Entropy-based algorithms for best basis selection

Adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals. It permits efficient compression of a variety of signals such as sound and images. The predefined libraries of modulated waveforms include orthogonal wavelet-packets, and localized trigonometric functions, have reasonably well controlled time-frequency localization properties. The idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost. The method relies heavily on the remarkable orthogonality properties of the new libraries: all expansions in a given library conserve energy, hence are comparable. Several cost functionals are useful; one of the most attractive is Shannon entropy, which has a geometric interpretation in this context.