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This paper considers a node-asynchronous implementation of rational (“IIR”) filters on graphs, in which the nodes are assumed to wake up randomly and independently from each other, and communicate only with their immediate neighbors. The underlying graph is allowed to be directed, possibly with a non-diagonalizable adjacency matrix. Since the nodes are allowed to act independently, the proposed implementation is practical for very large or autonomous networks where synchronization is difficult to achieve. Furthermore, the proposed algorithm is 1-hop localized on the graph irrespective of the order of the filter. The method is shown to converge in the mean-squared sense under a boundedness assumption on the filter as well as the graph operator. The result follows from the convergence of a more general randomized asynchronous state recursion, which is also presented in this paper. The algorithm is simulated on a random geometric graph, which numerically verifies the convergence.
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Node-Asynchronous Implementation of Filter Banks on Graphs
Filter banks on graphs are shown to be useful for analyzing data defined over networks, as they decompose a graph signal into components with low variation and high variation. Based on recent node-asynchronous implementation of graph filters, this study proposes an asynchronous implementation of filter banks on graphs. In the proposed algorithm nodes follow a randomized collect-compute-broadcast scheme: if a node is in the passive stage it collects the data sent by its incoming neighbors and stores only the most recent data. When a node gets into the active stage at a random time instance, it does the necessary filtering computations locally, and broadcasts a state vector to its outgoing neighbors. When the underlying filters (of the filter bank) are rational functions with the same denominator, the proposed filter bank implementation does not require additional communication between the neighboring nodes. However, computations done by a node increase linearly with the number of filters in the bank. It is also proven that the proposed asynchronous implementation converges to the desired output of the filter bank in the mean-squared sense under mild stability conditions. The convergence is verified also with numerical experiments.
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- Award ID(s):
- 1712633
- PAR ID:
- 10275654
- Date Published:
- Journal Name:
- Proc. Asil. Conf. Sig., Sys., and Comp
- Page Range / eLocation ID:
- 460 to 464
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IEEECONF51394.2020.9443349
