We propose and test a simple algorithmic framework for recovering images from blurry and noisy observations based on total variation (TV) regularization when a blurring point-spread function is given. Using a splitting technique, we construct an iterative procedure of alternately solving a pair of easy subproblems associated with an increasing sequence of penalty parameter values. The main computation at each iteration is three Fast Fourier Transforms (FFTs). We present numerical results showing that a rudimentary implementation of our algorithm already performs favorably in comparison with two of the existing start-of-the-art algorithms. In particular, it runs orders of magnitude faster than a number of existing algorithms for solving TVL2-based de-convolution problems to good accuracies.
CAAM Technical Report TR07-10, Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005, June 2007