Chasing butterflies: In search of efficient dictionaries

Luc Le Magoarou 1 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 : Dictionary learning aims at finding a frame (called dictionary) in which training data admits a sparse representation. Traditional dictionary learning is limited to relatively small-scale problems, because dense matrices associated to high-dimensional dictionaries can be costly to manipulate, both at the learning stage and when using this dictionary for tasks such as sparse coding. In this paper, inspired by usual fast transforms, we consider a dictionary structure allowing cheaper manipulation, and we propose a learning algorithm imposing this structure. The approach is demonstrated experimentally with the factorization of the Hadamard matrix and on image denoising.
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Luc Le Magoarou, Rémi Gribonval. Chasing butterflies: In search of efficient dictionaries. International Conference on Acoustics, Speech and Signal Processing (ICASSP), Apr 2015, Brisbane, Australia. ⟨10.1109/ICASSP.2015.7178579⟩. ⟨hal-01104696v2⟩

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