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Augmented Lagrangian variational formulations and alternating optimization have been adopted to solve distributed parameter estimation problems. The alternating direction method of multipliers (ADMM) is one of such formulations/optimization methods. Very recently, the number of applications of the ADMM, or variants of it, to solve inverse problems in image and signal processing has increased at an exponential rate. The reason for this interest is that ADMM decomposes a difficult optimization problem into a sequence of much simpler problems. In this paper, we use the ADMM to reconstruct piecewise-smooth distributed parameters of elliptical partial differential equations from noisy and linear (blurred) observations of the underlying field. The distributed parameters are estimated by solving an inverse problem with total variation (TV) regularization. The proposed instance of the ADMM solves, in each iteration, an l(2) and a decoupled l(2) - l(1) optimization problems. An operator splitting is used to simplify the treatment of the TV regularizer, avoiding its smooth approximation and yielding a simple yet effective ADMM reconstruction method compared with previously proposed approaches. The competitiveness of the proposed method, with respect to the state-of-the-art, is illustrated in simulated 1-D and 2-D elliptical equation problems, which are representative of many real applications.

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Sensor calibration plays an important role in instrument development and accuracy. This paper presents a method to calibrate current and voltage sensors specially dedicated to power quality measurements which can significantly reduce the distortions introduced by the sensors. The first approach to sensor calibration is based on the response of sensors to DC values imposed by a calibrator. The second method is an AC calibration, where a 50 Hz power signal is applied to the sensors also through a calibrator. The calibration coefficients are obtained by minimizing the output distortion. The minimized output distortion is assessed by the signal to noise and distortion ratio (SINAD) at the output of the sensor correction module.