Flexible Multi-layer Sparse Approximations of Matrices and Applications

Luc Le Magoarou (1) , Rémi Gribonval (1)

1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors. The approach relies on recent advances in non-convex optimization. It is first explained and analyzed in details and then demonstrated experimentally on various problems including dictionary learning for image denoising, and the approximation of large matrices arising in inverse problems.

Mots clés: inverse problems; image denoising; low complexity; dictionary learning; fast algorithms; Sparse representations

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

Luc Le Magoarou, Rémi Gribonval. Flexible Multi-layer Sparse Approximations of Matrices and Applications. 2015. ⟨hal-01167948v1⟩