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Multigrid methods for total variation

25 Feb 2025arXiv:2502.18659links table onlyarchive 2025-07-28

Felipe Guerra, Tuomo Valkonen

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Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging problems, specifically, their dual problems, for which we develop in detail the relevant coarse-grid problems. We demonstrate the performance of our method on total variation denoising and magnetic resonance imaging.

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