On the linear convergence rates of exchange and continuous methods for total variation minimization
Artikel i vetenskaplig tidskrift, 2020

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

Semi-infinite programming

Superresolution

Författare

Axel Flinth

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

Frederic de Gournay

Université de Toulouse

Pierre Weiss

Université de Toulouse

Mathematical Programming, Series B

0025-5610 (ISSN)

Vol. In Press

Ämneskategorier

Beräkningsmatematik

Reglerteknik

Matematisk analys

DOI

10.1007/s10107-020-01530-0

Mer information

Senast uppdaterat

2020-09-17