(14)



119877ROI =119878119894+ 119878119887

119878 (15)


119887is the






119872 times 119873 (16)










119880 = 4


119880 = 8





119864119879119909

=

119896

sum

119894

(2119864elec + 120576amp1198922

119894)119872 (17)




50

100

150

200

250

300

350

400

450

500

550

0 50 100 150 200 250Ener

gy co

nsum

ptio

n of

the t

rans

mitt

ing

node

(EJb

it)

Distance (m)









119864119862= 119873119862lowast 119862 lowast 119881

2

119889119889 (18)


0

200

400

600

800

1000

1200

0 50 100 150 200 250

Tota

l ene

rgy

cons

umpt

ion

(EJb

it)

Distance (m)







119862 The proposed











Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 05 1 15 2 25 3

The a

vera

ge lo

g-lik

eliho

od o

f tra

inin

g da

ta


minus1

minus2

minus3

minus4

minus5

minus6

minus7

minus8

minus9

minus10













pixels


119894=1sum119873

119895[119909 (119894 119895)]

2

sum119872

119894=1sum119873

119895[119909 (119894 119895) minus (119894 119895)]

2

PSNR = 10 log 2552

(1119872119873)sum119872

1sum119873

1[119909 (119894 119895) minus (119894 119895)]

2

(14)



119877ROI =119878119894+ 119878119887

119878 (15)


119887is the






119872 times 119873 (16)










119880 = 4


119880 = 8





119864119879119909

=

119896

sum

119894

(2119864elec + 120576amp1198922

119894)119872 (17)




50

100

150

200

250

300

350

400

450

500

550

0 50 100 150 200 250Ener

gy co

nsum

ptio

n of

the t

rans

mitt

ing

node

(EJb

it)

Distance (m)









119864119862= 119873119862lowast 119862 lowast 119881

2

119889119889 (18)


0

200

400

600

800

1000

1200

0 50 100 150 200 250

Tota

l ene

rgy

cons

umpt

ion

(EJb

it)

Distance (m)







119862 The proposed











Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119880 = 4


119880 = 8





119864119879119909

=

119896

sum

119894

(2119864elec + 120576amp1198922

119894)119872 (17)




50

100

150

200

250

300

350

400

450

500

550

0 50 100 150 200 250Ener

gy co

nsum

ptio

n of

the t

rans

mitt

ing

node

(EJb

it)

Distance (m)









119864119862= 119873119862lowast 119862 lowast 119881

2

119889119889 (18)


0

200

400

600

800

1000

1200

0 50 100 150 200 250

Tota

l ene

rgy

cons

umpt

ion

(EJb

it)

Distance (m)







119862 The proposed











Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

200

400

600

800

1000

1200

0 50 100 150 200 250

Tota

l ene

rgy

cons

umpt

ion

(EJb

it)

Distance (m)







119862 The proposed











Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article a multilayer improved rbm network based...

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