Matrix recovery using Split Bregman
This work addresses matrix recovery for applications like pattern recognition and recommender systems, but it is incremental as it builds on existing nuclear norm minimization methods.
The paper tackles the problem of recovering low-rank matrices from lower-dimensional projections by proposing a Split Bregman algorithm for nuclear norm minimization, resulting in improved convergence speed, higher success rates, and better accuracy with fewer measurements, as supported by empirical comparisons on NMSE, execution time, and success rate.
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.