On the linear convergence rates of exchange and continuous methods for total variation minimization - Archive ouverte HAL Access content directly
Journal Articles Mathematical Programming Year : 2020

On the linear convergence rates of exchange and continuous methods for total variation minimization

Abstract

We analyze an exchange algorithm for the numerical solution total-variation regularized inverse problems over the space M(Ω) of Radon measures on a subset Ω 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.
Fichier principal
Vignette du fichier
Linear_CV_Rate_Exchange_Flinth_Weiss_deGournay_2019.pdf (1.86 Mo) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-02136598 , version 1 (20-06-2019)
hal-02136598 , version 2 (24-07-2020)

Identifiers

Cite

Axel Flinth, Frédéric de Gournay, Pierre Weiss. On the linear convergence rates of exchange and continuous methods for total variation minimization. Mathematical Programming, 2020, ⟨10.1007/s10107-020-01530-0⟩. ⟨hal-02136598v2⟩
128 View
186 Download

Altmetric

Share

Gmail Facebook X LinkedIn More