Sparse Linear Representation

This paper studies the question of how well a signal can be reprsented by a sparse linear combination of reference signals from an overcomplete dictionary. When the dictionary size is exponential in the dimension of signal, then the exact characterization of the optimal distortion is given as a function of the dictionary size exponent and the number of reference signals for the linear representation. Roughly speaking, every signal is sparse if the dictionary size is exponentially large, no matter how small the exponent is. Furthermore, an iterative method similar to matching pursuit that successively finds the best reference signal at each stage gives asymptotically optimal representations. This method is essentially equivalent to successive refinement for multiple descriptions and provides a simple alternative proof of the successive refinability of white Gaussian sources.Comment: 5 pages, to appear in proc. IEEE ISIT, June 200

Sparse model identification using a forward orthogonal regression algorithm aided by mutual information

A sparse representation, with satisfactory approximation accuracy, is usually desirable in any nonlinear system identification and signal processing problem. A new forward orthogonal regression algorithm, with mutual information interference, is proposed for sparse model selection and parameter estimation. The new algorithm can be used to construct parsimonious linear-in-the-parameters models