Optimal subset selection for adaptive signal representation

A number of over-complete dictionaries such as wavelets, wave packets, cosine packets etc. have been proposed. Signal decomposition on such over-complete dictionaries is not unique. This non-uniqueness provides us with the opportunity to adapt the signal representation to the signal. The adaptation is based on sparsity, resolution and stability of the signal representation. The computational complexity of the adaptation algorithm is of primary concern. We propose a new approach for identifying the sparsest representation of a given signal in terms of a given over-complete dictionary. We assume that the data vector can be exactly represented in terms of a known number of vectors