A fast algorithm for reconstruction of spectrally sparse signals in super-resolution

Jian-Feng Cai; Suhui Liu; Weiyu Xu

doi:10.1117/12.2188489

24 August 2015 A fast algorithm for reconstruction of spectrally sparse signals in super-resolution

Jian-Feng Cai, Suhui Liu, Weiyu Xu

Proceedings Volume 9597, Wavelets and Sparsity XVI; 95970A (2015) https://doi.org/10.1117/12.2188489
Event: SPIE Optical Engineering + Applications, 2015, San Diego, California, United States

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.

Citation Download Citation

Jian-Feng Cai, Suhui Liu, and Weiyu Xu "A fast algorithm for reconstruction of spectrally sparse signals in super-resolution", Proc. SPIE 9597, Wavelets and Sparsity XVI, 95970A (24 August 2015); https://doi.org/10.1117/12.2188489

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