  Matrix recovery is the problem of recovering a low-rank matrix from a few
linear measurements. Recently, this problem has gained a lot of attention as it
is employed in many applications such as Netflix prize problem, seismic data
interpolation and collaborative filtering. In these applications, one might
access to additional prior information about the column and row spaces of the
matrix. These extra information can potentially enhance the matrix recovery
performance. In this paper, we propose an efficient greedy algorithm that
exploits prior information in the recovery procedure. The performance of the
proposed algorithm is measured in terms of the rank restricted isometry
property (R-RIP). Our proposed algorithm with prior subspace information
converges under a more milder condition on the R-RIP in compared with the case
that we do not use prior information. Additionally, our algorithm performs much
better than nuclear norm minimization in terms of both computational complexity
and success rate.
