Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descent

TL;DR

This paper introduces HSNLD, a fast non-convex algorithm for robust Hankel matrix recovery that effectively handles outliers and missing data, with convergence independent of matrix condition number.

Contribution

The paper presents a novel structured Newton-like descent algorithm for Hankel recovery, offering linear convergence and robustness against ill-conditioning.

Findings

HSNLD outperforms existing algorithms in synthetic data tests.

The method achieves accurate recovery with fewer iterations.

Convergence rate is independent of the Hankel matrix's condition number.

Abstract

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.