In this paper, we propose a sparsity-based despeckling approach. The first main contribution of this work is the elaboration of a sparse-coding algorithm adapted to the statistics of SAR images. In fact, in most of the sparse-coding algorithms dedicated to SAR data, a logarithmic transform is applied on the data to turn the speckle modeled by a multiplicative noise into an additive noise, then, a Gaussian prior is used. However , using a more suitable prior for SAR data avoids introducing artifacts. The second main contribution proposed is to evaluate how computing a map predicting the sparsity degree of each patch could bring an improvement compared to a traditional sparse-coding approach with a low-error rate based stopping criterion.