Low-rank Matrix Recovery from Noisy, Quantized and Erroneous Measurements

Abstract

This paper proposes a communication-reduced, cyber-resilient, and information-preserved data collection framework. Random noise and quantization are applied to the measurements before transmission to compress data and enhance data privacy. Leveraging the low-rank property of the data, we develop novel methods to recover the original data from quantized measurements even when partial measurements are corrupted. The data recovery is achieved through solving a constrained maximum likelihood estimation problem. The recovery error is proven to be order-wise optimal and decays in the same order as that of the state-of-the-art method when there is no corruption. The data accuracy is thus maintained while the data privacy is enhanced. A proximal algorithm with convergence guarantee is proposed to solve the nonconvex problem. The analyses are extended to situations when some measurements are lost, or when multiple copies of noisy, quantized measurements are sent for each data point. A new application of this framework for data privacy in power systems is discussed. Experiments on synthetic data and real synchrophasor data in power systems demonstrate the effectiveness of our method.