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.

翻译：本文研究鲁棒Hankel矩阵恢复问题，旨在从部分观测数据中同时剔除稀疏异常值并补全缺失项。我们提出一种新型非凸算法——Hankel结构化牛顿类下降法（HSNLD），用以解决鲁棒Hankel恢复问题。HSNLD具有线性收敛的高效特性，且其收敛速率与底层Hankel矩阵的条件数无关。在若干温和条件下，我们建立了该算法的恢复性能保证。在合成数据集和真实数据集上的数值实验表明，HSNLD相较于现有最优算法具有显著优越性。