Iterative Total Variation Regularization with Non-Quadratic Fidelity

• DOI: 10.1007/s10851-006-8302-3
• Publication Date: 2006-09-26T14:23:11Z
• Authors: Lin He; Martin Burger; Stanley J. Osher
• Keywords: 0101 mathematics; 01 natural sciences

A generalized iterative regularization procedure based on the total variation penalization is introduced for image denoising models with non-quadratic convex fidelity terms. By using a suitable sequence of penalty parameters we solve the issue of solvability of minimization problems arising in each step of the iterative procedure, which has been encountered in a recently developed iterative total variation procedure Furthermore, we obtain rigorous convergence results for exact and noisy data. We test the behaviour of the algorithm on real images in several numerical experiments using L 1 and L 2 fitting terms. Moreover, we compare the results with other state-of-the art multiscale techniques for total variation based image restoration.