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($\Omega$) 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.

References in corpus (2)

• The Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopy
• The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem

Cited by in corpus (9)

• A generalized conditional gradient method for dynamic inverse problems with optimal transport regularization
• TV-based Reconstruction of Periodic Functions
• Asymptotic linear convergence of fully-corrective generalized conditional gradient methods
• When does OMP achieve exact recovery with continuous dictionaries?
• Adaptive Superresolution in Deconvolution of Sparse Peaks
• On the Uniqueness of Solutions for the Basis Pursuit in the Continuum
• Towards optimal sensor placement for inverse problems in spaces of measures
• Proximal methods for point source localisation
• Localization of point scatterers via sparse optimization on measures