Correction of Simultaneous Bad Measurements by Exploiting the Low-rank Hankel Structure

This paper studies the robust principal component analysis (RPCA) problem with the objective to decompose a low-rank matrix and a sparse error matrix from their algebraic summation. If all the measurements in one column are erroneous, existing RPCA methods cannot recover the actual data in that column without additional prior information. Motivated by power system monitoring and magnetic resonance imaging (MRI) imaging, low-rank Hankel matrices are recently exploited to characterize the additional correlations among columns besides low-rankness. Exploiting the low-rank Hankel property, this paper develops an alternating-projection-based fast matrix decomposition algorithm, which can accurately recover the low-rank matrix with provable guarantees when simultaneous bad measurements happen across multiple columns consecutively. Numerical results are reported to evaluate the proposed algorithm.