A Proximal based strategy for solving Discrete Mumford-Shah and Ambrosio-Tortorelli models

This work is dedicated to joint image restoration and contour detection considering the Ambrosio-Tortorelli functional. Two proximal alternating minimization schemes with convergence guarantees are provided, PALM-AT and SL-PAM-AT, as well as closed-form expressions of the involved proximity operators. A thorough numerical study is conducted in order to evaluate the performance of both numerical schemes as well as comparisons to a more standard ℓ 1-based discrete Mumford-Shah functional