A non-local regularization strategy for image deconvolution

In this paper, we propose an inhomogeneous restoration (deconvolution) model under the Bayesian framework exploiting a non-parametric adaptive prior distribution derived from the appealing and natural image model recently proposed by Buades et al. [Buades, A., Coll, B., Morel, J.-M., 2005. A review of image denoising algorithms, with a new one. SIAM Multiscale Model. Simul. (SIAM Interdisc. J.), 4(2), 490–530] for pure denoising applications. This prior expresses that acceptable restored solutions are likely the images exhibiting a high degree of redundancy. In other words, this prior will favor solutions (i.e., restored images) with similar pixel neighborhood configurations. In order to render this restoration unsupervised, we have adapted the L-curve approach (originally defined for Tikhonov-type regularizations), for estimating our regularization parameter. The experiments herein reported illustrate the potential of this approach and demonstrate that this regularized restoration strategy performs competitively compared to the best existing state-of-the art methods employing classical local priors (or regularization terms) in benchmark tests.