Tree structured local basis selection using genetic algorithms

A genetic algorithm for the selection of wavelet packet bases for various tasks is proposed. We introduce a transform operator to convert the constrained combinatorial basis selection problem to an unconstrained numerical optimization problem. This algorithm offers a great deal of flexibility for the selection of wavelet packet bases in terms of different criteria for different tasks. To demonstrate the performance of this algorithm, we present two examples respectively for signal approximation and signal classification. Although the algorithm is described with wavelet packets, it can also be used for the selection of other tree structured local bases, such as local trigonometric bases.