A unified energy minimization framework for nonlocal regularization

We introduce a unifying framework for the non-local regularization of biomedical inverse problems. We choose the regularization functional as the sum of distances between pairs of patches in the image. We introduce a novel majorize minimize algorithm to minimize the proposed criterion. We observe that the first iteration of the algorithm to be very similar to the classical non-local regularization schemes. In addition to providing a novel interpretation for heuristic iterative nonlocal regularization schemes, the proposed scheme enables us to develop efficient optimization algorithms, design novel non-local schemes by choosing the distance metric, and minimize local minima problems. We demonstrate the benefits of the unified framework in deblurring and compressed sensing.