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Proceedings Paper

Fast and provable algorithms for spectrally sparse signal reconstruction via low-rank Hankel matrix completion (Conference Presentation)
Author(s): Jian-Feng Cai

Paper Abstract

A spectrally sparse signal of order r is a mixture of r damped or undamped complex sinusoids. This talk investigates the problem of reconstructing spectrally sparse signals from a random subset of n regular time domain samples, which can be reformulated as a low rank Hankel matrix completion problem. We introduce an iterative hard thresholding (IHT) algorithm and a fast iterative hard thresholding (FIHT) algorithm for efficient reconstruction of spectrally sparse signals via low rank Hankel matrix completion. Theoretical recovery guarantees have been established for FIHT, showing that O(r^2log^2(n)) number of samples are sufficient for exact recovery with high probability. Empirical performance comparisons establish significant computational advantages for IHT and FIHT. In particular, numerical simulations on 3D arrays demonstrate the capability of FIHT on handling large and high-dimensional real data.

Paper Details

Date Published: 26 September 2017
Proc. SPIE 10394, Wavelets and Sparsity XVII, 103941K (26 September 2017); doi: 10.1117/12.2272919
Show Author Affiliations
Jian-Feng Cai, Hong Kong Univ. of Science and Technology (Hong Kong, China)

Published in SPIE Proceedings Vol. 10394:
Wavelets and Sparsity XVII
Yue M. Lu; Dimitri Van De Ville; Manos Papadakis, Editor(s)

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