Painless Breakups—Efficient Demixing of Low Rank Matrices.

Assume we are given a sum of linear measurements of s different rank-r matrices of the form y=∑k=1sAk(Xk). When and under which conditions is it possible to extract (demix) the individual matrices Xk 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 introduce an Amalgam-Restricted Isometry Property which is especially suitable for demixing problems and prove that under appropriate 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 the empirical performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]