Modeling of Retinal Optical Coherence Tomography Based on Stochastic Differential Equations: Application to Denoising
| Autor: | Mahnoosh Tajmirriahi, Hossein Rabbani, Azhar Zam, Zahra Amini, Arsham Hamidi |
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| Rok vydání: | 2021 |
| Předmět: |
Models
Statistical Radiological and Ultrasound Technology Mathematical analysis Order (ring theory) Speckle noise Differential operator Stability (probability) Stable distribution Retina 030218 nuclear medicine & medical imaging Computer Science Applications Stable process 03 medical and health sciences Stochastic differential equation 0302 clinical medicine Computer Science::Computer Vision and Pattern Recognition Maximum a posteriori estimation Humans Electrical and Electronic Engineering Software Algorithms Tomography Optical Coherence Mathematics |
| Zdroj: | IEEE transactions on medical imaging. 40(8) |
| ISSN: | 1558-254X |
| Popis: | 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 $\boldsymbol {\alpha }\text{s}$ ) 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 $\boldsymbol {\alpha }\text{s}$ distribution. We applied fractional Laplacian operator to image and fitted s $\boldsymbol {\alpha }\text{s}$ 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 $\boldsymbol {\alpha }\text{s}$ 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. |
| Databáze: | OpenAIRE |
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