It seems surprising that so many users of remote sensing (including wireless networks) have yet to hear the 10-year-old message of compressive sensing: data from nature is “sparse,” so a small number of properly selected data points often allow one to reconstruct the original data set with high probability and/or low error rate. Put briefly, one can compress at the source, rather than collecting the whole set.

(Confusingly, the standard abbreviation for compressive sensing is “CS.” This review follows that convention, but also refers to “traditional CS,” that is, computer science.)

While the first CS papers were rather abstract, researchers have continued to expand the ideas of CS into more areas of applications involving more types of sensors. Here, the authors are interested in wireless sensor networks, that is, a geographically spread array of low-power sensors that communicate with each other by radio. CS has been used for such problems for a while; the innovation in this paper is more a result about “traditional CS” graph techniques. The sensors are the nodes and the radio links are the edges, as expected, but they choose to optimize power consumption under the reasonable assumption that batteries are hard to change. Thus, sensors should prefer to reduce transmitted power by only communicating with nearby sensors. Their intricate algorithms select collector nodes and active radio links to acquire the data using hybrid CS techniques. But this is also “traditional CS”: they even use Dijkstra’s all points shortest path algorithm in their new algorithm.

They present convincing simulations with random network configurations, which as usual raise questions about the applicability to deployed networks whose data may be intrinsically sparse due to spatial correlations.