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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Bibliographic Details
Published in:IEEE transactions on medical imaging Vol. 40; no. 8; pp. 2129 - 2141
Main Authors: Tajmirriahi, Mahnoosh, Amini, Zahra, Hamidi, Arsham, Zam, Azhar, Rabbani, Hossein
Format: Journal Article
Language:English
Published: United States IEEE 01.08.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0278-0062
1558-254X
1558-254X
DOI:10.1109/TMI.2021.3073174