Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science submitted time 2023-02-14 Cooperative journals: 《桂林电子科技大学学报》
Abstract： The reconstruction problem of spatio-temporal signals can be cast as recovering differential smooth time-varying
graph signals. For the optimization problem, the existing distributed algorithm based on gradient descent method shows
slow convergence when the condition number of the Hessian matrix of the problem is large which leads to a large reconstruction
error when the maximum iteration number is limited in an observation interval. Therefore, an online distributed reconstruction
algorithm based on approximate Newton's method is proposed in the paper, whose principle is to decompose the
original optimization problem into a series of local problems on subgraphs through subgraph decomposition and find these
solutions, and then obtain the approximate global optimal solution via fusion average of local solutions between each subgraph.
According to the gap between the approximate solution and the actual one, it can be proved that the decompostion
and fusion matrix obtained in this way is sparse and can be regarded as the approximate Hessian inverse. Hence, the algorithm
replaces the approximate matrix into the classical Newton iterative formula which can be implemented in a distributed
manner due to the structural sparsity of the approximate matrix. Simulation results show that the proposed algorithm has
faster convergence rate and smaller reconstruction error, and requires less communication cost compared with the existing
algorithm.
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