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Recently, there has been growing interest in the analysis of spectrograms ofElectroEncephaloGram (EEG), particularly to study the neural correlates of(un)-consciousness during General Anesthesia (GA). Indeed, it has been shownthat order three tensors (channels x frequencies x times) are a natural anduseful representation of these signals. However this encoding entailssignificant difficulties, especially for convolutional sparse coding (CSC) asexisting methods do not take advantage of the particularities of tensorrepresentation, such as rank structures, and are vulnerable to the high levelof noise and perturbations that are inherent to EEG during medical acts. Toaddress this issue, in this paper we introduce a new CSC model, named KruskalCSC (K-CSC), that uses the Kruskal decomposition of the activation tensors toleverage the intrinsic low rank nature of these representations in order toextract relevant and interpretable encodings. Our main contribution, TC-FISTA,uses multiple tools to efficiently solve the resulting optimization problemdespite the increasing complexity induced by the tensor representation. We thenevaluate TC-FISTA on both synthetic dataset and real EEG recorded during GA.The results show that TC-FISTA is robust to noise and perturbations, resultingin accurate, sparse and interpretable encoding of the signals.

Tensor Convolutional Sparse Coding with Low-Rank activations, an application to EEG analysis