Distributed reconstruction of time-varying graph signals via a modified Newton’s method |
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| Institution: | 1. School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China;2. National and Local Joint Engineering Research Center of Satellite Navigation Positioning and Location Service, Guilin 541004, China;3. School of Information Technology, Deakin University, Waurn Ponds, Victoria 3216, Australia;1. Department of Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, China;2. City University of Hong Kong Chengdu Research Institute, Chengdu 610200, China;1. College of Control Science and Engineering, Bohai University, Jinzhou 121013, China;2. College of Mathematics, Bohai University, Jinzhou 121013, China;1. School of Chemical and Environmental Engineering, Liaoning University of Technology, Jinzhou, Liaoning, 121001, China;2. College of Science, Liaoning University of Technology, Jinzhou, Liaoning, 121001, China |
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| Abstract: | This paper develops a distributed reconstruction algorithm, that can be implemented efficiently, for time-varying graph signals. The reconstruction problem is formulated as an unconstrained optimization problem that minimizes the weighted sum of the data fidelity term and the regularization term. The regularizer used is the nonsmoothness measure of the temporal difference signal. The classical Newton’s method can be used to solve the optimization problem. However, computation of the Hessian matrix inverse is required, and this does not scale well with the graph size. Furthermore, a distributed implementation is not possible. An approximation to the inverse Hessian, that exploits the graph topology, is developed here. The resulting iterative algorithm can be implemented in a distributed manner, and scales well with the graph size. Convergence analysis of the algorithm is presented, which shows convergence to the global optimum. Numerical results, using both synthetic and real world datasets, will demonstrate the superiority of the proposed reconstruction algorithm over existing methods. |
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