Sampling and Reconstruction of Signals on Product Graphs
Guillermo Ortiz-Jimenez (Student TU Delft)
Mario Coutino (TU Delft - Signal Processing Systems)
S.P. Chepuri (TU Delft - Signal Processing Systems)
G.J.T. Leus (TU Delft - Signal Processing Systems)
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Abstract
In this paper, we consider the problem of subsampling and reconstruction of signals that reside on the vertices of a product graph, such as sensor network time series, genomic signals, or product ratings in a social network. Specifically, we leverage the product structure of the underlying domain and sample nodes from the graph factors. The proposed scheme is particularly useful for processing signals on large-scale product graphs. The sampling sets are designed using a low-complexity greedy algorithm and can be proven to be near-optimal. To illustrate the developed theory, numerical experiments based on real datasets are provided for sampling 3D dynamic point clouds and for active learning in recommender systems.