Sampling in a Union of Frame Generated Subspaces.

MAGALÍ ANASTASIO; CARLOS CABRELLI

Sampling Theory in Signal and Image Processing

Sampling Publisher

Año: 2009 vol. 8 p. 261 - 286

1530-6429

A new paradigm in sampling theory has been developed recently by Lu and Do.In this new approach the classical linear model is replaced by a non-linear, but structuredmodel consisting of a union of subspaces. This is the natural approach for the new theory ofcompressed sampling, representation of sparse signals and signals with finiterate of innovation. In this article we extend the theory of Lu and Do,for the case that the subspaces in the union are shift-invariant spaces. We describe  the subspaces by means of frame generators instead of orthonormal bases.We show that, the one to one and stability  conditions for  the sampling operator, are valid for this more general case.