2019/09/29 by Marcus Carlsson, Carlsson, Marcus, Daniele Gerosa +3 · 1 citation
Engineering · Mathematics · #Advanced SAR Imaging Techniques #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1909.13363
openalex publication_date 2019/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Low rank recovery problems have been a subject of intense study in recent years. While the rank function is useful for regularization it is difficult to optimize due to its non-convexity and discontinuity. The standard remedy for this is to exchange the rank function for the convex nuclear norm, which is known to favor low rank solutions under certain conditions. On the downside the nuclear norm exhibits a shrinking bias that can severely distort the solution in the presence of noise, which motivates the use of stronger non-convex alternatives. In this paper we study two such formulations. We characterize the critical points and give sufficient conditions for a low rank stationary point to be unique. Moreover, we derive conditions that ensure global optimality of the low rank stationary point and show that these hold under moderate noise levels.