In the last decades satellite imagery has increased in both quantity and quality and so has its influence in numerical weather forecasting. Compared to conventional observations, satellite images show significant advantages and drawbacks. On the one hand, satellites can provide regularly dense observations of any region on earth. On the other hand, images show spatially correlated errors. Most of the time, the management of observation error correlations is simplified in data assimilation methods. In order to incorporate consistent information, the no correlation hypothesis is usually accounted for by observation thinning methods in association to variance inflation. Thoses two operations result in discarding a huge part of the information content of satellite image sequences. In this talk, we investigate a method based on the wavelet transform in order to represent (at an affordable cost) some of the observation error correlation in variational data assimilation context. The proposed approach consists in considering an image sequence in the wavelet space instead of the pixel space. We show that the diagonal of the covariance matrix in a wavelet space (if well chosen) is able to represent an important part of the error covariance (in the pixel space). The benefit of this approach is demonstrated on twin experiments involving a 2D-shallow water model and synthetic observations.