Journal ArticleDeeply Learned Robust Matrix Completion for Large-scale Low-rank Data RecoveryCai, HanQin [School of Data, Mathematical, and Statistical Sciences and the Department of Computer Science, University of Central Florida, Orlando, FL, USA]; Kundu, Chandra [School of Data, Mathematical, and Statistical Sciences, University of Central Florida, Orlando, FL, USA]; Liu, Jialin [School of Data, Mathematical, and Statistical Sciences and the Department of Computer Science, University of Central Florida, Orlando, FL, USA]; Yin, Wotao [Damo Academy, Alibaba US, Bellevue, WA, USA]Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable non-convex approach, coined Learned Robust Matrix Completion (LRMC), for large-scale RMC problems. LRMC enjoys low computational complexity with linear convergence. Motivated by the proposed theorem, the free parameters of LRMC can be effectively learned via deep unfolding to achieve optimum performance. Furthermore, this paper proposes a flexible feedforward-recurrent-mixed neural network framework that extends deep unfolding from fixed-number iterations to infinite iterations. The superior empirical performance of LRMC is verified with extensive experiments against state-of-the-art on synthetic datasets and real applications, including video background subtraction, ultrasound imaging, face modeling, and cloud removal from satellite imagery.IEEE2026-01-2910673482IEEE Transactions on Pattern Analysis and Machine Intelligence1 to 150162-8828https://doi.org/10.1109/TPAMI.2026.36590412304489National Science Foundation