“rank-one measurements”

Jointly low-rank and bisparse recovery: Questions and partial answers

Abstract: We investigate the problem of recovering jointly $r$-rank and $s$-bisparse matrices from as few linear measurements as possible, considering arbitrary measurements as well as rank-one measurements. In both cases, we show that \(m ≍ r s łn(en/s)\) measurements make the recovery possible in theory, meaning via a nonpractical algorithm.