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",
month="January 1,",
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