Fast and Robust Spectrally Sparse Signal Recovery: A Provable Non-Convex Approach via Robust Low-Rank Hankel Matrix Reconstruction
share
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 constructed from x, and develop an efficient non-convex algorithm, coined Accelerated Alternating Projections for Robust Low-Rank Hankel Matrix Reconstruction (AAP-Hankel). The high computational efficiency and low space complexity of AAP-Hankel 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 AAP-Hankel. Empirical performance comparisons on synthetic and real-world datasets demonstrate the computational advantages of AAP-Hankel, in both efficiency and robustness aspects.
READ FULL TEXT