Abstract
We consider the decentralised consensus optimisation problem arising from in-situ seismic tomography in large-scale sensor networks. Unlike traditional seismic imaging performed in a centralised location, each node in this setting privately holds an objective function and partial data. The goal of each node is to obtain the optimal solution of the whole seismic image, while communicating only with its immediate neighbours. We present a fast decentralised gradient descent method and prove that this novel method can reach optimal convergence rate of where k is the number of communication/iteration rounds. A gossip-based asynchronous version is also proposed which is preferable when there is a divergence on the processing speed of the nodes. Extensive numerical experiments on synthetic and real-world sensor network seismic data demonstrate that the proposed algorithms significantly outperform existing methods.
Published Version
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