Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descent
This work addresses a domain-specific problem in signal processing or data analysis, offering incremental improvements in efficiency for Hankel matrix recovery.
The paper tackles the problem of robust Hankel matrix recovery by removing sparse outliers and filling missing entries from partial observations, proposing the HSNLD algorithm that achieves linear convergence independent of condition number and shows superior performance in experiments.
This paper studies the robust Hankel recovery problem, which simultaneously removes the sparse outliers and fulfills missing entries from the partial observation. We propose a novel non-convex algorithm, coined Hankel Structured Newton-Like Descent (HSNLD), to tackle the robust Hankel recovery problem. HSNLD is highly efficient with linear convergence, and its convergence rate is independent of the condition number of the underlying Hankel matrix. The recovery guarantee has been established under some mild conditions. Numerical experiments on both synthetic and real datasets show the superior performance of HSNLD against state-of-the-art algorithms.