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

2019/06/24 by Axel Flinth, Flinth, Axel, Frédéric de Gournay +3 · 1 citation
Engineering · Mathematics · #FOS: Electrical engineering #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Optimization and Control (math.OC) #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1906.09919

openalex publication_date 2019/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Atomic Decomposition by Basis Pursuit
• The Sliding Frank-Wolfe Algorithm and its Application to\n Super-Resolution Microscopy
• Exact solutions of infinite dimensional total-variation regularized\n problems

Cited by

• Lazifying point insertion algorithms in spaces of measures

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