Convergence of Plug-and-Play ADMM with Adaptive Linear Symmetric Denoisers

Plug-and-Play alternating directions method of multipliers (PnP-ADMM) is an emerging paradigm for image reconstruction. It is obtained by replacing the proximal operator (associated with the regularizer) in ADMM with a powerful denoiser. Remarkably, it has exhibited great success in many imaging applications. Owing to its iterative manner, convergence analysis has been an active research topic. Recently, the convergence of PnP-ADMM with fixed linear symmetric denoisers has been proved. Notably, an adaptive denoiser generally achieves superior performance compared to its fixed version. Inspired by this observation, we extend the fixed linear symmetric denoisers to adaptive ones in this paper. Under a mild assumption, the convergence of PnP-ADMM with adaptive linear symmetric denoisers is proved for inpainting, deblurring, and superresolution. Experimental results on the above three tasks demonstrate our convergence theory. Meanwhile, PnP-ADMM with adaptive linear symmetric denoisers displays an enormous improvement over the one with the fixed version.