93 research outputs found
The achievable performance of convex demixing
Demixing is the problem of identifying multiple structured signals from a
superimposed, undersampled, and noisy observation. This work analyzes a general
framework, based on convex optimization, for solving demixing problems. When
the constituent signals follow a generic incoherence model, this analysis leads
to precise recovery guarantees. These results admit an attractive
interpretation: each signal possesses an intrinsic degrees-of-freedom
parameter, and demixing can succeed if and only if the dimension of the
observation exceeds the total degrees of freedom present in the observation
Load curve data cleansing and imputation via sparsity and low rank
The smart grid vision is to build an intelligent power network with an
unprecedented level of situational awareness and controllability over its
services and infrastructure. This paper advocates statistical inference methods
to robustify power monitoring tasks against the outlier effects owing to faulty
readings and malicious attacks, as well as against missing data due to privacy
concerns and communication errors. In this context, a novel load cleansing and
imputation scheme is developed leveraging the low intrinsic-dimensionality of
spatiotemporal load profiles and the sparse nature of "bad data.'' A robust
estimator based on principal components pursuit (PCP) is adopted, which effects
a twofold sparsity-promoting regularization through an -norm of the
outliers, and the nuclear norm of the nominal load profiles. Upon recasting the
non-separable nuclear norm into a form amenable to decentralized optimization,
a distributed (D-) PCP algorithm is developed to carry out the imputation and
cleansing tasks using networked devices comprising the so-termed advanced
metering infrastructure. If D-PCP converges and a qualification inequality is
satisfied, the novel distributed estimator provably attains the performance of
its centralized PCP counterpart, which has access to all networkwide data.
Computer simulations and tests with real load curve data corroborate the
convergence and effectiveness of the novel D-PCP algorithm.Comment: 8 figures, submitted to IEEE Transactions on Smart Grid - Special
issue on "Optimization methods and algorithms applied to smart grid
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