Painless Breakups -- Efficient Demixing of Low Rank Matrices

2017/03/29 by Strohmer, Thomas, Wei, Ke
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1703.09848

Abstract

Assume we are given a sum of linear measurements of s different rank-r matrices of the form y = ∑_k=1^s A_k (X_k). When and under which conditions is it possible to extract (demix) the individual matrices X_k from the single measurement vector y? And can we do the demixing numerically efficiently? We present two computationally efficient algorithms based on hard thresholding to solve this low rank demixing problem. We prove that under suitable conditions these algorithms are guaranteed to converge to the correct solution at a linear rate. We discuss applications in connection with quantum tomography and the Internet-of-Things. Numerical simulations demonstrate empirically the performance of the proposed algorithms.

Related

• Iterative Hard Thresholding for Low-Rank Recovery from Rank-One Projections
• Nonconvex Matrix Factorization from Rank-One Measurements
• Iterative Thresholding for Demixing Structured Superpositions in High\n Dimensions
• Low-rank matrix recovery via rank one tight frame measurements
• Jointly Low-Rank and Bisparse Recovery: Questions and Partial Answers