Modeling of Retinal Optical Coherence Tomography Based on Stochastic Differential Equations: Application to Denoising

In this paper a statistical modeling, based on stochastic differential equations (SDEs), is proposed for retinal Optical Coherence Tomography (OCT) images. In this method, pixel intensities of image are considered as discrete realizations of a Levy stable process. This process has independent increm...

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Vydáno v:IEEE transactions on medical imaging Ročník 40; číslo 8; s. 2129 - 2141
Hlavní autoři: Tajmirriahi, Mahnoosh, Amini, Zahra, Hamidi, Arsham, Zam, Azhar, Rabbani, Hossein
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States IEEE 01.08.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Alternating direction method of multipliers~(ADMM) algorithm
Differential equations
Formulas (mathematics)
Fractals
fractional Laplacian
Goodness of fit
Histograms
Image classification
Image segmentation
Laplace equations
Laplace transforms
Mathematical model
Mathematical models
Noise
Noise reduction
Operators (mathematics)
Optical Coherence Tomography
optical coherence tomography~(OCT) image
Optimization
Pixels
Regularization
Retina
Statistical analysis
Statistical models
Statistical tests
stochastic differential equation (SDE)
Stochastic processes
Stochasticity
Technological innovation
Tomography
ISSN:0278-0062, 1558-254X, 1558-254X
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Abstract In this paper a statistical modeling, based on stochastic differential equations (SDEs), is proposed for retinal Optical Coherence Tomography (OCT) images. In this method, pixel intensities of image are considered as discrete realizations of a Levy stable process. This process has independent increments and can be expressed as response of SDE to a white symmetric alpha stable (s <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\alpha }\text{s} </tex-math></inline-formula>) noise. Based on this assumption, applying appropriate differential operator makes intensities statistically independent. Mentioned white stable noise can be regenerated by applying fractional Laplacian operator to image intensities. In this way, we modeled OCT images as s <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\alpha }\text{s} </tex-math></inline-formula> distribution. We applied fractional Laplacian operator to image and fitted s <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\alpha }\text{s} </tex-math></inline-formula> to its histogram. Statistical tests were used to evaluate goodness of fit of stable distribution and its heavy tailed and stability characteristics. We used modeled s <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\alpha }\text{s} </tex-math></inline-formula> distribution as prior information in maximum a posteriori (MAP) estimator in order to reduce the speckle noise of OCT images. Such a statistically independent prior distribution simplified denoising optimization problem to a regularization algorithm with an adjustable shrinkage operator for each image. Alternating Direction Method of Multipliers (ADMM) algorithm was utilized to solve the denoising problem. We presented visual and quantitative evaluation results of the performance of this modeling and denoising methods for normal and abnormal images. Applying parameters of model in classification task as well as indicating effect of denoising in layer segmentation improvement illustrates that the proposed method describes OCT data more accurately than other models that do not remove statistical dependencies between pixel intensities.
AbstractList In this paper a statistical modeling, based on stochastic differential equations (SDEs), is proposed for retinal Optical Coherence Tomography (OCT) images. In this method, pixel intensities of image are considered as discrete realizations of a Levy stable process. This process has independent increments and can be expressed as response of SDE to a white symmetric alpha stable (s [Formula Omitted]) noise. Based on this assumption, applying appropriate differential operator makes intensities statistically independent. Mentioned white stable noise can be regenerated by applying fractional Laplacian operator to image intensities. In this way, we modeled OCT images as s [Formula Omitted] distribution. We applied fractional Laplacian operator to image and fitted s [Formula Omitted] to its histogram. Statistical tests were used to evaluate goodness of fit of stable distribution and its heavy tailed and stability characteristics. We used modeled s [Formula Omitted] distribution as prior information in maximum a posteriori (MAP) estimator in order to reduce the speckle noise of OCT images. Such a statistically independent prior distribution simplified denoising optimization problem to a regularization algorithm with an adjustable shrinkage operator for each image. Alternating Direction Method of Multipliers (ADMM) algorithm was utilized to solve the denoising problem. We presented visual and quantitative evaluation results of the performance of this modeling and denoising methods for normal and abnormal images. Applying parameters of model in classification task as well as indicating effect of denoising in layer segmentation improvement illustrates that the proposed method describes OCT data more accurately than other models that do not remove statistical dependencies between pixel intensities.
