As it turns out, convex optimization is being seen by a few folks as the new least square. As wwalker mentioned, convex optimization is currently being used in solving for measurements taken with hardware implementing compressive sensing (or compressed sensing or compressive sampling). The A/D converter is just one of the application of compressive sensing. One of the most well known example is that of the single pixel camera at rice but there are many others. I have listed most of the known hardware implementing compressive sensing here:
One should note that while convex optimization has given some real impetus to the field (by providing theoretical bounds), signal reconstruction is also using speedier techniques nowadays even though linear programming techniques remains some sort of gold standard. For those of you interested in the subject, I write a small blog on the subject of CS:
http://igorcarron.googlepages.com/compressedsensinghardware
One should note that while convex optimization has given some real impetus to the field (by providing theoretical bounds), signal reconstruction is also using speedier techniques nowadays even though linear programming techniques remains some sort of gold standard. For those of you interested in the subject, I write a small blog on the subject of CS:
http://nuit-blanche.blogspot.com/search/label/CS
and have written a page trying to summarize our current understanding in this page(it is a bit technical):
http://igorcarron.googlepages.com/cs
Cheers,
Igor.