Low Rank Activations for Tensor-Based Convolutional Sparse Coding
| Autor: | Laurent Oudre, Julien Audiffren, Pierre Humbert, Nicolas Vayatis |
|---|---|
| Přispěvatelé: | CB - Centre Borelli - UMR 9010 (CB), Service de Santé des Armées-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay)-Université de Paris (UP), Laboratoire de Traitement et Transport de l'Information (L2TI), Université Sorbonne Paris Nord |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Multivariate statistics
Optimization problem Rank (linear algebra) Computer science SIGNAL (programming language) Structure (category theory) 02 engineering and technology Tensor algebra 01 natural sciences Constraint (information theory) 010104 statistics & probability Tensor (intrinsic definition) 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Tensor 0101 mathematics Neural coding Algorithm [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing ComputingMilieux_MISCELLANEOUS |
| Zdroj: | ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2020, Barcelona, France. pp.3252-3256, ⟨10.1109/ICASSP40776.2020.9053402⟩ ICASSP |
| DOI: | 10.1109/ICASSP40776.2020.9053402⟩ |
| Popis: | In this article, we propose to extend the classical Convolutional Sparse Coding model (CSC) to multivariate data by introducing a new tensor CSC model that enforces sparsity and low-rank constraint on the activations. The advantages of this model are threefold. First, by using tensor algebra, this model takes into account the underlying structure of the data. Second, this model allows for complex atoms but enforces fewer activations to decompose the data, resulting in an improved summary (dictionary) and a better reconstruction of the original multivariate signal. Third, the number of parameters to be estimated are greatly reduced by the low-rank constraint. We exhibit the associated optimization problem and propose a framework based on alternating optimization to solve it. Finally, we evaluate it on both synthetic and real data. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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