Iterative Methods for Total Variation Denoising

Abstract

. 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. Key words. Total Variation, denoising, image reconstruction, multigrid methods, confocal microscopy, fixed point iteration. 1. Introduction. The problem of denoising, or estimating an underlying function from error-contaminated observations, occurs in a number of important applications, particularly in probability density estimation and image reconstruction. Consider the model equation z = u + ffl; (1.1) where u represents the desired true solution, ffl represents error, and z represents t...

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