Tensor Convolutional Dictionary Learning With CP Low-Rank Activations

In this paper, we propose to extend the standard Convolutional Dictionary Learning problem a tensor representation where activations are constrained be “low-rank” through Canonical Polyadic decomposition. We show that additional constraint increases robustness of CDL with respect noise and improve interpretability final results. addition, discuss in detail advantages introduce two algorithms, based on ADMM or FISTA, efficiently solve problem. by exploiting low rank property activations, they achieve lower complexity than main algorithms. Finally, evaluate our approach wide range experiments, highlighting modularity tensorial low-rank formulation.