Exact matrix completion via convex optimization

作者：Emmanuel J. Candès, Benjamin Recht · 发表于：Communications of the ACM · 年份：2012 · DOI：10.1145/2184319.2184343 · 被引用次数：1029 · 研究领域：Sparse and Compressive Sensing Techniques、Blind Source Separation Techniques、Photoacoustic and Ultrasonic Imaging

Suppose that one observes an incomplete subset of entries selected from a low-rank matrix. When is it possible to complete the matrix and recover the entries that have not been seen? We demonstrate that in very general settings, one can perfectly recover all of the missing entries from most sufficiently large subsets by solving a convex programming problem that finds the matrix with the minimum nuclear norm agreeing with the observed entries. The techniques used in this analysis draw upon parallels in the field of compressed sensing, demonstrating that objects other than signals and images can be perfectly reconstructed from very limited information.