IEEE Trans Image Process - An alternating direction algorithm for total variation reconstruction of distributed parameters.

Tópicos

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Resumo

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.

Resumo Limpo

augment lagrangian variat formul altern optim adopt solv distribut paramet estim problem altern direct method multipli admm one formulationsoptim method recent number applic admm variant solv invers problem imag signal process increas exponenti rate reason interest admm decompos difficult optim problem sequenc much simpler problem paper use admm reconstruct piecewisesmooth distribut paramet ellipt partial differenti equat noisi linear blur observ under field distribut paramet estim solv invers problem total variat tv regular propos instanc admm solv iter l decoupl l l optim problem oper split use simplifi treatment tv regular avoid smooth approxim yield simpl yet effect admm reconstruct method compar previous propos approach competit propos method respect stateoftheart illustr simul d d ellipt equat problem repres mani real applic

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