In this paper, we study the problem of low-rank matrix sensing where the goal is to reconstruct a matrix exactly using a small number of linear measurements. Existing methods for the problem either rely on measurement operators such as random element-wise sampling which cannot recover arbitrary low-rank matrices or require the measurement operator to satisfy the Restricted Isometry Property (RI...

Finding a suitable measurement matrix is an important topic in compressed sensing. Though the known random matrix, whose entries are drawn independently from a certain probability distribution, can be used as a measurement matrix and recover signal well, in most cases, we hope the measurement matrix imposed with some special structure. In this paper, based on random graph models, we show that t...