Joint Vertex-Time Filtering on Graphs with Random Node-Asynchronous Updates
نویسندگان
چکیده
In graph signal processing signals are defined over a graph, and filters designed to manipulate the variation of graph. On other hand, time domain treats as series, digital in time. This study focuses on notion vertex-time filters, which manipulates time-dependent both simultaneously. The key aspects proposed filtering operations due random asynchronous behavior nodes, they follow collect-compute-broadcast scheme. For analysis randomized operations, this first considers variant linear discrete-time state-space models, each state variable gets updated randomly independently (and asynchronously) every iteration. Unlike previous studies that analyzed similar models under certain assumptions input signal, model most general setting with arbitrary signals, lay foundations for operations. shows exponentials continue be eigenfunctions statistical sense spite nature model. also presents necessary sufficient condition mean-squared stability underlying transition matrix is neither nor recursions. Then, proven mean-square stable if only filter, operator update probabilities satisfy condition. results show some unstable (in synchronous case) can implemented manner presence asynchronicity, demonstrated by numerical examples.
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ژورنال
عنوان ژورنال: IEEE Access
سال: 2021
ISSN: ['2169-3536']
DOI: https://doi.org/10.1109/access.2021.3109288