Abstract : We present here an algorithm for restoration of irregularly sampled images with blur and noise. The good accuracy of non-quadratic regularizers in this type of problems was shown in recent articles, but their computational cost is prohibitive because the approximation space was trigonometric polynomials. Here we model the image as a cubic spline and prevent instability phenomena due to irregularity and blur by minimizing the total variation with a quadratic data-fitting term. The algorithm is the well-known Forward-Backward which is well adapted to our l1-l2 problem. We compare our method to the existing ones, including very efficient non-quadratic ones based on Fourier models. Our results are equivalent in term of SNR to the best existing method, but it is 20 to 50 times faster.