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Sparse representations in nested non-linear models

Angélique Drémeau 1 Patrick Héas 2 Cédric Herzet 3
2 ASPI - Applications of interacting particle systems to statistics
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
3 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
Abstract : Following recent contributions in non-linear sparse represen-tations, this work focuses on a particular non-linear model, defined as the nested composition of functions. Recalling that most linear sparse representation algorithms can be straight-forwardly extended to non-linear models, we emphasize that their performance highly relies on an efficient computation of the gradient of the objective function. In the particular case of interest, we propose to resort to a well-known technique from the theory of optimal control to estimate the gradient. This computation is then implemented into the optimization procedure proposed byCan es et al., leading to a non-linear extension of it.
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https://hal.inria.fr/hal-01096254
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Submitted on : Wednesday, December 17, 2014 - 10:05:59 AM
Last modification on : Friday, March 19, 2021 - 11:36:02 AM
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Angélique Drémeau, Patrick Héas, Cédric Herzet. Sparse representations in nested non-linear models. IEEE International Conference on Speech, Acoustic and Signal Processing (ICASSP), May 2014, Firenze, Italy. ⟨10.1109/ICASSP.2014.6855147⟩. ⟨hal-01096254⟩

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