Simultaneous deconvolution and denoising using a second order variational approach applied to image super resolution

The aim of a Super resolution (SR) technique is to construct a high-resolution image from a sequence of observed low-resolution ones of the same scene. One major roadblock of an SR reconstitution is removing noise and blur without destroying edges. We propose a novel multiframe image SR algorithm based on a convex combination of Bilateral Total Variation and a non-smooth second order variational regularization, using a controlled weighting parameter. We prove the existence of a minimizer of the proposed energy in the space of functions of bounded Hessian. The minimization of the convex functional is performed with a fast primal-dual algorithm. The simulation results and real experiments show the performance of the proposed algorithm in avoiding undesirable artifacts compared to other methods in the literature.