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Zbl 0847.65083
Vogel, C.R.; Oman, M.E.
Iterative methods for total variation denoising. (English)
[J] SIAM J. Sci. Comput. 17, No.1, 227-238 (1996). ISSN 1064-8275; ISSN 1095-7197/e

The paper is concerned with computing the minimization of the total variation (TV)-penalized least squares functional. A fixed point algorithm is presented and compared with other minimization schemes. This is an alternative approach to minimizing the functional considered in the paper, called ``lagged diffusivity fixed point iteration'' and denoted by FP. \par A variant of the cell-centered finite difference multigrid method of {\it R. E. Ewing} and {\it J. Shen} [A multigrid algorithm for the cell-centered finite difference scheme. Proc. 6th Copper Mountain Conf. Multigrid Methods, April 1993, NASA Conf. Publ. 3224 (1993)] is implemented for solving the (large and sparse) linear subproblems. In the last section, numerical results are performed. A numerical comparison of three methods applied to minimize the TV-penalized least squares functional is presented: the FP iteration, Newton's method, and the steepest descent method. The results obtained by the three methods are close.
[I.Coroian (Baia Mare)]

MSC 2000:: *65N55 Multigrid methods; domain decomposition (BVP of PDE)
65H10 Systems of nonlinear equations (numerical methods)
65N06 Finite difference methods (BVP of PDE)

Keywords: total variation denoising; total variation penalized least squares functional; lagged diffusivity fixed point iteration; fixed point algorithm; cell-centered finite difference multigrid method; numerical results; numerical comparison; Newton's method; steepest descent method

Cited in: Zbl 1145.92021 Zbl 1131.65057 Zbl 0923.65037

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