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Near Minimax Line Spectral Estimation

By Gongguo Tang, Badri Narayan Bhaskar and Benjamin Recht

Abstract

This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery problem with a continuous, infinite dictionary. We show how to compute the estimator via semidefinite programming and provide guarantees on its mean-square error rate. We derive a complementary minimax lower bound on this estimation rate, demonstrating that our approach nearly achieves the best possible estimation error. Furthermore, we establish bounds on how well our estimator localizes the frequencies in the signal, showing that the localization error tends to zero as the number of samples grows. We verify our theoretical results in an array of numerical experiments, demonstrating that the semidefinite programming approach outperforms two classical spectral estimation techniques

Topics: Approximate support recovery, Atomic norm, Compressive sensing, Infinite dictionary, Line spectral estimation, Minimax rate, Sparsity, Stable recovery, Superresolution
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.307.6884
Provided by: CiteSeerX
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