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

• Published in: IEEE transactions on instrumentation and measurement 2024-01, Vol.73, p.1-1
• Main Authors: Tajmirriahi, Mahnoosh, Amini, Zahra, Rabbani, Hossein
• Format: Article
• Language: English
• Subjects: Algorithms; alpha stable; Alternating direction method of multipliers; Differential equations; Differential geometry; Estimation; Mathematical models; Mixture model; Mixture models; Noise reduction; Optical Coherence Tomography; optical coherence tomography (OCT); Probabilistic models; Probability density function; Probability density functions; Retina; Self-similar; Self-similarity; Signal processing algorithms; Statistical analysis; Statistical tests
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/TIM.2023.3346489

In this paper, an incorporation of statistical differential equation (SDE), and geometrical characteristics is applied to develop a mixture model of symmetric α-stable distributions (sαs) 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 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 (eADMM) algorithm is formulated and developed to utilize sαs 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 sub-problems. 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 be suitable for an effective description of the random nature of normal and abnormal OCT images independent of the capturing device.