A REGULARIZATION APPROACH TO JOINT BLUR IDENTIFICATION AND IMAGE-RESTORATION

The primary difficulty with blind image restoration, or joint blur ide ntification and image restoration, is insufficient information, This c alls for proper incorporation of a priori knowledge about the image an d the point-spread function (PSF), A well-known space-adaptive regular ization method for image restoration is extended to address this probl em, This new method effectively utilizes, among others, the piecewise smoothness of both the image and the PSF. It attempts to minimize a co stfunction consisting of a restoration error measure and two regulariz ation terms (one for the image and the other for the blur) subject to other hard constraints, A scale problem inherent to the cost function is identified, which, if not properly treated, may hinder the minimiza tion/blind restoration process. Alternating minimization is proposed t o solve this problem so that algorithmic efficiency as well as simplic ity is significantly increased. Two implementations of alternating min imization based on steepest descent and conjugate gradient methods are presented, Good performance is observed with numerically and photogra phically blurred images, even though no stringent assumptions about th e structure of the underlying blur operator is made.