It sounded like a broad-spectrum communications monitor.
If you want to know who's broadcasting anywhere in the range from 1MHz to 10GHz (example only -- I don't know the real range for this device), that's a bandwidth of 9.999 GHz.
You could scan freqencies sequentially, but it's slow and you might miss something. You can't afford to build a 20 GHz A-to-D converter, and even if you could, you don't want to build a computer big enough to process the resulting 80 GB/s data stream (assuming a 40 GHz sample rate with 16-bit samples).
The compressive sampling process is what allows you to sample at a lower rate (as long as you can assume that the signal you're looking for doesn't use too much of the total bandwidth). The convex optimization is apparently used to decide how to do the sampling in a way that's guaranteed to recover your signal.
The convex optimization is used to reconstruct the original signal.
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.
Thanks for the clarification, Igor -- my knowledge of this is second-hand, from a friend's description of an interesting project he's working on. I had never heard of compressive sampling or convex optimization before that, and it was eye-opening to see what's possible.
