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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

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