Wavelet compression schemes (such as JPEG2000) lead to very specific visual artifacts due to the quantization of noisy wavelet coefficients. They have highly spatialy-correlated structure that makes it difficult to be removed with standard denoising algorithms. In this work, we propose a joint denoising and decompression method that combines a data-fitting term which takes into account the quantization process and an implicit prior contained in a stateof-the-art denoising CNN.