Satellites images can provide a lot of information on the earth system evolution. Although those sequences are frequently used, the importance of spatial error correlation is rarely taken into account in practice. This results in discarding a huge part of the information content of satellite image sequences. In this talk, we investigate a method based on wavelet or curvelet transforms to represent (at an affordable cost) some of the observation error correlation in a data assimilation context. We address the topic of monitoring the initial state of a system through the variational assimilation of images corrupted by a spatially correlated noise. The feasibility and the reliability of the approach is demonstrated in an academic context with a 2D Shallow-Water model.