We propose a restoration algorithm for band limited images that considers irregular (perturbed) sampling, denoising, and deconvolution. We explore the application of a family of regularizers that allow to control the spectral behavior of the solution combined with the irregular to regular sampling algorithms proposed by H.G. Feichtinger, K. Gröchenig, M. Rauth and T. Strohmer. Moreover, the constraints given by the image acquisition model are incorporated as a set of local constraints. And the analysis of such constraints leads to an early stopping rule meant to improve the 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 zoom.