We propose a restoration algorithm for band limited images that considers irregular/n(perturbed) sampling, denoising, and deconvolution. We explore the application of a family of/nregularizers that allow to control the spectral behavior of the solution combined with the irregular to/nregular sampling algorithms proposed by H.G. Feichtinger, K. Gr¨ochenig, M. Rauth and T. Strohmer./nMoreover, the constraints given by the image acquisition model are incorporated as a set of local/nconstraints. And the analysis of such constraints leads to an early stopping rule meant to improve/nthe speed of the algorithm. Finally we present experiments focused on the restoration of satellite images, where the micro-vibrations are responsible of the type of distortions we are considering here. We will compare results of the proposed method with previous methods and show an extension to/nzoom.