Signal representation by generalized nonorthogonal Gaussian wavelet groups using lattice networks

The authors describe a general method for signal representation using nonorthogonal basis functions that are composed of Gaussians. The Gaussians can be combined into groups with predetermined configuration that can approximate any desired basis function. The same configuration at different scales forms a set of self-similar wavelets. The general scheme is demonstrated by representing a natural signal using an arbitrary basis function. The basic methodology is demonstrated by two novel schemes for efficient representation of 1-D and 2-D signals using Gaussian basis functions (BFs). Special methods are required here since the Gaussian functions are nonorthogonal. The first method uses a paradigm of maximum energy reduction interlaced with the A* heuristic search. The second method uses an adaptive lattice system to find the minimum-squared error of the BFs onto the signal, and a lateral-vertical suppression network to select the most efficient representation in terms of data compression