In this paper a statistical modeling, based on stochastic differential equations (SDEs), is proposed for retinal Optical Coherence Tomography (OCT) images. In this method, pixel intensities of image are considered as discrete realizations of a Levy stable process. This process has independent increments and can be expressed as response of SDE to a white symmetric alpha stable (s <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\alpha }\text{s} </tex-math></inline-formula>) noise. Based on this assumption, applying appropriate differential operator makes intensities statistically independent. Mentioned white stable noise can be regenerated by applying fractional Laplacian operator to image intensities. In this way, we modeled OCT images as s <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\alpha }\text{s} </tex-math></inline-formula> distribution. We applied fractional Laplacian operator to image and fitted s <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\alpha }\text{s} </tex-math></inline-formula> to its histogram. Statistical tests were used to evaluate goodness of fit of stable distribution and its heavy tailed and stability characteristics. We used modeled s <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\alpha }\text{s} </tex-math></inline-formula> distribution as prior information in maximum a posteriori (MAP) estimator in order to reduce the speckle noise of OCT images. Such a statistically independent prior distribution simplified denoising optimization problem to a regularization algorithm with an adjustable shrinkage operator for each image. Alternating Direction Method of Multipliers (ADMM) algorithm was utilized to solve the denoising problem. We presented visual and quantitative evaluation results of the performance of this modeling and denoising methods for normal and abnormal images. Applying parameters of model in classification task as well as indicating effect of denoising in layer segmentation improvement illustrates that the proposed method describes OCT data more accurately than other models that do not remove statistical dependencies between pixel intensities.
In this paper a statistical modeling, based on stochastic differential equations (SDEs), is proposed for retinal Optical Coherence Tomography (OCT) images. In this method, pixel intensities of image are considered as discrete realizations of a Levy stable process. This process has independent increments and can be expressed as response of SDE to a white symmetric alpha stable (s [Formula: see text]) noise. Based on this assumption, applying appropriate differential operator makes intensities statistically independent. Mentioned white stable noise can be regenerated by applying fractional Laplacian operator to image intensities. In this way, we modeled OCT images as s [Formula: see text] distribution. We applied fractional Laplacian operator to image and fitted s [Formula: see text] to its histogram. Statistical tests were used to evaluate goodness of fit of stable distribution and its heavy tailed and stability characteristics. We used modeled s [Formula: see text] distribution as prior information in maximum a posteriori (MAP) estimator in order to reduce the speckle noise of OCT images. Such a statistically independent prior distribution simplified denoising optimization problem to a regularization algorithm with an adjustable shrinkage operator for each image. Alternating Direction Method of Multipliers (ADMM) algorithm was utilized to solve the denoising problem. We presented visual and quantitative evaluation results of the performance of this modeling and denoising methods for normal and abnormal images. Applying parameters of model in classification task as well as indicating effect of denoising in layer segmentation improvement illustrates that the proposed method describes OCT data more accurately than other models that do not remove statistical dependencies between pixel intensities.In this paper a statistical modeling, based on stochastic differential equations (SDEs), is proposed for retinal Optical Coherence Tomography (OCT) images. In this method, pixel intensities of image are considered as discrete realizations of a Levy stable process. This process has independent increments and can be expressed as response of SDE to a white symmetric alpha stable (s [Formula: see text]) noise. Based on this assumption, applying appropriate differential operator makes intensities statistically independent. Mentioned white stable noise can be regenerated by applying fractional Laplacian operator to image intensities. In this way, we modeled OCT images as s [Formula: see text] distribution. We applied fractional Laplacian operator to image and fitted s [Formula: see text] to its histogram. Statistical tests were used to evaluate goodness of fit of stable distribution and its heavy tailed and stability characteristics. We used modeled s [Formula: see text] distribution as prior information in maximum a posteriori (MAP) estimator in order to reduce the speckle noise of OCT images. Such a statistically independent prior distribution simplified denoising optimization problem to a regularization algorithm with an adjustable shrinkage operator for each image. Alternating Direction Method of Multipliers (ADMM) algorithm was utilized to solve the denoising problem. We presented visual and quantitative evaluation results of the performance of this modeling and denoising methods for normal and abnormal images. Applying parameters of model in classification task as well as indicating effect of denoising in layer segmentation improvement illustrates that the proposed method describes OCT data more accurately than other models that do not remove statistical dependencies between pixel intensities.
