Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization

Understand

Plug-and-Play (PnP) methods solve ill-posed inverse problems through iterative proximal algorithms by replacing a proximal operator by a denoising operation.

• When applied with deep neural network denoisers, these methods have shown state-of-the-art visual performance for image restoration problems.
• However, their theoretical convergence analysis is still incomplete.
• Most of the existing convergence results consider nonexpansive denoisers, which is non-realistic, or limit their analysis to strongly convex data-fidelity terms in the inverse problem to solve.