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

arXiv: https://arxiv.org/abs/2406.07409 · HTML: https://mlsanity.com/paper/2406.07409/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 52 references that are in the map.
- First posted on arXiv 11 Jun 2024.

## Builds on (most cited first, 20 of 20)

- [Accelerating Ill-Conditioned Low-Rank Matrix Estimation via Scaled Gradient Descent](https://mlsanity.com/paper/2005.08898/) (2020)
- [Non-convex Robust PCA](https://mlsanity.com/paper/1410.7660/) (2014)
- [Fast Algorithms for Robust PCA via Gradient Descent](https://mlsanity.com/paper/1605.07784/) (2016)
- [Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection](https://mlsanity.com/paper/2110.05649/) (2021)
- [Accelerated Alternating Projections for Robust Principal Component Analysis](https://mlsanity.com/paper/1711.05519/) (2017)
- [Robust CUR Decomposition: Theory and Imaging Applications](https://mlsanity.com/paper/2101.05231/) (2021)
- [Guarantees of Riemannian Optimization for Low Rank Matrix Completion](https://mlsanity.com/paper/1603.06610/) (2016)
- [Laplacian Convolutional Representation for Traffic Time Series Imputation](https://mlsanity.com/paper/2212.01529/) (2022)
- [Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation](https://mlsanity.com/paper/2010.07422/) (2020)
- [Robust Spectral Compressed Sensing via Structured Matrix Completion](https://mlsanity.com/paper/1304.8126/) (2013)
- [Nearly-optimal Robust Matrix Completion](https://mlsanity.com/paper/1606.07315/) (2016)
- [Robust PCA by Manifold Optimization](https://mlsanity.com/paper/1708.00257/) (2017)
- [Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Sampling](https://mlsanity.com/paper/2208.09723/) (2022)
- [Structured Low-Rank Algorithms: Theory, MR Applications, and Links to Machine Learning](https://mlsanity.com/paper/1910.12162/) (2019)
- [Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completion](https://mlsanity.com/paper/2204.03316/) (2022)
- [Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption](https://mlsanity.com/paper/2305.04080/) (2023)
- [Riemannian CUR Decompositions for Robust Principal Component Analysis](https://mlsanity.com/paper/2206.09042/) (2022)
- [Structured low-rank matrix completion for forecasting in time series analysis](https://mlsanity.com/paper/1802.08242/) (2018)
- [Spectral Compressed Sensing via Projected Gradient Descent](https://mlsanity.com/paper/1707.09726/) (2017)
- [On the Robustness of Cross-Concentrated Sampling for Matrix Completion](https://mlsanity.com/paper/2401.15566/) (2024)

## Built on by (most cited first, 3 of 3)

- [Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recovery](https://mlsanity.com/paper/2410.16826/) (2024)
- [Structured Sampling for Robust Euclidean Distance Geometry](https://mlsanity.com/paper/2412.10664/) (2024)
- [Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling](https://mlsanity.com/paper/2608.03928/) (2026)

## Abstract (arXiv)

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.