Multivariate Convolutional Sparse Coding with Low Rank Tensor

Abstract : This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model achieves a significantly more efficient encoding of the multivariate signal-particularly in the high order/ dimension setting-resulting in better performance. We prove that our model is closely related to the Kruskal tensor regression problem, offering interesting theoretical guarantees to our setting. Furthermore, we provide an efficient optimization algorithm based on alternating optimization to solve this model. Finally, we evaluate our algorithm with a large range of experiments, highlighting its advantages and limitations.
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Pré-publication, Document de travail
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https://hal.archives-ouvertes.fr/hal-02196166
Contributeur : Pierre Humbert <>
Soumis le : vendredi 9 août 2019 - 08:24:19
Dernière modification le : dimanche 11 août 2019 - 01:09:45

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  • HAL Id : hal-02196166, version 1
  • ARXIV : 1908.03367

Citation

Pierre Humbert, Julien Audiffren, Laurent Oudre, Nicolas Vayatis. Multivariate Convolutional Sparse Coding with Low Rank Tensor. 2019. ⟨hal-02196166⟩

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