Multichannel Hankel Matrix Completion Through Nonconvex Optimization

This paper studies the multichannel missing data recovery problem when the measurements are generated by a dynamical system. A new model, termed multichannel low-rank Hankel matrices, is proposed to characterize the intrinsic low-dimensional structures in multichannel time series. The data recovery problem is formulated as a nonconvex optimization problem, and two fast algorithms (AM-FIHT and RAM-FIHT), both with linear convergence rates, are developed to recover the missing points with provable performance guarantees. The required number of observations is significantly reduced, compared with conventional low-rank completion methods. Our methods are verified through numerical experiments on synthetic data and recorded synchrophasor data in power systems.