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

arXiv: https://arxiv.org/abs/1906.09919 · HTML: https://mlsanity.com/paper/1906.09919/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2019.

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## Abstract (arXiv)

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.