Evolutionary-based methods for adaptive signal representation

In spite of the good decomposition properties offered by wavelet-packet bases, it is well known that more flexible decompositions are required. On the other hand, one well known disadvantage of wavelet transforms is the lack of shift invariance. We propose the use of an evolutionary approach as the main tool for searching adaptive signal representations. The algorithm generates a population of solutions based on basis expansions of multi-filter, time-shifted, wavelet-packet libraries. The approach of organizing libraries of bases as a tree has been extended to construct a joint tree, to guide the process of generating shifted wavelet-packet transforms. The standard time-frequency diagram has been extended to enable the representation of shifted packet basis. We show that the evolutionary approach may be used as a flexible tool for obtaining signal representations in overcomplete dictionaries. (C) 2001 Elsevier Science B.V. All rights reserved.