Deep Proximal Gradient Method for Learned Convex Regularizers

We consider the problem of simultaneously learning a convex penalty function and its proximity operator for image reconstruction from incomplete measurements. Our goal is to apply Accelerated Proximal Gradient Method (APGM) using a learned proximity operator in place of the true proximity operator of the learned penalty function. Starting from a Gaussian image denoiser, we learn an associated penalty function and its proximity operator. The learned penalty function offers provable reconstruction guarantees, whereas access to its proximity operator presents the opportunity to achieve APGM convergence rates, which are faster than those of subgradient descent approaches.