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arXiv · 1206.5882

Exact Recovery of Sparsely-Used Dictionaries

Daniel A. Spielman·Huan Wang·John Wright
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Abstract

We consider the problem of learning sparsely used dictionaries with an arbitrary square dictionary and a random, sparse coefficient matrix. We prove that $O (n \log n)$ samples are sufficient to uniquely determine the coefficient matrix. Based on this proof, we design a polynomial-time algorithm, called Exact Recovery of Sparsely-Used Dictionaries (ER-SpUD), and prove that it probably recovers the dictionary and coefficient matrix when the coefficient matrix is sufficiently sparse. Simulation results show that ER-SpUD reveals the true dictionary as well as the coefficients with probability higher than many state-of-the-art algorithms.

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Daniel A. Spielman, Huan Wang, John Wright. 2012-06-26. Exact Recovery of Sparsely-Used Dictionaries. https://arxiv.org/abs/1206.5882

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