Shuman, David I.
Vandergheynst, Pierre
Frossard, Pascal
Chebyshev Polynomial Approximation for Distributed Signal Processing
Proceedings of IEEE International Conference on Distributed Computing in Sensor Systems
978-1-4577-0513-7
Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals collected by sensor networks. The proposed method features approximations of the graph Fourier multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We demonstrate how the proposed method can be used in a distributed denoising task, and show that the communication requirements of the method scale gracefully with the size of the network.
Chebyshev polynomial approximation;
denoising;
distributed optimization;
regularization;
signal processing on graphs;
spectral graph theory;
wireless sensor networks;
2011
http://infoscience.epfl.ch/record/165369/files/Shuman_et_al_DCOSS_2011_1.pdf;