Many compression algorithms consist of quantizing the coefficients of an image in a linear basis. This introduces compression noise that often look like ringing. Recently some authors proposed variational methods to reduce those artifacts. They consists of minimizing a regularizing functional in the set of antecedents of the compressed image. In this paper we propose a fast algorithm to solve that problem. Our experiments lead us to the conclusion that these algorithms effectively reduce oscillations but also reduce contrasts locally. To handle that problem, we propose a fast contrast enhancement procedure. Experiments on a large dataset suggest that this procedure effectively improves the image quality at low bitrates.