Characterizing the maximum parameter of the total-variation denoising through the pseudo-inverse of the divergence - Archive ouverte HAL
Conference Papers Year : 2017

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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Dates and versions

hal-01412059 , version 1 (07-12-2016)

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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. Signal Processing with Adaptive Sparse Structured Representations (SPARS'17), Jun 2017, Lisbon, Portugal. ⟨hal-01412059⟩
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