Parameter space study of optimal scale-dependent weights in TV image denoising

Abstract

We investigate the choice of finite-dimensional parameter spaces within a bilevel optimization framework for selecting scale-dependent weights in total variation image denoising with non-uniform noise. Due to the pointwise box constraints on the parameter function, we prove existence of Lagrange multipliers in low regularity spaces, and derive a first-order optimality system. To cope with the difficulties related to the lack of regularity, a Moreau-Yosida regularization is introduced and convergence of the regularized optimal parameters towards the optimal weight for the original problem is verified. For each regularized bilevel problem a second-order quasi-Newton algorithm is proposed, together with a semismooth Newton scheme for solving the lower-level problem. Finally, several numerical tests are carried out to compare the different parameter space choices and draw some conclusions.

Keywords:

• Total variation image denoising
• Bilevel optimization
• non-uniform noise
• spatially dependent parameter

2020 Mathematics Subject Classifications:

• 68Q25
• 68R10
• 68U05

Disclosure statement

No potential conflict of interest was reported by the author(s).