Learning optimal wavelets from overcomplete representations

Abstract

Efficient and robust representation of signals has been the focus of a number of areas of research. Wavelets represent one such representation scheme that enjoys desirable qualitites such as time-frequency localization. Once the Mother wavelet has been selected, other wavelets can be generated as translated and dilated versions of the Mother wavelet in the 1D case. In the 2D case tensor product of two 1D wavelets is the most often used transform. Over complete representation of wavelets has proved to be of great advantage, both in sparse coding of complex scenes and multi-media data compression. On the other hand over completeness raises a number of technical difficulties for robust computation and systematic generalization of constructions beyond their original application domains.