Optimal Non-linear models

ALDROUBI, AKRAM; CABRELLI, CARLOS A.; MOLTER, URSULA M.

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

UNION MATEMATICA ARGENTINA

Lugar: Bahia Blanca; Año: 2009 vol. 49 p. 217 - 225

0041-6932

This paper is a survey about recent results on sparse representations and optimal models in different settings. Given a set of functions, we show that there exists an optimal collection of subspaces minimizing the sum of the square of the distances between each function and its closest subspace in the collection. Further, this collection of subspaces gives the best sparse representation for the given data, in a sense defined later, and provides an optimal model for sampling in a union of subspaces.