Gaussian and Poisson noise identification using non-convex optimization with <i>L</i>²-norm power constraints

This article tackles the main issues related to image restoration, including the preservation of contours, removal of the staircasing effect, and reduction of mixture noise. For this purpose, we introduced a novel minimization problem, based on a PDE-constrained whose nonlinear structure relies on the solution itself. For the non-convex cost function, it contains a novel regularization that strikes a balance between edge enhancement and smoothness. The model employs a robust fidelity term based on the L 2 -norm to ensure accurate reconstruction. A comprehensive theoretical analysis establishes the well-posedness of the model, and the ADMM method is used to solve the minimization problem. Extensive experiments demonstrate the model’s numerical efficiency and its effectiveness in addressing mixed noise and maintaining image detail.