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Iterative methods for total variation denoising. (English) Zbl 0847.65083

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.

A variant of the cell-centered finite difference multigrid method of R. E. Ewing and 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.

65N55Multigrid methods; domain decomposition (BVP of PDE)
65H10Systems of nonlinear equations (numerical methods)
65N06Finite difference methods (BVP of PDE)