论文标题
结构化梯度下降，用于快速稳健的低级Hankel基质完成
Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completion
论文作者
论文摘要
我们研究了低级别Hankel矩阵的强大矩阵完成问题，该问题检测到极端异常值造成的稀疏腐败，而我们试图从部分观察中恢复原始的Hankel矩阵。在本文中，我们探讨了方便的Hankel结构，并提出了一种新型的非凸算法，即Hankel结构化梯度下降（HSGD），以解决强大的Hankel矩阵完成问题。与最先进的工厂相比，HSGD具有高度计算和样品有效的效率。在某些轻度假设下，已经针对HSGD建立了线性收敛速率的恢复保证。 HSGD的经验优势在合成数据集和现实世界核磁共振信号上均得到验证。
We study the robust matrix completion problem for the low-rank Hankel matrix, which detects the sparse corruptions caused by extreme outliers while we try to recover the original Hankel matrix from the partial observation. In this paper, we explore the convenient Hankel structure and propose a novel non-convex algorithm, coined Hankel Structured Gradient Descent (HSGD), for large-scale robust Hankel matrix completion problems. HSGD is highly computing- and sample-efficient compared to the state-of-the-arts. The recovery guarantee with a linear convergence rate has been established for HSGD under some mild assumptions. The empirical advantages of HSGD are verified on both synthetic datasets and real-world nuclear magnetic resonance signals.
