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

Mahnoosh Tajmirriahi, Zahra Amini, Arsham Hamidi, Azhar Zam, Hossein Rabbani

Research output: Contribution to journalArticlepeer-review


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 (sα s) 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 α s distribution. We applied fractional Laplacian operator to image and fitted s α s 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 α s 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.

Original languageEnglish (US)
Article number9404198
Pages (from-to)2129-2141
Number of pages13
JournalIEEE Transactions on Medical Imaging
Issue number8
StatePublished - Aug 2021


  • Alternating direction method of multipliers~(ADMM) algorithm
  • fractional Laplacian
  • optical coherence tomography(OCT) image
  • stochastic differential equation (SDE)

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering


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