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arXiv · 1910.05859

Accelerated Structured Alternating Projections for Robust Spectrally Sparse Signal Recovery

HanQin Cai·Jian-Feng Cai·Tianming Wang·Guojian Yin
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Abstract

Consider a spectrally sparse signal $\boldsymbol{x}$ that consists of $r$ complex sinusoids with or without damping. We study the robust recovery problem for the spectrally sparse signal under the fully observed setting, which is about recovering $\boldsymbol{x}$ and a sparse corruption vector $\boldsymbol{s}$ from their sum $\boldsymbol{z}=\boldsymbol{x}+\boldsymbol{s}$. In this paper, we exploit the low-rank property of the Hankel matrix formed by $\boldsymbol{x}$, and formulate the problem as the robust recovery of a corrupted low-rank Hankel matrix. We develop a highly efficient non-convex algorithm, coined Accelerated Structured Alternating Projections (ASAP). The high computational efficiency and low space complexity of ASAP are achieved by fast computations involving structured matrices, and a subspace projection method for accelerated low-rank approximation. Theoretical recovery guarantee with a linear convergence rate has been established for ASAP, under some mild assumptions on $\boldsymbol{x}$ and $\boldsymbol{s}$. Empirical performance comparisons on both synthetic and real-world data confirm the advantages of ASAP, in terms of computational efficiency and robustness aspects.

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HanQin Cai, Jian-Feng Cai, Tianming Wang, Guojian Yin. 2019-10-13. Accelerated Structured Alternating Projections for Robust Spectrally Sparse Signal Recovery. https://doi.org/10.1109/tsp.2021.3049618

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