On the Convergence of the Lagged Diffusivity Fixed Point Method in Total Variation Image Restoration

摘要: In this paper we show that the lagged diffusivity fixed point algorithm introduced by Vogel and Oman in [ SIAM J. Sci. Comput., 17 (1996), pp. 227--238] to solve problem of total variation denoising, proposed Rudin, Osher, Fatemi Phys. D, 60 (1992), 259--268], is a particular instance class algorithms Voss Eckhardt Computing, 25 (1980), 243--251], whose origins can be traced back Weiszfeld's original work for minimizing sum Euclidean lengths Tohoku Math. J., 43 (1937), 355--386]. There have recently appeared several proofs convergence [G. Aubert et al., Technical report 94-01, Informatique, Signaux Systemes de Sophia Antipolis, 1994], [A. Chambolle P.-L. Lions, 9509, CEREMADE, 1995], [D. C. Dobson R. Vogel, Numer. Anal., 34 (1997), 1779--1791]. Here present proof global linear using framework [H. U. Eckhart, 243--251] give bound rate iteration agrees with our experimental results. These results are also valid suitable generalizations algorithm.