A new approach to the optimal choice of a wavelet for signal representation

Abstract

A new optimization approach for the design of discrete orthogonal wavelets of support less than or equal to some given integer that leads to the best approximation to a given finite support signal up to a desired scale is discussed. A new global hybrid optimization strategy, involving the combination of simulated annealing and Hooke-Jeeves algorithms is developed and applied to minimize certain cost functions defined by an error function between original and approximated signals and wavelet admissibility conditions. The method converts the constrained minimization over the parameters that define discrete finite support orthogonal wavelets into an unconstrained one and can be implemented much faster than any other algorithms presented in literature.