RPCA with Log-Schatten Norm and Adaptive Histogram Equalization for Medical Imaging

Medical imaging, especially cancer and retinal fundus analysis, is often compromised by artifacts and heavy noise and artifact, which can hinder accurate diagnosis. Existing low-rank sparse component methods, such as RPCA with the conventional nuclear norm, assume uniform singular value weights, which may not hold true due to noise variations in images. We recently developed RPCA with the log-weighted nuclear norm, which addresses some of these issues but still relies on weight selection, potentially introducing bias. To overcome these limitations, we propose a novel method that integrates RPCA with Log-Schatten Norm (LSN) and Adaptive Histogram Equalization (AHE) for medical imaging and clinical purposes. The Log-Schatten Norm improves singular value penalization and structure preservation, while AHE enhances contrast and reduces noise. The method is formulated as an optimization problem and solved using the Alternating Direction Method for Multipliers (ADMM). Experimental results on publicly available retinal and cancer image datasets demonstrate that our method outperforms existing methods in enhancing overall image quality, making it a promising tool for medical imaging applications.