1 research outputs found
Accelerated Structured Alternating Projections for Robust Spectrally Sparse Signal Recovery
Consider a spectrally sparse signal that consists of
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 and a sparse corruption vector
from their sum .
In this paper, we exploit the low-rank property of the Hankel matrix formed by
, 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 and . Empirical performance
comparisons on both synthetic and real-world data confirm the advantages of
ASAP, in terms of computational efficiency and robustness aspects