Aspects of Total Variation RegularizedL1Function Approximation

Abstract

The total variation--based image denoising model of Rudin, Osher, and Fatemi [Phys. D, 60, (1992), pp. 259--268] has been generalized and modified in many ways in the literature; one of these modifications is to use the L¹ -norm as the fidelity term. We study the interesting consequences of this modification, especially from the point of view of geometric properties of its solutions. It turns out to have interesting new implications for data-driven scale selection and multiscale image decomposition.