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arXiv · 1611.07971

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

Yue M. Lu·Jon Oñativia·Pier Luigi Dragotti
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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.

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Yue M. Lu, Jon Oñativia, Pier Luigi Dragotti. 2016-11-23. Sparse Representation in Fourier and Local Bases Using ProSparse: A Probabilistic Analysis. https://arxiv.org/abs/1611.07971

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