Sparse Representation in Fourier and Local Bases Using ProSparse: A Probabilistic Analysis
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.
Cite
@article{arxiv.1611.07971,
title = {Sparse Representation in Fourier and Local Bases Using ProSparse: A Probabilistic Analysis},
author = {Yue M. Lu and Jon Oñativia and Pier Luigi Dragotti},
journal= {arXiv preprint arXiv:1611.07971},
year = {2017}
}