You don't have to have a space probe near Saturn, or Herschel at L2 to be limited by bandwidth issues, here are two other areas that are traditionally limited in bandwidth by the medium and where compressive sensing solutions are being investigated:
- Toward Underwater Video Transmission by Laura Dubreuil Vall (Master's thesis)
- Power Line Communications A Playground for Communications Theory and Applied Signal Processing by Lutz Lampe
In the underwater video case, there is a short attempt at comparing MPEG4 with compressed sensing (see section 2.3.3) and as expected with a plain vanilla compressive sensing approach, you cannot get better or rival MPEG4 (0.45% compression ratio versus 15% for CS). It need to be said often, plain vanilla CS will not compete head to head with MPEG4. The current expectation though would be for some sort of structured sparsity to actually get to the numbers of MPEG4.
I am much more endeared by the prospect of CS being useful in the home though. PLC is a very old technology (my parents were using audio based PLC systems forty years ago) and it would be an interesting twist if some of this technology could come out of the niche market it is in thanks to new techniques like compressive sensing.
Especially, if CS could use the framework developed in cognitive radio (that seems to go nowhere for broadcast if I am reading Gonzalo Vazquez-Vilar's blog correctly)