Solving Vision Problems via Filtering

We propose a new, filtering approach for solving a large number of regularized inverse problems commonly found in computer vision. Traditionally, such problems are solved by finding the solution to the system of equations that expresses the first-order optimality conditions of the problem. This can be slow if the system of equations is dense due to the use of nonlocal regularization, necessitating iterative solvers such as successive over-relaxation or conjugate gradients. In this paper, we show that similar solutions can be obtained more easily via filtering, obviating the need to solve a potentially dense system of equations using slow iterative methods. Our filtered solutions are very similar to the true ones, but often up to 10 times faster to compute.