Robust Principal Component Analysis for Retinal Image Enhancement

Recent concerns in biomedical image processing revolve around robustly detecting outliers and noise. A major challenge in emerging statistical and mathematical domains involves accurately recovering the true underlying object from highly distorted data matrices. Although various methods, such as \(L_{1}\) norm-based image recovery, have been proposed, they may introduce bias in parameter estimates, particularly in high-dimensional retinal images. To address this drawback, we propose robust principal component analysis (RPCA) with affine transformation (AT) and rank prior information (RPI), denoted as RPCA with AT \(+\) RPI. This method leverages convex optimization to enhance the quality of retinal images while mitigating the impact of outliers and occlusions. However, RPCA with AT \(+\) RPI is limited by single subspace parameters. Subsequently, we introduce a new method called RPCA with AT \(+\) \(L_{2,1}\) norms to develop a technique robust to irritating effects, outliers, and defects in high-dimensional images considering multiple parameters from multiple subspace. While convex optimization is employed to determine the involved variables including AT, these methods lack robustness in multi-array data. To overcome this challenge, we introduce a novel approach called Tensor RPCA with AT \(+\) \(L_{2,1}\) norms to mitigate the impact of outliers and noise in multi-array data considering each slice of images as tensor to find the true underlying retinal images. To reduce computational complexity, we employ the Alternating Direction Method of Multipliers (ADMMs) to generate a new set of recursive equations. These equations are iteratively updated to optimize variables and affine transformations in a round-robin fashion. Simulation results demonstrate the superiority of our proposed methods over state-of-the-art works, particularly evident in three different retinal images sourced from public databases.