Multilevel FISTA for Image Restoration

This paper presents a multilevel fast iterative soft thresholding algorithm (FISTA), based on the use of the Moreau envelope to incorporate correction from coarse models, which is easy to compute when the explicit form of the proximal operator for the considered functions is known. This approach is supported by strong theoretical guarantees: we prove both the rate of convergence and the convergence of the iterates to a minimum in the convex case, an important result for ill-posed problems. We evaluate our approach on image restoration problems and we show that it outperforms classical FISTA for large-scale images.