EPFL | Biomedical Imaging Group | Signal Downsampling

Downsampling of Signals on Graphs via Maximum Spanning Trees

H.Q. Nguyen, M.N. Do

IEEE Transactions on Signal Processing, vol. 63, no. 1, pp. 182–191, January 1, 2015.

Downsampling of signals living on a general weighted graph is not as trivial as of regular signals where we can simply keep every other samples. In this paper we propose a simple, yet effective downsampling scheme in which the underlying graph is approximated by a maximum spanning tree (MST) that naturally defines a graph multiresolution. This MST-based method significantly outperforms the two previous downsampling schemes, coloring-based and SVD-based, on both random and specific graphs in terms of computations and partition efficiency quantified by the graph cuts. The benefit of using MST-based downsampling for recently developed critical-sampling graph wavelet transforms in compression of graph signals is demonstrated.

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AUTHOR="Nguyen, H.Q. and Do, M.N.",
TITLE="Downsampling of Signals on Graphs via Maximum Spanning Trees",
JOURNAL="{IEEE} Transactions on Signal Processing",
YEAR="2015",
volume="63",
number="1",
pages="182--191",
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