Signal adaptive wavelet design using genetic algorithms

While discrete wavelet transforms offer a powerful combination of computational efficiency and compact representation for a broad range of signals, they are often designed without any prior knowledge of the signals under analysis. In this paper, we provide a methodology for constructing customized wavelets and multirate filterbanks through the application of a generalized cost function on available training data. In particular, we design wavelets that provide maximal discrimination between several signal classes, with the cost function directly tied to classification performance. Since the relationship between the filter coefficients and correct classification may be exceedingly complicated, the optimization is performed using a genetic algorithm. The multirate filterbank is implemented in a lattice-type structure, know as lifting, which facilitates the incorporation of constraints on the search space. In addition to demonstrating the successful design of signal-adaptive wavelets, this paper validates the use of genetic algorithms as a powerful class of tools for complex system optimization. The method is applied to acoustic scattering data with classification performance evaluated in relation to both non-adaptive biorthogonal wavelets and signal-adaptive wavelets based on linear predictive constraints.