Matching Pursuit Shrinkage in Hilbert Spaces

Tieyong Zeng (1) , François Malgouyres (2)

1 HKBU - Hong Kong Baptist University
2 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper, we study a variant of the Matching Pursuit named Matching Pursuit Shrinkage. Similarly to the Matching Pursuit it seeks for an approximation of a datum living in a Hilbert space by a sparse linear expansion in an enumerable set of atoms. The difference with the usual Matching Pursuit is that, once an atom has been selected, we do not erase all the information along the direction of this atom. Doing so, we can evolve slowly along that direction. The goal is to attenuate the negative impact of bad atom selections. We analyse the link between the shrinkage function used by the algorithm and the fact that the result belongs to an lp space.

Mots clés: Dictionary; Matching pursuit; Shrinkage; Sparse representation

Domaines: Optimisation et contrôle [math.OC]

Tieyong Zeng, François Malgouyres. Matching Pursuit Shrinkage in Hilbert Spaces. Signal Processing, 2011, 91 (12), pp.2754-2766. ⟨10.1016/j.sigpro.2011.04.010⟩. ⟨hal-00638380⟩