Matching pursuit shrinkage in Hilbert spaces

In this paper, we study a variant of the matching pursuit named matching pursuit shrinkage. Similar to the matching pursuit it seeks for an approximation of a datum living in a Hilbert space by a sparse linear expansion in a countable 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 analyze the link between the shrinkage function used by the algorithm and the fact that the result belongs to l2, l1 and l0 space. Experimental results are also reported to show the potential application of the proposed algorithm.