On the linear convergence rates of exchange and continuous methods for total variation minimization
Journal article, 2021

We analyze an exchange algorithm for the numerical solution total-variation regularized inverse problems over the space M(Omega) of Radon measures on a subset Omega of R-d. Our main result states that under some regularity conditions, the method eventually converges linearly. Additionally, we prove that continuously optimizing the amplitudes of positions of the target measure will succeed at a linear rate with a good initialization. Finally, we propose to combine the two approaches into an alternating method and discuss the comparative advantages of this approach.

Inverse problems

Total variation minimization

Superresolution

Semi-infinite programming

Author

Axel Flinth

Chalmers, Mathematical Sciences, Analysis and Probability Theory

University of Gothenburg

Frederic de Gournay

University of Toulouse

Pierre Weiss

University of Toulouse

Mathematical Programming

0025-5610 (ISSN) 1436-4646 (eISSN)

Vol. 190 1-2 221-257

Subject Categories

Computational Mathematics

Control Engineering

Mathematical Analysis

DOI

10.1007/s10107-020-01530-0

More information

Latest update

7/6/2023 1