2010/10/12 by Massimo Fornasier, Holger Rauhut, Fornasier, Massimo +3 · 1 citation
Computer Science · Engineering · Medicine · #49M30 #52A41 #65J22 #65K10 #Advanced MRI Techniques and Applications #Blind Source Separation Techniques #Electrical and Bioimpedance Tomography #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1010.2471
openalex publication_date 2010/10/12 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We present and analyze an efficient implementation of an iteratively\nreweighted least squares algorithm for recovering a matrix from a small number\nof linear measurements. The algorithm is designed for the simultaneous\npromotion of both a minimal nuclear norm and an approximatively low-rank\nsolution. Under the assumption that the linear measurements fulfill a suitable\ngeneralization of the Null Space Property known in the context of compressed\nsensing, the algorithm is guaranteed to recover iteratively any matrix with an\nerror of the order of the best k-rank approximation. In certain relevant cases,\nfor instance for the matrix completion problem, our version of this algorithm\ncan take advantage of the Woodbury matrix identity, which allows to expedite\nthe solution of the least squares problems required at each iteration. We\npresent numerical experiments that confirm the robustness of the algorithm for\nthe solution of matrix completion problems, and demonstrate its competitiveness\nwith respect to other techniques proposed recently in the literature.\n