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In this paper, we propose a novel method of source localization over a diffusion field based on distributed sparse optimization. We consider a sensor network over a planer field to measure spatiotemporal data of the diffusion process. We formulate the problem of estimation of the initial distribution (i.e. localization) as a distributed regularized least squares problem over multi-agent networks, assuming that the initial distribution is sparse in the space domain. For this problem, we propose a distributed sparse optimization algorithm called Cooperative Iterative Shrinkage Thresholding (CoopIST) algorithm. We show that the states of the agents asymptotically agree on an optimal solution of the regularized least squares problem by the proposed CoopIST algorithm. We also investigate the convergence rate in terms of the error of the time-averaged total cost. In addition, we present simulation results of a source localization problem with a two-dimensional diffusion process to show the effectiveness of the proposed method.

Distributed sparse optimization for source localization over diffusion fields with cooperative spatiotemporal sensing