Approximations with evolutionary pursuit

In recent years there has been growing interest in nonlinear signal approximations and atomic decomposition of functions. We propose a new approach to optimize overcomplete decompositions from several dictionaries. The methodology, referred to as evolutionary pursuit, relies on evolutionary computation techniques to optimize well-adapted approximations. Searching for the best approximation for a given signal is viewed as a stochastic optimization process. Stochastic perturbation parameters are introduced to improve both stability and robustness in the process of combining components from multiple dictionaries. The utility of these parameters in the analysis is justified in terms of the theory of frames, and tested in applications. The proposed method is applied to a collection of representative experimental tests, and the results compared with equivalent results from alternative approaches.