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Proceedings Paper

A fast algorithm for reconstruction of spectrally sparse signals in super-resolution
Author(s): Jian-Feng Cai; Suhui Liu; Weiyu Xu
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Paper Abstract

We propose a fast algorithm to reconstruct spectrally sparse signals from a small number of randomly observed time domain samples. Different from conventional compressed sensing where frequencies are discretized, we consider the super-resolution case where the frequencies can be any values in the normalized continuous frequency domain [0; 1). We first convert our signal recovery problem into a low rank Hankel matrix completion problem, for which we then propose an efficient feasible point algorithm named projected Wirtinger gradient algorithm(PWGA). The algorithm can be further accelerated by a scheme inspired by the fast iterative shrinkage-thresholding algorithm (FISTA). Numerical experiments are provided to illustrate the effectiveness of our proposed algorithm. Different from earlier approaches, our algorithm can solve problems of large scale efficiently.

Paper Details

Date Published: 24 August 2015
PDF: 7 pages
Proc. SPIE 9597, Wavelets and Sparsity XVI, 95970A (24 August 2015); doi: 10.1117/12.2188489
Show Author Affiliations
Jian-Feng Cai, The Univ. of Iowa (United States)
Suhui Liu, The Univ. of Iowa (United States)
Weiyu Xu, The Univ. of Iowa (United States)

Published in SPIE Proceedings Vol. 9597:
Wavelets and Sparsity XVI
Manos Papadakis; Vivek K. Goyal; Dimitri Van De Ville, Editor(s)

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