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 to existing minimization schemes. A multigrid method for solving (large, sparse) linear subproblems is investigated. Numerical results are presented for oneand two-dimensional examples; in particular, the algorithm is applied to actual data obtained from confocal microscopy.