Local Self-Similar Solution of ADMM for Denoising of Retinal OCT Images

In this article, an incorporation of stochastic differential equation (SDE), and geometrical characteristics is applied to develop a mixture model of symmetric
$\alpha $
-stable (
$\text{s}\alpha \text{s}$
) distributions for white process representation of retinal optical coherence tomography (OCT) images. According to validation by statistical tests, this model well justifies the heavy-tailed nature of the probability density function (pdf) of OCT images. In addition, the proposed mixture model provides statistically independent and localized prior information for the maximum a posteriori (MAP) estimation. To declare this advantage, for the first time, the extended alternating direction method of multipliers (eADMMs) algorithm is formulated and developed to utilize
$\text{s}\alpha \text{s}$
mixture prior to noise reduction of OCT images. This algorithm contributes a mixture model in the ADMM algorithm and simplifies the denoising problem into the localized component-specific proximal subproblems. Experimental results indicate that the proposed method is visually and quantitatively outstanding for the denoising of normal and abnormal OCT images of various devices. The results also demonstrate that the mixture model prior can improve denoising of OCT images in particular for preserving the structural information and texture features. This makes the proposed model suitable for an effective description of the random nature of normal and abnormal OCT images independent of the capturing device.