13 september 201513 september 201513 september 2015 ewing christian college (an autonomous college...

April 21, 2023April 21, 2023 Ewing Christian College (An Autonomous Ewing Christian College (An Autonomous College of Allahabad University), College of Allahabad University),

Allahabad Allahabad

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Image Restoration of

Medical Images using

Iteration methods

Dr Anil Kumar Singh Reader

Department of Physics & computer Science

Ewing Christian College, Allahabad

(The college with the Potential for Excellence

Awarded by UGC, New Delhi )

(An Autonomous constituent college of Allahabad University, Allahabad).

( [email protected])

Anil Kumar Singh


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Plan of presentationPlan of presentation1 Introduction 1 Introduction

22 Mathematics of Imaging SystemMathematics of Imaging System

33 Experimental DetailsExperimental Details

4 Future Experimental Details4 Future Experimental Details


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INTRODUCTIONINTRODUCTION1.1. Biological molecules are complex systems.Biological molecules are complex systems.

2.2. The true conformation is a network of loops, twists The true conformation is a network of loops, twists and folds, all stacked together in a and folds, all stacked together in a well-defined well-defined

dynamical 3D structure. In this morphology, in dynamical 3D structure. In this morphology, in general general that gives the protein, its “life” and that that gives the protein, its “life” and that determines determines its activity, its role.its activity, its role.

3.3. The determination of the 3D structure of The determination of the 3D structure of biological biological

molecules and the way in which this structure is linked molecules and the way in which this structure is linked to the function and to the function and to the sequence is its to the sequence is its

fundamental fundamental importance. importance.


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IMAGEIMAGE

Any two dimensional function that bears information Any two dimensional function that bears information can be considered as image.can be considered as image. Image gives a logical and quantitative description of theImage gives a logical and quantitative description of the properties of the function. properties of the function.

The two dimensional function, f (x, y), where x and The two dimensional function, f (x, y), where x and y are spatial (plane) Coordinates and the magnitude of y are spatial (plane) Coordinates and the magnitude of

‘f’ at any pair of coordinates (x, y) is called intensity or ‘f’ at any pair of coordinates (x, y) is called intensity or gray level of the image at that point. gray level of the image at that point.


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Digital ImageDigital Image

Digital image is an array of real or complex Digital image is an array of real or complex number of finite & discrete quantities which is number of finite & discrete quantities which is represented by a finite number of bits i.e. (0,1). represented by a finite number of bits i.e. (0,1).

The field of digital image processing refers to the The field of digital image processing refers to the processing digital images (a finite number of processing digital images (a finite number of elements) by means of a digital computer. These elements) by means of a digital computer. These elements are referred to as picture elements (Pixel) elements are referred to as picture elements (Pixel) of digital image.of digital image.


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Outline of Imaging SystemOutline of Imaging System

IntroductionIntroduction

- Image Blurring- Image Blurring

- Need for Image Deblurring/Deconvolution - Need for Image Deblurring/Deconvolution Image Deblurring /Deconvolution ApproachImage Deblurring /Deconvolution Approach

- Direct Approach- Direct Approach

- Inverse Approach- Inverse Approach Observation Model/ Blur Modeling Observation Model/ Blur Modeling Point Spread Function and its Type (PSF)Point Spread Function and its Type (PSF)


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ABBREVIATIONSABBREVIATIONS

PSF - Point Spread FunctionPSF - Point Spread Function

SDF - Spectral Density FunctionSDF - Spectral Density Function

MEM - Maximum Entropy MethodMEM - Maximum Entropy Method

MAP - Maximum a PosteriorMAP - Maximum a Posterior

ML - Maximum LikelihoodML - Maximum Likelihood

FT - Fourier TransformFT - Fourier Transform


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Cont…Cont…

SNR - Signal to Noise RatioSNR - Signal to Noise Ratio

ISNR-Improvement in Signal to Noise RatioISNR-Improvement in Signal to Noise Ratio

MSE- Mean Square ErrorMSE- Mean Square Error

AWGN - Additive White Gaussian NoiseAWGN - Additive White Gaussian Noise

BSNR - Blur SNRBSNR - Blur SNR

OTF - Optical Transfer FunctionOTF - Optical Transfer Function


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Deblurring / Deconvolution ApproachDeblurring / Deconvolution Approach

- Direct Approach• Using advanced sensor technology( High SNR,

Narrow beam)

- More sophisticated H/W component and focusing mechanism

• Improved Scanning, Sampling ,quantisation of image

- Inverse Approach

• Mathematical processing of measured data,

taking in account cause of degradation of true data.

