Orateur
Description
The discrete Mumford–Shah formulation leads to a challenging nonconvex optimization problem involving the joint minimization of two variables, typically addressed through alternating minimization methods such as PALM and its variants.
In this talk, I will present a connection between the discrete Mumford–Shah formulation and a class of composite minimization problems for which majorization–minimization algorithms have recently been developed. Under assumptions satisfied by the main applications of interest, I will show that these two formulations are equivalent, offering a different perspective on Mumford–Shah-type optimization problems.
I will then discuss numerical comparisons between the resulting majorization–minimization approach and PALM-based methods in two applications: Modulo Sampling, a nonlinear signal reconstruction problem, and image contour detection from noisy data.