From Event: SPIE Optical Engineering + Applications, 2017
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.
Jian-Feng Cai, "Fast and provable algorithms for spectrally sparse signal reconstruction via low-rank Hankel matrix completion (Conference Presentation)," Proc. SPIE 10394, Wavelets and Sparsity XVII, 103941K (Presented at SPIE Optical Engineering + Applications: August 09, 2017; Published: 26 September 2017); https://doi.org/10.1117/12.2272919.5589093915001.
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