Preconditioned edge-preserving image deblurring and denoising

Preconditioned conjugate gradient (PCC) algorithms have been successfully u sed to significantly reduce the number of iterations in Tikhonov regulariza tion techniques for image restoration. Nevertheless, in many cases Tikhonov regularization is inadequate, in that it produces images that are oversmoo thed across intensity edges. Edge-preserving regularization can overcome th is inconvenience but has a higher complexity, in that it involves non-conve x optimization. In this paper, we show how the use of preconditioners can i mprove the computational performance of Edgepreserving image restoration as well. In particular, we adopt an image model which explicitly accounts for a constrained binary line process, and a mixed-annealing algorithm that al ternates steps of stochastic updating of the lines with steps of preconditi oned conjugate gradient-based estimation of the intensity. The presence of the line process requires a specific preconditioning strategy to manage the particular structure of the matrix of the equivalent least squares problem . Experimental results are provided to show the satisfactory performance of the method, both with respect to the quality of the restored images and th e computational saving. (C) 2001 Elsevier Science B.V. All rights reserved.