Abstract
Wavelet transforms have in the past decade found a home in a variety of signal processing applications, including data compression, de-noising, and feature detection. Compactly-supported orthonormal (ON) wavelets in particular are desirable due to properties such as good frequency and time localization, efficient analysis and synthesis computation via quadrature mirror filter banks, and the existence of a complete parametrization. The methods for designing an ON wavelet appropriate for a particular application range from picking a wavelet from one of the (small number of) well-known wavelet families, such as the Daubechies, to the computationally expensive full parameter optimizations of an objective function over the space of all compactly-supported ON wavelets. In this talk we suggest an approach that represents a compromise between the above methods, in which we assemble comprehensive collections of smooth wavelet shapes from the continuum of ON wavelets, allowing ON wavelet matching to be performed by simple library selection.

In the library construction algorithm presented, we perform a non-uniform sampling of the N-dimensional spaces of compactly-supported ON wavelets by solving a chain of successive optimization sub-problems to yield libraries of various sizes. We evaluate library performance by applying constructed 1D--5D libraries to a variety of natural and man-made signals in an entropy-based wavelet selection algorithm, and compare library performance to a full parameter optimization and to a Daubechies wavelet decomposition. The results suggest that libraries of reasonable size (e.g., 32 in 4D) can represent a viable alternative to a full parameter optimization, achieving a compromise between optimality and efficiency.