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

• 成果类型: Article
• 署名作者: Flinth, Axel; de Gournay, Frederic; Weiss, Pierre
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Gothenburg; Chalmers University of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01530-0
• 发表日期: 2021
• 页码: 221-257
• 关键词: conditional gradient; Inverse problems; SPARSE; RECOVERY

摘要

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.