Matrix Recovery Using Split Bregman

In this paper we address the problem of recovering a matrix, with inherent low rank structure, from its lower dimensional projections. This problem is frequently encountered in wide range of areas including pattern recognition, wireless sensor networks, control systems, recommender systems, image/video reconstruction etc. Both in theory and practice, the most optimal way to solve the low rank matrix recovery problem is via nuclear norm minimization. In this paper, we propose a Split Bregman algorithm for nuclear norm minimization. The use of Bregman technique improves the convergence speed of our algorithm and gives a higher success rate. Also, the accuracy of reconstruction is much better even for cases where small number of linear measurements are available. Our claim is supported by empirical results obtained using our algorithm and its comparison to other existing methods for matrix recovery. The algorithms are compared on the basis of NMSE, execution time and success rate for varying ranks and sampling ratios.