In this paper a statistical modeling, based on stochastic differential equations (SDEs), is proposed for retinal Optical Coherence Tomography (OCT) images. In this method, pixel intensities of image are considered as discrete realizations of a Levy stable process. This process has independent increments and can be expressed as response of SDE to a white symmetric alpha stable (sαs) noise. Based on this assumption, applying appropriate differential operator makes intensities statistically independent. Mentioned white stable noise can be regenerated by applying fractional Laplacian operator to image intensities. In this way, we modeled OCT images as sαs distribution. We applied fractional Laplacian operator to image and fitted sαs to its histogram. Statistical tests were used to evaluate goodness of fit of stable distribution and its heavy tailed and stability characteristics. We used modeled sαs distribution as prior information in maximum a posteriori (MAP) estimator in order to reduce the speckle noise of OCT images. Such a statistically independent prior distribution simplified denoising optimization problem to a regularization algorithm with an adjustable shrinkage operator for each image. Alternating Direction Method of Multipliers (ADMM) algorithm was utilized to solve the denoising problem. We presented visual and quantitative evaluation results of the performance of this modeling and denoising methods for normal and abnormal images. Applying parameters of model in classification task as well as indicating effect of denoising in layer segmentation improvement illustrates that the proposed method describes OCT data more accurately than other models that do not remove statistical dependencies between pixel intensities.
Author Amini, Zahra
Tajmirriahi, Mahnoosh
Hamidi, Arsham
Zam, Azhar
Rabbani, Hossein
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BackLink https://www.ncbi.nlm.nih.gov/pubmed/33852382$$D View this record in MEDLINE/PubMed
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Cites_doi 10.1364/BOE.8.000162
10.1109/TMI.2020.2998066
10.1016/S0378-4371(02)00961-5
10.1137/S1064827598344169
10.1109/30.920468
10.1109/EMBC.2019.8857653
10.3182/20120711-3-BE-2027.00310
10.1016/j.media.2013.05.006
10.1016/j.compbiomed.2016.02.003
10.1109/SPMB47826.2019.9037832
10.1364/BOE.3.000927
10.1109/18.382009
10.1109/TIP.2012.2210725
10.1364/OL.30.003051
10.1364/BOE.8.003903
10.1007/s12652-018-0823-2
10.1016/j.bspc.2018.02.011
10.1364/AO.58.006233
10.1109/TMI.2017.2772963
10.1109/TMI.2009.2038375
10.1364/BOE.379551
10.1016/j.optcom.2012.10.053
10.1364/BOE.9.005129
10.1007/978-981-32-9291-8_10
10.1109/TMI.2016.2519439
10.1109/EMBC.2017.8037831
10.1007/s11042-019-07999-y
10.2174/157340508786404044
10.1364/OE.27.012289
10.1109/TIP.2005.857249
10.1109/TSP.2006.890843
10.1080/01621459.1980.10477573
10.1002/jbio.201960135
10.1109/TMI.2014.2374354
10.1038/ncomms15845
10.1109/CVPR.2005.38
10.1103/PhysRevE.76.021116
