# A Survey on Matrix Completion: Perspective of Signal Processing

arXiv: https://arxiv.org/abs/1901.10885 · HTML: https://mlsanity.com/paper/1901.10885/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2019.

## Built on by (most cited first, 6 of 6)

- [Matrix Completion via Non-Convex Relaxation and Adaptive Correlation Learning](https://mlsanity.com/paper/2203.02189/) (2022)
- [An extrapolated and provably convergent algorithm for nonlinear matrix decomposition with the ReLU function](https://mlsanity.com/paper/2503.23832/) (2025)
- [ORKA: Accelerated Kaczmarz Algorithms for Signal Recovery from One-Bit Samples](https://mlsanity.com/paper/2301.03467/) (2022)
- [SparGE: Sparse Coding-based Patient Similarity Learning via Low-rank Constraints and Graph Embedding](https://mlsanity.com/paper/2202.01427/) (2022)
- [Matrix Completion via Residual Spectral Matching](https://mlsanity.com/paper/2412.10005/) (2024)
- [Fast exact recovery of noisy matrix from few entries: the infinity norm approach](https://mlsanity.com/paper/2501.19224/) (2025)

## Abstract (arXiv)

Matrix completion (MC) is a promising technique which is able to recover an intact matrix with low-rank property from sub-sampled/incomplete data. Its application varies from computer vision, signal processing to wireless network, and thereby receives much attention in the past several years. There are plenty of works addressing the behaviors and applications of MC methodologies. This work provides a comprehensive review for MC approaches from the perspective of signal processing. In particular, the MC problem is first grouped into six optimization problems to help readers understand MC algorithms. Next, four representative types of optimization algorithms solving the MC problem are reviewed. Ultimately, three different application fields of MC are described and evaluated.