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Matrix recovery is the problem of recovering a low-rank matrix from a fewlinear measurements. Recently, this problem has gained a lot of attention as itis employed in many applications such as Netflix prize problem, seismic datainterpolation and collaborative filtering. In these applications, one mightaccess to additional prior information about the column and row spaces of thematrix. These extra information can potentially enhance the matrix recoveryperformance. In this paper, we propose an efficient greedy algorithm thatexploits prior information in the recovery procedure. The performance of theproposed algorithm is measured in terms of the rank restricted isometryproperty (R-RIP). Our proposed algorithm with prior subspace informationconverges under a more milder condition on the R-RIP in compared with the casethat we do not use prior information. Additionally, our algorithm performs muchbetter than nuclear norm minimization in terms of both computational complexityand success rate.

A Greedy Algorithm for Matrix Recovery with Subspace Prior Information