2024/10/22 by Paris V. Giampouras, Giampouras, Paris, HanQin Cai +3
Engineering · Mathematics · #Advanced Image Fusion Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2410.16826
openalex publication_date 2024/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we focus on a matrix factorization-based approach to recover low-rank \it asymmetric matrices from corrupted measurements. We propose an \it Overparameterized Preconditioned Subgradient Algorithm (OPSA) and provide, for the first time in the literature, linear convergence rates independent of the rank of the sought asymmetric matrix in the presence of gross corruptions. Our work goes beyond existing results in preconditioned-type approaches addressing their current limitation, i.e., the lack of convergence guarantees in the case of \it asymmetric matrices of unknown rank. By applying our approach to (robust) matrix sensing, we highlight its merits when the measurement operator satisfies a mixed-norm restricted isometry property. Lastly, we present extensive numerical experiments that validate our theoretical results and demonstrate the effectiveness of our approach for different levels of overparameterization and outlier corruptions.