An innovative non-variational framework for denoising impulsive Cauchy noise in medical imaging

Abstract

We introduce an innovative non-variational framework designed to address impulsive Cauchy noise in images. This approach utilizes a coupled system that integrates image decomposition techniques with the $p(x, t)$-Laplacian operator, successfully preserving texture and edge details. Our initial analysis focuses on the theoretical foundations of the proposed model, where we employ the Galerkin method to confirm its well-posedness.In addition, we apply our method to COVID MRI chest images, demonstrating its effectiveness in reducing noise while maintaining critical anatomical details. Experimental results show that our approach consistently outperforms existing denoising techniques, highlighting its robustness and effectiveness in medical imaging contexts, particularly in enhancing the quality of MRI scans affected by impulsive noise.