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Iterative Methods for Total Variation Denoising

Total variation (TV) methods are very effective for recovering “blocky,” possibly discontinuous, images from noisy data. A fixed point algorithm for minimizing a TV penalized least squares functional is presented and compared with existing minimization schemes. A variant of the cell-centered finite difference multigrid method of Ewing and Shen is implemented for solving the (large, sparse) linear subproblems. Numerical results are presented for one- and two-dimensional examples; in particular, the algorithm is applied to actual data obtained from confocal microscopy.