The underlying compressive sensing theory says that if you do a measurement of a sparse signal, then convex optimization should allow you to recover that signal with high to overwhelming probability. The reason compressive sensing is interesting is that: - the process of taking measurement is linear (no iteration a la JPEG), thereby allowing one to foresee very low powered sensors. - the number of measurements is expected to be much smaller than what the Nyquist-Shannon theorem says (Nyquist is just a sufficient condition, not a necessary one), thereby realizing a de-facto compression of the signal with no a priori on the shape of that signal (except the knowledge that it is sparse) - the measurements are automatically encrypted.
In the case of the broad-spectrum communications monitor, the message is known to be sparsely located all over the frequencies.
Igor.