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Distributed Autoregressive Moving Average Graph Filters
"... Abstract—We introduce the concept of autoregressive moving average (ARMA) filters on a graph and show how they can be implemented in a distributed fashion. Our graph filter design philosophy is independent of the particular graph, meaning that the filter coefficients are derived irrespective of th ..."
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Abstract—We introduce the concept of autoregressive moving average (ARMA) filters on a graph and show how they can be implemented in a distributed fashion. Our graph filter design philosophy is independent of the particular graph, meaning that the filter coefficients are derived irrespective of the graph. In contrast to finiteimpulse response (FIR) graph filters, ARMA graph filters are robust against changes in the signal and/or graph. In addition, when timevarying signals are considered, we prove that the proposed graph filters behave as ARMA filters in the graph domain and, depending on the implementation, as first or higher order ARMA filters in the time domain. Index Terms—Distributed timevarying computations, graph filters, graph Fourier transform, signal processing on graphs. I.
Discrete signal processing on graphs: Sampling theory,” arXiv preprint arXiv:1503.05432
, 2015
"... Abstract—We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that the perfect recovery is possible for graph signals bandlimited under the graph Fourier transform, and the samp ..."
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Abstract—We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that the perfect recovery is possible for graph signals bandlimited under the graph Fourier transform, and the sampled signal coefficients form a new graph signal, whose corresponding graph structure is constructed from the original graph structure, preserving frequency contents. By imposing a specific structure on the graph, graph signals reduce to finite discretetime signals and the proposed sampling theory works reduces to classical signal processing. We further establish the connection to frames with maximal robustness to erasures as well as compressed sensing, and show how to choose the optimal sampling operator, how random sampling works on circulant graphs and ErdősRényi graphs, and how to handle fullband graph signals by using graph filter
DISTRIBUTED ALGORITHM FOR GRAPH SIGNAL INPAINTING
"... ABSTRACT We present a distributed and decentralized algorithm for graph signal inpainting. The previous work obtained a closedform solution with matrix inversion. In this paper, we ease the computation by using a distributed algorithm, which solves graph signal inpainting by restricting each node ..."
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ABSTRACT We present a distributed and decentralized algorithm for graph signal inpainting. The previous work obtained a closedform solution with matrix inversion. In this paper, we ease the computation by using a distributed algorithm, which solves graph signal inpainting by restricting each node to communicate only with its local nodes. We show that the solution of the distributed algorithm converges to the closedform solution with the corresponding convergence speed. Experiments on online blog classification and temperature prediction suggest that the convergence speed of the proposed distributed algorithm is competitive with that of the centralized algorithm, especially when a graph tends to be regular. Since a distributed algorithm does not require to collect data to a center, it is more practical and efficient.
Stochastic Graph Filtering on TimeVarying GraphsEXTENDED VERSION
"... Abstract—We have recently seen a surge of work on distributed graph filters, extending classical results to the graph setting. State of the art filters have however only been examined from a deterministic standpoint, ignoring the impact of stochasticity in the computation (e.g., temporal fluctuation ..."
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Abstract—We have recently seen a surge of work on distributed graph filters, extending classical results to the graph setting. State of the art filters have however only been examined from a deterministic standpoint, ignoring the impact of stochasticity in the computation (e.g., temporal fluctuation of links) and input (e.g., the value of each node is a random process). Initiating the study of stochastic graph signal processing, this paper shows that a prominent class of graph filters, namely autoregressive moving average (ARMA) filters, are suitable for the stochastic setting. In particular, we prove that an ARMA filter that operates on a stochastic signal over a stochastic graph is equivalent, in the mean, to the same filter operating on the expected signal over the expected graph. We also characterize the variance of the output and we provide an upper bound for its average value among different nodes. Our results are validated by numerical simulations. I.