Low-Rank Matrix Recovery From Noisy, Quantized, and Erroneous Measurements - 2018


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

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