Preconditioned edge-preserving image deblurring and denoising

Preconditioned conjugate gradient (PCG) algorithms have been successfully used to significantly reduce the number of iterations in Tikhonov regularization techniques for image restoration. Nevertheless, in many cases Tikhonov regularization is inadequate, in that it produces images that are oversmoothed across intensity edges. Edge-preserving regularization can overcome this inconvenience but has a higher complexity, in that it involves non-convex optimization. In this paper, we show how the use of preconditioners can improve the computational performance of edge-preserving 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 alternates steps of stochastic updating of the lines with steps of preconditioned 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 the computational saving.