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Characterizing the maximum parameter of the total-variation denoising through the pseudo-inverse of the divergence
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DELEDALLE, Charles-Alban | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PAPADAKIS, Nicolas | |
| hal.structure.identifier | Laboratoire Traitement et Communication de l'Information [LTCI] | |
| dc.contributor.author | SALMON, Joseph | |
| hal.structure.identifier | Institut de Mathématiques de Bourgogne [Dijon] [IMB] | |
| dc.contributor.author | VAITER, Samuel | |
| dc.date.created | 2016-12-07 | |
| dc.date.issued | 2017 | |
| dc.date.conference | 2017-06-05 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.subject.en | Pseudo-inverse | |
| dc.subject.en | Divergence | |
| dc.subject.en | Regularization | |
| dc.subject.en | Total-variation | |
| dc.title.en | Characterizing the maximum parameter of the total-variation denoising through the pseudo-inverse of the divergence | |
| dc.type | Communication dans un congrès | |
| dc.subject.hal | Informatique [cs]/Traitement des images | |
| dc.subject.hal | Statistiques [stat]/Théorie [stat.TH] | |
| dc.subject.hal | Informatique [cs]/Traitement du signal et de l'image | |
| dc.identifier.arxiv | 1612.03080 | |
| bordeaux.conference.title | Signal Processing with Adaptive Sparse Structured Representations (SPARS'17) | |
| bordeaux.country | PT | |
| bordeaux.conference.city | Lisbon | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01412059 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | oui | |
| hal.conference.end | 2017-06-08 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01412059v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2017&rft.au=DELEDALLE,%20Charles-Alban&PAPADAKIS,%20Nicolas&SALMON,%20Joseph&VAITER,%20Samuel&rft.genre=unknown |
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