To obtain high quality image


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Deblurring Approach(Cont…)Deblurring Approach(Cont…)

Direct Measurement

True Scene

INVERSE Problem Solution

- Measurement/Observation Model of

Point Spread Function(PSF) of system

- Algorithm for processing of measured data


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Now a posteriori probability p( f / g), is obtained by using Bayes’s theorem of conditional probability

( | ) ( )( | )

( )

p g f p fp f g

p g

( ) /

( ) /i i

k k

p f f N

p g g N

where, p(fi), p(gi) are probability of an event at the ith , kth location in the original image array f and blurred image g-,

Mathematical Formulation of Pixels


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( / )k i ijp g f h

( | ) ( )( | )

( | ) ( )k i i

i kk j jj

p g f p fp f g

p g f p f

Baye’s theorem on conditional probabilities used to relate the event at the ith location in original image array and event at the kth location in the blurred image array, by using fact


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Total probability theorem by Bayes’Total probability theorem by Bayes’TheoremTheorem

( ) ( ) ( )( )

( ) ( )

k i i ki

k k i ij

p g f p f p gp f

p g f p f

ki ki i

k kj jj

h gf f

h f


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Regularization of Van Cittert's Regularization of Van Cittert's algorithm algorithm Van Cittert's iteration is: Van Cittert's iteration is: RR((nn) () (xx, , yy) = ) = II((xx, , yy) - ) - PP((xx,,yy) * ) * OO((nn) () (xx, , yy). ).

The regularization by the significant The regularization by the significant structures leads to the original structures leads to the original structures. structures.


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The basic idea of our method consists of detecting, The basic idea of our method consists of detecting, at each scale, structures of a given size in the at each scale, structures of a given size in the residual residual RR((nn)()(xx,,yy) and putting them in the ) and putting them in the restored image restored image OO((nn)()(xx,,yy). ).

The process finishes when no more structures are The process finishes when no more structures are detected. Then, we have separated the image detected. Then, we have separated the image II((xx,,yy) into two images and ) into two images and RR((xx,,yy) is the restored ) is the restored image, which does not contain any noise, and image, which does not contain any noise, and RR((xx,,yy) is the final residual which does not contain ) is the final residual which does not contain any structure. any structure.

RR is our estimation of the noise is our estimation of the noise NN((xx,,yy). ).


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The Experimental part of Research

Prostate


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TheThe experimental results for Prostate tissue of rat experimental results for Prostate tissue of rat by administration ofby administration of

(i) “Alpha blockens((i) “Alpha blockens(αα)” and )” and (ii) “Terazosin((ii) “Terazosin(ββ)”. )”.

The LandWeber method with Wavelet Filtering The LandWeber method with Wavelet Filtering adaptively restored images have better quality than adaptively restored images have better quality than the LandWeber restored ones based on visual the LandWeber restored ones based on visual observations and on an objective criterion of merit observations and on an objective criterion of merit SNR, MAE & MAD which accounts for the noise SNR, MAE & MAD which accounts for the noise masking property of the visual system.masking property of the visual system.


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Dr. A. k. Singh\My Documents\rajeev\bp11.jpg');i=imresize(i,.3);

[j, map]=rgb2ind (i, 256);

0 50 100 150 200 250

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k=imcropk=imcrop imshow (k, map) imshow (k, map)

Image HistogramImage Histogram of of the Croped Image the Croped Image (c25 .jpg) (c25 .jpg)

Alpha blockens(Alpha blockens(αα))

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Crop the portion of Image:Crop the portion of Image:k=imcropk=imcrop

imshow (k, map) imshow (k, map) Terazosin (Terazosin (ββ))

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Original Image Image(1.jpg)

Using Median Filter (d) Using Adaptive Filter PSNR = 46.3049 PSNR = 49.8637

(2.jpg)


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(a) Original Crop Image (b) Original gray Image (3.jpg)

Using Median Filter (d) Using Adaptive Filter PSNR = 24.0391 PSNR = 24.5606 (4.jpg


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Outline of the Future Outline of the Future Experimental PartExperimental Part

1. What is fluorescence?

2. Fluorescent molecules

3. Equipment for biomolecules in fluorescence experiments and the Bayes’ frame work

4. Some applications & examples


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S0

S1

T0

transition involving emission/absorption of photon

radiationless transition

abso

rptio

n

+hν

fluor

esce

nce

-hν

inte

rnal

co

nver

sion

inte

rsys

tem

cr

ossi

ngin

tern

al

conv

ersi

on

FluorescenceFluorescence


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FluorescenceFluorescenceproperties that can be measuredproperties that can be measured

• Spectra (environmental effects)

• Fluorescence life times

• Polarization (orientation and dynamics)

• Excitation transfer (distances -> dynamics)

• Location of fluorescence


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The CellThe Cell


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3-D Fluorescence Microscopy Imaging


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2. Fluorescence

1. Molecular Mechanisms of Fluorescence


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Electronic states of molecules

Molecular orbitals

2 electrons per orbital

optical transitions

HOMO

LUMO


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+

+ +

+

+ +

N1

N3

C2

C4

C5

C6

+

H O4

O2

C1’ sugar

electron network

+

n

H

H

H

H

sp3

Electronic structure of the thymine base.


