Learning Dictionaries as Sums of Kronecker Products

Cassio Fraga Dantas (1) , Rémi Gribonval (1) , Renato R Lopes (2) , Michele N da Costa (2)

1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
2 DSPCom - Digital Signal Processing and Communications laboratory [Campinas]

The choice of an appropriate dictionary is a crucial step in the sparse representation of a given class of signals. Traditional dictionary learning techniques generally lead to unstructured dictionaries which are costly to deploy and do not scale well to higher dimensional signals. In order to overcome such limitation, we propose a learning algorithm that constrains the dictionary to be a sum of Kronecker products of smaller sub-dictionaries. A special case of the proposed structure is the widespread separable dictionary. This approach, named SuKro, is evaluated experimentally on an image denoising application.

Mots clés: Dictionary Learning; Kronecker product; Nuclear norm penalty; Image denoising

Domaines: Traitement du signal et de l'image [eess.SP]

Cassio Fraga Dantas, Rémi Gribonval, Renato R Lopes, Michele N da Costa. Learning Dictionaries as Sums of Kronecker Products. SPARS 2017 - Signal Processing with Adaptive Sparse Structured Representations workshop, Jun 2017, Lisbon, Portugal. . ⟨hal-01514044⟩