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Learning fast dictionaries for sparse representations using low-rank tensor decompositions

Cassio Fraga Dantas 1 Jérémy E Cohen 2 Rémi Gribonval 1 
1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : A new dictionary learning model is introduced where the dictionary matrix is constrained as a sum of R Kronecker products of K terms. It offers a more compact representation and requires fewer training data than the general dictionary learning model, while generalizing Tucker dictionary learning. The proposed Higher Order Sum of Kroneckers model can be computed by merging dictionary learning approaches with the tensor Canonic Polyadic Decomposition. Experiments on image denoising illustrate the advantages of the proposed approach.
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Submitted on : Friday, April 27, 2018 - 5:25:51 PM
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Cassio Fraga Dantas, Jérémy E Cohen, Rémi Gribonval. Learning fast dictionaries for sparse representations using low-rank tensor decompositions. LVA/ICA 2018 - 14th International Conference on Latent Variable Analysis and Signal Separation, Jul 2018, Guildford, United Kingdom. pp.456-466, ⟨10.1007/978-3-319-93764-9_42⟩. ⟨hal-01709343v2⟩

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