10.1109/TMI.2016.2556080
10.1109/ICCV.2015.36
10.1109/TIP.2020.2984896
10.1016/j.compbiomed.2019.01.010
10.1109/TMI.2016.2611503
10.1016/j.bspc.2019.101632
10.1117/1.JBO.21.9.096004
10.3390/app10186247
10.1109/TMI.2013.2271904
10.1103/PhysRevLett.97.138102
10.1109/TIP.2020.2994454
10.1117/1.429925
10.2307/2334448
10.1017/CBO9781107415805
10.1109/ICIVC.2018.8492869
10.1201/9780203738818
10.1364/BOE.377021
10.1109/TSP.2010.2091638
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References ref57
ref13
ref56
ref12
ref59
ref15
ref58
ref14
ref53
ref52
ref55
ref11
ref54
ref10
ref17
ref19
ref18
klebanov (ref8) 2015
ref51
ref46
ref45
ref48
ref47
ref42
ref44
ref43
ref49
ref7
jain (ref50) 1989
ref9
ref4
ref3
ref6
ref5
guo (ref41) 2021; 70
ref40
ref35
ref34
ref37
ref36
ref31
ref30
ref33
ref32
ref39
ref38
mayer (ref62) 2008
markkanen (ref2) 2016
ref24
ref23
ref26
ref25
ref20
ref22
amini (ref16) 2017; 22
ref21
ref28
ref27
ref29
ibragimov (ref1) 2012; 9
ref60
ref61
References_xml – ident: ref21
  doi: 10.1364/BOE.8.000162
– year: 1989
  ident: ref50
  publication-title: Fundamentals of Digital Image Processing
– ident: ref25
  doi: 10.1109/TMI.2020.2998066
– ident: ref52
  doi: 10.1016/S0378-4371(02)00961-5
– ident: ref59
  doi: 10.1137/S1064827598344169
– ident: ref4
  doi: 10.1109/30.920468
– ident: ref19
  doi: 10.1109/EMBC.2019.8857653
– ident: ref13
  doi: 10.3182/20120711-3-BE-2027.00310
– ident: ref61
  doi: 10.1016/j.media.2013.05.006
– ident: ref20
  doi: 10.1016/j.compbiomed.2016.02.003
– ident: ref35
  doi: 10.1109/SPMB47826.2019.9037832
– ident: ref30
  doi: 10.1364/BOE.3.000927
– ident: ref5
  doi: 10.1109/18.382009
– ident: ref56
  doi: 10.1109/TIP.2012.2210725
– ident: ref10
  doi: 10.1364/OL.30.003051
– ident: ref22
  doi: 10.1364/BOE.8.003903
– ident: ref24
  doi: 10.1007/s12652-018-0823-2
– ident: ref34
  doi: 10.1016/j.bspc.2018.02.011
– ident: ref36
  doi: 10.1364/AO.58.006233
– ident: ref23
  doi: 10.1109/TMI.2017.2772963
– ident: ref14
  doi: 10.1109/TMI.2009.2038375
– ident: ref44
  doi: 10.1364/BOE.379551
– year: 2016
  ident: ref2
  article-title: Cauchy difference priors for edge-preserving Bayesian inversion with an application to X-ray tomography
  publication-title: arXiv 1603 06135
– ident: ref29
  doi: 10.1016/j.optcom.2012.10.053
– ident: ref37
  doi: 10.1364/BOE.9.005129
– ident: ref45
  doi: 10.1007/978-981-32-9291-8_10
– ident: ref15
  doi: 10.1109/TMI.2016.2519439
– ident: ref18
  doi: 10.1109/EMBC.2017.8037831
– ident: ref43
  doi: 10.1007/s11042-019-07999-y
– ident: ref60
  doi: 10.2174/157340508786404044
– ident: ref40
  doi: 10.1364/OE.27.012289
– ident: ref49
  doi: 10.1109/TIP.2005.857249
– ident: ref47
  doi: 10.1109/TSP.2006.890843
– ident: ref53
  doi: 10.1080/01621459.1980.10477573
– ident: ref38
  doi: 10.1002/jbio.201960135
– ident: ref32
  doi: 10.1109/TMI.2014.2374354
– ident: ref27
  doi: 10.1038/ncomms15845
– ident: ref55
  doi: 10.1109/CVPR.2005.38
– ident: ref48
  doi: 10.1103/PhysRevE.76.021116
