Multivariate Convolutional Sparse Coding with Low Rank Tensor
arXiv:1908.03367
The paper proposes a multivariate convolutional sparse coding method that uses tensor algebra and CP decomposition to enforce element-wise sparsity and low-rank structure in activation tensors, offering efficient encoding and theoretical links to Kruskal tensor regression.
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.