Convergence of the alternating minimization algorithm for blind deconvolution

Blind deconvolution refers to the image processing task of restoring the or iginal image from a blurred version without the knowledge of the blurring f unction. One approach that has been proposed recently [T. Chan, C, Wong, IE EE Trans. Image Process. 7 (1998) 370-375; Y. You, M, Kaveh, IEEE Trans, Im age Process. 5 (1996) 416-428] is a joint minimization model in which an ob jective function is set up consisting of three terms: the data fitting term , and the regularization terms for the image and the blur. This model impli citly defines a one parameter family of blurred images and point spread fun ctions (PSFs), from which the user can decide, usually using additional inf ormation, which is the "best" restored image. To find a local minimum of th e objective function, we use an alternating minimization (AM) procedure [Y. You, M. Kaveh, IEEE Trans. Image Process. 5 (1996) 416-428] in which we fi x either the blur or the image and minimize respect to the other variable, each step of which is a standard non-blind deconvolution problem. While the model is not convex and thus allows multiple solutions, we have found that the AM procedure always converges globally, but with the converged solutio n depending on the initial guess. In this paper, we give an analysis of the AM procedure which explains the convergence behavior and the observed robu stness of the method. (C) 2000 Elsevier Science Inc. All rights reserved.