Experiments on Non-Orthogonal Signal Representation

Abstract

The problem of non-orthogonal signal representation we consider here consists of expressing the signal as a linear superposition of non-orthogonal waveforms. Such waveforms are selected from a set of functions, in general redundant, which is called a dictionary. The techniques we discuss to address the problem are in the line of the adaptive matching pursuit methods. Potential advantages, arising from the freedom to decide on the dictionary, are illustrated by considering dictionaries of different nature. Further potential advantages, arising simply by relaxing the orthogonality condition, are illustrated by introducing a non-orthogonal set of wavelets which originates from the orthogonal Haar basis.