Accelerated Structured Alternating Projections for Robust Spectrally Sparse Signal Recovery

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...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on signal processing 2021, Vol.69, p.809-821
Main Authors: Cai, HanQin, Cai, Jian-Feng, Wang, Tianming, Yin, Guojian
Format: Article
Language:English
Subjects:
Acceleration
Algorithms
Alternating projections
Approximation
Complexity
Computational efficiency
Computing time
Convergence
Damping
Hankel matrices
low-rank hankel matrix recovery
Matrix decomposition
Minimization
Nuclear magnetic resonance
Performance assessment
Recovery
Robustness (mathematics)
Signal reconstruction
Sine waves
Sparse matrices
sparse outliers
Spectra
spectrally sparse signal
Structured matrices
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 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 \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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2021.3049618