national aerospace university “kharkov aviation institute” spie remote sensing 2015 1...

National Aerospace University “Kharkov Aviation Institute”

SPIE Remote Sensing 20151

Performance prediction for 3D filtering of multichannel images

Oleksii Rubel1, Ruslan Kozhemiakin1, Sergey Abramov1, Vladimir Lukin1, Benoit Vozel2, Kacem Chehdi2

1Department of Transmitters, Receivers and Signal Processing, National Aerospace University, Kharkov, Ukraine

2IETR UMR CNRS University of Rennes 1 – Enssat, Lannion, France


Prediction of denoising efficiency 2

• The DCT-based filters and, particularly, the conventional DCT-based filter have demonstrated high efficiency for a wide class of images and noise models.

• Component-wise DCT-based denoising often produces unsatisfactory results for multichannel imagery (vector processing is able to work better).

• Modifications of the DCT-based filter for multichannel images have been already proposed (MC-DCT).

• In practice, there are cases when filtering does not provide effective noise removal or even decrease visual quality.

• It could be good to predict denoising efficiency before starting image filtering.• The main goal of prediction consists in obtaining some fast and accurate estimates of

quality metrics without carrying out filtering itself. • As an estimate of image quality and denoising efficiency, traditional peak SNR

(PSNR) metric can be used. • Since PSNR is expressed in dB, the contribution of filtering to quality increasing can

be measured and expressed by improvement of this metric (IPSNR).


Conventional DCT-based denoising and its modification for multichannel images

3

,m,nB,

,m,nB,m,nBm,nB

in

ininout

0 ,SDCTB inDin 2

where is input transformed block, Sin denotes an input block in spatial domain, n and m are

indices of DCT coefficients in block, σ is standard deviation noise, β is thresholding parameter (the recommended value is 2.7).

Afterward, inverse DCT is performed for the considered block, and then filtered values for overlapping blocks are collected together.

Conventional DCT filter for grayscale images:

The standard 2D DCT-based filter is a quite simple image processing procedure. It performs 2-dimensional DCT for full-overlapping blocks that are usually of fixed size 8x8 pixels. After performing 2D DCT in each block, hard thresholding procedure is commonly applied:


Conventional DCT-based denoising and its modification for multichannel images

4

Multichannel DCT filter:

An easy way to process corresponding blocks from different channels collaboratively is to use 3D DCT. It is possible and reasonable to split (separate) it into 2D and 1D transforms. 2D DCT is used for single-channel processing, so it can be applied to each block successively from all channels. Each transformed block can be stretched into a vector and all obtained vectors can be gathered into joint 2D array. Finally, this array can be transformed by 1D DCT with regard to certain DCT coefficients. Thus, the hard thresholding procedure would be the following:

,l,kB,

,l,kB,l,kBl,kB

Din

3Din

3Din3D

out

30

where k is index of DCT coefficient 1…64 for 8x8 block, l is index of channel.


Image statistics in DCT domain5

• The DCT-based denoising removes DCT coefficients that are regarded to be noisy. The number of removed or preserved DCT coefficients strictly influences denoising efficiency.

• For prediction, probability that coefficients in image blocks will be removed or saved can be used.

),m,n(q,m,nB,

),m,n(q,m,nB,q,m,nE

in

inout

0

1 ,q,m,nEqPmn,

out 63

where q is an index of a analyzed block (q=1,…,Q), α is the thresholding parameter used for prediction), Pασ is a set of local probability estimates in a processed image blocks. The simplest way to use the set of local estimates of probabilities is to calculate their mean and to substitute it into the fitted curve.

,q,l,kB,

,q,l,kB,q,l,kE

Din

Din3D

out

3

3

0

1 ,164,,,

3 LqlkEPlk

D

out

where k is index in block of some channel in vector representation, l denotes channel index, L is the number of channels.

The adapted version of Eout for multichannel images filters is based on analysis of DCT-coefficient amplitudes in 3D blocks:


Basic prediction methodology6

• Prediction is based on assumption that there is an a priori obtained dependence of output parameter (metric) on input parameter (image/noise statistic). .

• For dependence obtaining, scatter-plots have been formed where a given probability serves as an argument (input) and a corresponding metric as an ordinate of a scatter-plot point.

• Each point is obtained for a test image corrupted by AWGN with a given variance, then filtered and analyzed (by analysis here we mean calculation of an analyzed metric, for IPSNR).

• Having a scatter-plot, a curve is fitted into it to describe dependence of a predicted metric on an input statistical parameter.

• For prediction performance characterization, traditional determination coefficient or goodness of fit R2 is used. High values of R2 indicate quite good predicting performance.

• It is enough to have about 300…500 local estimates of probability Pασ for effective prediction.• A used statistical parameter is calculated for a given image under assumption of known variance of

noise. Then, this parameter(s) is used as argument of a fitted curve, and a predicted value of an analyzed metric is obtained.

Analyzing different approaches to fitting, it has been established that for P0.5σ, the following expression of fitting function is suitable:

,PObexpaMetrici

ασiipred

where Metricpred is a predicted metric, a and bi are coefficients of fitting functions, Oi is a statistical operator, i.e. a parameter characterizing the distribution of local estimates of Pασ.