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Relaxation between electronic statesRelaxation between electronic states


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K. Brejc et.al., PNAS 94 (1997) 2306

1 nm

Green-fluorescentGreen-fluorescent protein (GFP) protein (GFP)


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FLUORESCENCE MEASUREMENTSFLUORESCENCE MEASUREMENTS

Information given by each property of Information given by each property of fluorescence photons:fluorescence photons:

- Spectrum- Spectrum

- Delay after excitation (lifetime)- Delay after excitation (lifetime)

- Polarization- Polarization


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SpectraSpectra

Laser exc fluo

Spectrograph

DetectorSample

exc fluo

Fluo. intensity

Excitation spectrumFluorescence spectrum


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Fluorescence LifetimeFluorescence Lifetime

Pulsed laser

Sample

Detector

Filter

time

Laser pulses

photons delay

delay, t

number

fluote

/


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Studies of interaction and dynamicsStudies of interaction and dynamics(molecular ruler)(molecular ruler)

Association of two biomolecules

Dynamics ofa biomolecule


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Fluorescence Correlation SpectroscopyFluorescence Correlation Spectroscopy

t

I(t)

I(t+

)()()2( tItIg

Keeps track of the fluctuations of the fluorescence intensity.

log

g(2)


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Biochemical Biochemical PathwaysPathways


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ApplicationsApplicationsProbing of ‘interesting’ molecular regions with the Probing of ‘interesting’ molecular regions with the goal of trying to determiner whether they are goal of trying to determiner whether they are involved in molecular recognition, activity and others.involved in molecular recognition, activity and others.

Computer-assisted drug design with a certain specific Computer-assisted drug design with a certain specific protein as target.protein as target.

Changes in molecular properties, such as production Changes in molecular properties, such as production of chimeric enzymes with a different catalytic of chimeric enzymes with a different catalytic activity (biochemical engineering).activity (biochemical engineering).

Effects of mutations on stability and activity.Effects of mutations on stability and activity.

Computation of affinities and other properties.Computation of affinities and other properties.

Mechanism of action & Structure-function Mechanism of action & Structure-function relationships.relationships.


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Our Vision of BiologyOur Vision of Biology

Exploit Exploit – Linear-scaling algorithmsLinear-scaling algorithms– Parallel computingParallel computing– ModelsModels

Semiempirical HamiltoniansSemiempirical HamiltoniansDensity Functional TheoryDensity Functional TheoryHartree-Fock TheoryHartree-Fock TheoryQuantum Monte-CarloQuantum Monte-Carlo

– Exploit ensemble generation protocolsExploit ensemble generation protocolsNovel sampling approachesNovel sampling approachesUse classical models to generate ensemblesUse classical models to generate ensembles

– SpectroscopySpectroscopyNMRNMRX-rayX-ray

– Exploit statistical approachesExploit statistical approachesLeverage the repetitive nature of biologyLeverage the repetitive nature of biologyBioinformatics databasesBioinformatics databases


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Research GroupResearch Group

Dr. Anil K. Singh, P.I.,Dr. Anil K. Singh, P.I.,

Dr. Anjani K. Singh, Co-P.I., Dr. Anjani K. Singh, Co-P.I., Shiv Kumar Vaishy, Shiv Kumar Vaishy, Project Fellow of UGC Major Project Project Fellow of UGC Major Project

Biophysics Lab, Deptt. of Physics, Biophysics Lab, Deptt. of Physics, (Star deptt. awarded by UGC) (Star deptt. awarded by UGC)

Ewing Christian College, Allahabad.Ewing Christian College, Allahabad.

Prof. R.S. Yadav, Co-P.I., Supervisor Prof. R.S. Yadav, Co-P.I., Supervisor

Deptt. of Computer Science & Engineering, Deptt. of Computer Science & Engineering,

MNNIT, AllahabadMNNIT, Allahabad..

Dr. Gopal Gupta, Scientist, CDRI, Lucknow.Dr. Gopal Gupta, Scientist, CDRI, Lucknow.


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Thank you Thank you

13 september 201513 september 201513 september 2015 ewing christian college (an autonomous college...

Documents

allahabadthe college

allahabad anil kumar

digital imagedigital

digital computer

dimensional function

processing digital images

finite number of elements

finite number of bits