If I were you, I'd go for something related to Compressed Sensing. Even though my Ph.D. is not on this subject, I've come across it couple of months ago and it looks quite interesting, and it's relatively a new topic too (correct me if i'm wrong). Violating the Nyquist Sampling rate has never been that scientific and fun I suppose. Give it a shot, read a couple of papers (there are really good review papers out there that can give you a good introduction, you might want to visit this website for a good start).
Good luck and try to have fun while doing it, that's a must!