A Kaczmarz Method for Low Rank Matrix Recovery

The Kaczmarz method [1], [2], [3] was initially proposed as a row-based technique for reconstructing signals by finding the solutions to overdetermined linear systems. Its usefulness has seen wide application in irregular sampling and tomography [4], [5], [6]. In recent years, several modifications to the Kaczmarz update iterations have improved the recovery capabilities [7], [8], [9], [10], [11]. In particular, signal sparsity was exploited in [12], [13] and low-rankness in [14] to improve the rate of convergence in the overdetermined case while also enabling recovery from underdetermined linear systems.