We propose a new method to solve a problem of image restoration with many different aspects: reconstruction from irregular samples, deconvolution and denoising. The model we propose is robust to different kind of noises, in particular, impulse and Gaussian noise. We compare our results to the ones obtained in [1] and show that our problem presents some advantages particularly in satellite imaging. At last, we conclude on a discussion about resolution schemes for variational problems' minimization and propose some faster resolution shemes for our problem and the one in [1].