A Measurement-Efficient Low-Rank Matrix Recovery Approach

This paper presents a novel low-rank matrix recovery approach that jointly performs measurement collection and matrix estimation to improve the overall sample efficiency under unknown rank information. It builds on a key observation that the minimum number of measurements needed for matrix rank estimation can be much less than that for matrix recovery. Such a gap in measurement requirements is first delineated in closes form through empirical quantification. Then, capitalizing on this quantified gap on measurements, a two-step procedure is developed for adaptive measurement collection. The actual rank of the matrix is estimated in the first step, which informs the number of measurements to be collected in the second step for low-rank matrix recovery. Simulations corroborate that our approach can considerably reduce the total number of required measurements for matrix recovery in practice. The improvement in sample efficiency is particularly pronounced for large-scale applications where low-rank matrix estimation is of great relevance.