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Characterizing the maximum parameter of the total-variation denoising through the pseudo-inverse of the divergence

Abstract : We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated in details for the total-variation. Though, it is of importance when tuning the regularization parameter as it allows fixing an upper-bound on the grid for which the optimal parameter is sought. We establish a closed form expression for the one-dimensional case, as well as an upper-bound for the two-dimensional case, that appears reasonably tight in practice. This problem is directly linked to the computation of the pseudo-inverse of the divergence, which can be quickly obtained by performing convolutions in the Fourier domain.
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https://hal.archives-ouvertes.fr/hal-01412059
Contributor : Charles-Alban Deledalle <>
Submitted on : Wednesday, December 7, 2016 - 7:37:46 PM
Last modification on : Monday, May 4, 2020 - 11:04:04 AM
Document(s) archivé(s) le : Tuesday, March 21, 2017 - 1:26:53 PM

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  • HAL Id : hal-01412059, version 1
  • ARXIV : 1612.03080

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Charles-Alban Deledalle, Nicolas Papadakis, Joseph Salmon, Samuel Vaiter. Characterizing the maximum parameter of the total-variation denoising through the pseudo-inverse of the divergence. SPARS 2017 (Signal Processing with Adaptive Sparse Structured Representations), Jun 2017, Lisbon, Portugal. ⟨hal-01412059⟩

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