On the representation of functions with Gaussian wave packets (Q421207)

The authors introduce Gaussian wave packets in pursuit of representation of functions in which the representation is invariant under translation, modulation, scale, rotation and anisotropic dilation. Properties of continuous and discrete representations are discussed. For the discrete two dimensional case, the authors develop fast algorithms for the application of the analysis and synthesis operators. A main objective for using Gaussian wave packets is to obtain a sparse approximation of functions. They also introduce sparse methods for highly redundant representations that employ some of the analytic properties of Gaussian wave packet for gaining computational efficiency.