Aspects of Total Variation Regularized L 1 Function Approximation

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 L 1 -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.