# Heuristic Parameter Choices for Total Variation Regularization

Elena Resmerita^{*}

We present a numerical study of heuristic (noiselevel-free) regularization parameter choice rules for linear inverse problems with total variation regularization. Such type of regularization is frequently employed in image and signal processing tasks, such as denoising or deblurring. We review convergence results for total variation regularization and propose some generalizations of two well-known heuristic parameter choice rules, the quasi-optimality principle and the Hanke–Raus rules. We investigate the feasibility of these rules using different concepts of convergence such as convergence in the Bregman distance and strict convergence in one and two dimensions by numerical simulation.

Mathematics Subject Classification: 65R30

Keywords: Total variation regularization; heuristic parameter choice rules; strict convergence metric; Bregman distance; quasi-optimality rule; Hanke–Raus rule

Minisymposion: Computational Methods for Inverse Problems/Control Problems in Banach Spaces