Compressed sensing (CS) has matured rapidly and should continue to do so for some time. In CS, a so-called sparse signal is accurately observed using a very small number of samples. Early applications used a fixed sampling scheme, but the need to reduce power consumption and transmission costs in wireless sensor networks (WSNs), among other applications, has led to the idea of an adaptive approach.

Typically, a vector x of dimension N is observed as y = Φ • x, where y has dimension M << N. The sampling rate is then M/N. The authors propose changing M depending on how quickly a signal is changing; a quiescent signal should be sampled at a lower rate. In their application to meteorological data, they contrast relative humidity (RH), which generally changes slowly, with rapidly changing precipitation rate (PR). They conclude that the RH sampling rate can be substantially lower than the PR rate (but see below). One might even wonder if using an error-detecting code might be adequate when the system is in a quiescent state. The authors present good data comparing their scheme to existing schemes.

An intrinsic difficulty with this topic is the proper interpretation of the word “rate.” I think most readers will interpret rate as a time period (in their data 1/120 Hz). But the “sampling rate” in question is actually the ratio of the number of sensors polled to the total number of sensors. Perhaps it would be clearer to call this the “coding rate.”

The example of RH leads one to ask how the proposed system would perform in the event of (effective) discontinuities. While RH generally changes slowly, during frontal passage, it can be effectively discontinuous.