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We analyze an exchange algorithm for the numerical solution total-variationregularized inverse problems over the space M($\Omega$) of Radon measures on asubset $\Omega$ of R d. Our main result states that under some regularityconditions, the method eventually converges linearly. Additionally, we provethat continuously optimizing the amplitudes of positions of the target measurewill succeed at a linear rate with a good initialization. Finally, we proposeto combine the two approaches into an alternating method and discuss thecomparative advantages of this approach.

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