Edge detection based on variational regularization for mixed noise removal

Edge detection plays a fundamental role in image processing, as edges contain critical structural information. This paper proposes a novel edge detection model designed to simultaneously achieve robust noise suppression and precise edge localization. Within the Bayesian maximum a posteriori estimation framework, we develop a modified Mumford-Shah (MMS) variational model that incorporates image prior knowledge with probability density functions characterizing both Poisson and Gaussian noise distributions. To efficiently solve the resulting variational problem, we employ the alternating direction method of multipliers (ADMM), which decomposes the energy minimization into several tractable subproblems. We further provide theoretical analysis demonstrating the algorithm's convergence under specific conditions. Extensive numerical experiments across varying levels of mixed noise contamination demonstrate that our method significantly outperforms classical edge detection approaches in both efficiency and accuracy.