期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 69, 期 -, 页码 809-821出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2021.3049618
关键词
Sparse matrices; Acceleration; Nuclear magnetic resonance; Damping; Convergence; Minimization; Matrix decomposition; Alternating projections; low-rank hankel matrix recovery; sparse outliers; spectrally sparse signal
资金
- Hong Kong Research Grant Council (HKRGC) [16306317, 16309219]
This paper investigates the robust recovery problem for spectrally sparse signals and proposes a highly efficient nonconvex algorithm called ASAP. By utilizing the low-rank property of the Hankel matrix and employing fast computations with structured matrices, ASAP achieves high computational efficiency and low space complexity for robust recovery of corrupted low-rank matrices. The theoretical recovery guarantee with a linear convergence rate and empirical performance comparisons demonstrate the advantages of ASAP in terms of computational efficiency and robustness.
Consider a spectrally sparse signal 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 x and a sparse corruption vector s from their sum z = x + s. In this paper, we exploit the low-rank property of the Hankel matrix formed by x, and formulate the problem as the robust recovery of a corrupted low-rank Hankel matrix. We develop a highly efficient nonconvex 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 x and 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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