An Automatic Pixel-Wise Multi-Penalty Approach to Image Restoration

This work tackles the problem of image restoration, a crucial task in many fields of applied sciences, focusing on removing degradation caused by blur and noise during the acquisition process. Drawing inspiration from the multi-penalty approach based on the Uniform Penalty principle, discussed in previous work, here we develop a new image restoration model and an iterative algorithm for its effective solution. The model incorporates pixel-wise regularization terms and establishes a rule for parameter selection, aiming to restore images through the solution of a sequence of constrained optimization problems. To achieve this, we present a modified version of the Newton Projection method, adapted to multi-penalty scenarios, and prove its convergence. Numerical experiments demonstrate the efficacy of the method in eliminating noise and blur while preserving the image edges.