Rank-Constrained Solutions to Linear Matrix Equations Using PowerFactorization

作者：Justin P. Haldar, Diego Hernando · 发表于：IEEE Signal Processing Letters · 年份：2009 · DOI：10.1109/lsp.2009.2018223 · 被引用次数：163 · 研究领域：Sparse and Compressive Sensing Techniques、Blind Source Separation Techniques、Direction-of-Arrival Estimation Techniques

Algorithms to construct/recover low-rank matrices satisfying a set of linear equality constraints have important applications in many signal processing contexts. Recently, theoretical guarantees for minimum-rank matrix recovery have been proven for nuclear norm minimization (NNM), which can be solved using standard convex optimization approaches. While nuclear norm minimization is effective, it can be computationally demanding. In this work, we explore the use of the PowerFactorization (PF) algorithm as a tool for rank-constrained matrix recovery. Empirical results indicate that incremented-rank PF is significantly more successful than NNM at recovering low-rank matrices, in addition to being faster.