Hyperspectral test images: EO-1 Hyperion7

For fitting functions obtaining, five relative noise levels (input PSNR = 20, 25, 30, 35 and 40 dB) and 20 Hyperion test images (with low cloud-cover, less than 10% from the overall image covered area) have been used. There are 220 unique spectral channels covering spectrum from 357 to 2576 nm. The images of radiometric product have 242 bands, 256 samples and approximately 3130 rows. For multichannel processing, the following groups of sub-bands: 31...40, 121...130, 166...175 and 211…220 have been used.

EO1H0140292014267110KF.L1R

EO1H0380382013106110K2.L1R

EO1H0410292013199110KF.L1R

EO1H0440332015125110KF.L1R


Hyperspectral test images: EO-1 Hyperion8

where S is the estimated dynamic range of an image. As the test set, Hyperion images divided into small parts with the size 256x256 pixels (voxels) have been used.

EO1H0410292013199110KF.L1R

Due to different dynamic ranges of sub-band images, relative noise levels have been used. To obtain an estimate of dynamic range, the difference between 0.99 and 0.01 quantiles in each sub-band was calculated. Standard deviation of artificially added noise has been calculated to produce PSNR values: 20, 25, 30, 35 and 40 dBs for noisy images:

20 ,10PSNR

S


Multichannel DCT-based denoising performance

9

The improvement of PSNR provided by 5- and 10-channels can be better than one-channel denoising by about 3-5 dB. As result, the output image is considerably better, many fine details are preserved.

PSNR = 20 dB (noisy) PSNR = 24.06 dB (1-channel denoising)

PSNR = 28.31 dB (5-channels denoising) PSNR = 29.99 dB (10-channels denoising)


Predicted IPSNR performance using mean of P0.5σ for multichannel denoising

10

Multichannel DCT-based prediction produces lighter and more homogenous maps that means more efficient joint denoising than component-wise.

P0.5σ = 0.3141-channel denoising

P0.5σ = 0.3435-channels denoising

P0.5σ = 0.35110-channels denoising


IPSNR prediction using mean of P0.5σ for 1-channel denoising

11

• The dashe lines correspond to the same input PSNRs for images from different bands.• It is well seen that all sub-band results are quite compact and form some trend. • Totally, the scatter-plot contains almost 50000 points provided from 5 relative noise levels, 20 test

images and about 12 sub-images obtained from them.• The obtained set of P0.5σ covers full range of possible values which is important for fitting and

prediction.• The values of IPSNR are not much scattered with respect to fitted curve. That means that high

prediction performance (accuracy) can be provided for IPSNR.• The presented scatter-plot clearly shows strong and obvious dependence of IPSNR on P0.5σ.


IPSNR prediction using mean of P0.5σ for multichannel denoising

12

If more channels are used in joint denoising, the obtained results (scatter-plot points) become less scattered and most of points move to higher P0.5σ.


IPSNR prediction using mean of P0.5σ for multichannel denoising

13

The difference in increasing IPSNR for the cases of 7-10 channels processed jointly is not essential. That means that often there is no necessity to use maximally possible number of channels.


Universal IPSNR prediction for multichannel denoising

14

It is seen well that results from different sub-ranges are compatible for their joint use for prediction.


Goodness of fit for fitting functions 15

• Goodness of fit parameter values are very high, R2 > 0.98 for all functions. Note that R2 > 0.9 means that two variables are strictly connected.• Estimated parameters a and b for all functions are very close. As a result, the obtained functions are

similar, have close goodness of fit and, potentially, could be used for other data. • 3D filtering provides by 1…6 dB better IPSNR compared to component-wise processing. Due to this, it

occurs that it is almost always expedient to apply 3D denoising to improve multichannel RS images.• Prediction method can be applied to denoising results obtained from filtering of different bands or groups

of neighbor bands filtered jointly. The obtained prediction functions for different cases are very similar; then, it is possible to obtain generalized function with high goodness of fit that can be used for different cases effectively.

Channels a b R2

1 0.086 12.948 0.981

3 0.093 12.798 0.98

4 0.091 12.858 0.984

5 0.083 13.129 0.985

6 0.083 13.111 0.986

7 0.078 13.283 0.985

8 0.077 13.322 0.986

9 0.072 13.513 0.986

10 0.071 13.561 0.986

All 0.084 13.076 0.984


Conclusions16

• The proposed prediction method uses image statistical parameters in DCT domain that can be easily calculated.

• The estimated statistical parameters are strictly connected with DCT-based denoising mechanism and efficiency.

• Prediction method and DCT-based denoising are easily extended to multichannel images.

• It is possible to predict improvement of PSNR for multichannel-DCT filter by fitting functions obtained in offline mode.

• Similar ranges of denoising results (IPSNR) and prediction parameter P0.5σ for multichannel filtering with different number of jointly processed channels make procedure universal respect to data nature.

• The fitted functions have high goodness of fit values that means high prediction performance.

• The proposed prediction method is very fast and can be extended to other filters

and noise models.


Performance prediction for 3D filtering of multichannel images

17

Thank you!

Benoit Vozel - [email protected]

Oleksii Rubel - [email protected]

Ruslan Kozhemiakin - [email protected]

Sergey Abramov - [email protected]

Vladimir Lukin - [email protected]

Kacem Chehdi - [email protected]

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