– ident: ref28
  doi: 10.1109/TMI.2016.2556080
– ident: ref58
  doi: 10.1109/ICCV.2015.36
– volume: 9
  year: 2012
  ident: ref1
  publication-title: Gaussian Random Processes
– ident: ref26
  doi: 10.1109/TIP.2020.2984896
– ident: ref42
  doi: 10.1016/j.compbiomed.2019.01.010
– volume: 70
  start-page: 1
  year: 2021
  ident: ref41
  article-title: Unsupervised denoising of optical coherence tomography images with nonlocal-generative adversarial network
  publication-title: IEEE Trans Instrum Meas
– ident: ref3
  doi: 10.1109/TMI.2016.2611503
– ident: ref39
  doi: 10.1016/j.bspc.2019.101632
– ident: ref12
  doi: 10.1117/1.JBO.21.9.096004
– year: 2015
  ident: ref8
  article-title: Tempered distributions: Does universal tempering procedure exist?
  publication-title: arXiv 1505 02068
– ident: ref51
  doi: 10.3390/app10186247
– ident: ref31
  doi: 10.1109/TMI.2013.2271904
– ident: ref11
  doi: 10.1103/PhysRevLett.97.138102
– ident: ref17
  doi: 10.1109/TIP.2020.2994454
– ident: ref9
  doi: 10.1117/1.429925
– ident: ref54
  doi: 10.2307/2334448
– ident: ref46
  doi: 10.1017/CBO9781107415805
– ident: ref57
  doi: 10.1109/ICIVC.2018.8492869
– volume: 22
  start-page: 86011
  year: 2017
  ident: ref16
  article-title: Optical coherence tomography image denoising using Gaussianization transform
  publication-title: J Biomed Opt
– start-page: 160
  year: 2008
  ident: ref62
  article-title: Fuzzy C-means clustering for retinal layer segmentation on high resolution OCT images
  publication-title: Proc 19th Biennial Int EURASIP Conf (BIOSIGNAL)
– ident: ref7
  doi: 10.1201/9780203738818
– ident: ref33
  doi: 10.1364/BOE.377021
– ident: ref6
  doi: 10.1109/TSP.2010.2091638
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Snippet In this paper a statistical modeling, based on stochastic differential equations (SDEs), is proposed for retinal Optical Coherence Tomography (OCT) images. In...
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SubjectTerms Algorithms
Alternating direction method of multipliers~(ADMM) algorithm
Differential equations
Formulas (mathematics)
Fractals
fractional Laplacian
Goodness of fit
Histograms
Image classification
Image segmentation
Laplace equations
Laplace transforms
Mathematical model
Mathematical models
Noise
Noise reduction
Operators (mathematics)
Optical Coherence Tomography
optical coherence tomography~(OCT) image
Optimization
Pixels
Regularization
Retina
Statistical analysis
Statistical models
Statistical tests
stochastic differential equation (SDE)
Stochastic processes
Stochasticity
Technological innovation
Tomography
Title Modeling of Retinal Optical Coherence Tomography Based on Stochastic Differential Equations: Application to Denoising
URI https://ieeexplore.ieee.org/document/9404198
https://www.ncbi.nlm.nih.gov/pubmed/33852382
https://www.proquest.com/docview/2556486508
https://www.proquest.com/docview/2513248365
Volume 40
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