Sparse Representation in Fourier and Local Bases Using ProSparse: A Probabilistic Analysis

Citation:

Y. M. Lu, J. Oñativia, and P. L. Dragotti, “Sparse Representation in Fourier and Local Bases Using ProSparse: A Probabilistic Analysis,” IEEE Transactions on Information Theory, In Press.

Abstract:

Finding the sparse representation of a signal in an overcomplete dictionary has attracted a lot of attention over the past years. This paper studies ProSparse, a new polynomial complexity algorithm that solves the sparse representation problem when the underlying dictionary is the union of a Vandermonde matrix and a banded matrix. Unlike our previous work which establishes deterministic (worst-case) sparsity bounds for ProSparse to succeed, this paper presents a probabilistic average-case analysis of the algorithm. Based on a generating-function approach, closed-form expressions for the exact success probabilities of ProSparse are given. The success probabilities are also analyzed in the high-dimensional regime. This asymptotic analysis characterizes a sharp phase transition phenomenon regarding the performance of the algorithm.

arXiv:1611.07971 [cs.IT]

Last updated on 12/06/2017