2018/12/14 by Abiy Tasissa, Tasissa, Abiy, Rongjie Lai +1 · 1 citation
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1812.05786
openalex publication_date 2018/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper considers theoretical analysis of recovering a low rank matrix given a few expansion coefficients with respect to any basis. The current approach generalizes the existing analysis for the low-rank matrix completion problem with sampling under entry sensing or with respect to a symmetric orthonormal basis. The analysis is based on dual certificates using a dual basis approach and does not assume the restricted isometry property (RIP). We introduce a condition on the basis called the correlation condition. This condition can be computed in time O(n3) and holds for many cases of deterministic basis where RIP might not hold or is NP hard to verify. If the correlation condition holds and the underlying low rank matrix obeys the coherence condition with parameter ν, under additional mild assumptions, our main result shows that the true matrix can be recovered with very high probability from O(nrνlog2n) uniformly random expansion coefficients.