Atomic decomposition with evolutionary pursuit

An atomic decomposition of a signal is an expression of the signal as a superposition of a parametric collection of waveforms. Basis expansions, especially orthogonal cases such as Fourier and wavelet bases, are the most commonly used atomic models. To meet the demands of time-frequency phenomena, signals can be modeled using overcomplete dictionaries. In this paper we propose a new methodology to optimize redundant, non-linear approximations from several dictionaries. The methodology, referred to as evolutionary pursuit, relies on evolutionary computation techniques to select well-adapted approximations. The proposed model may be regarded as a stochastic optimization approach to the problem of searching for an optimal composition of dictionary elements. The main motivation is the application of this model to construct adaptive atomic analyzers, based on overcomplete but sparse representations. A test environment is proposed to assess recognition of time-frequency atoms in signal spaces. (C) 2002 Elsevier Science (USA). All rights reserved.