Robust Binary Image Deconvolution with Positive Semidefinite Programming

This paper reports on a novel approach to binary image deconvolution using Positive Semidefinite (PSD) Programming. We note the combinatorial nature of this problem: binary image deconvolution requires the minimization of a global energy function over binary variables, taking into account not only both local similarity and spatial context, but more specifically the relationship between individual pixel values and the point spread function. We subsequently modify the problem to a convex relaxation of the original problem without introducing additional parameters. We first compute the optimal solution of the convex relaxation based on PSD programming, and then use the randomized-hyperplane method to find the combinatorial solution to the original problem. We apply our approach to a collection of blurred binary images, and show the advantages of this approach in binary image deconvolution.