In German you say "Keine zwei Schneeflocken sind gleich", which says something like, "there are no snow flakes which are completely equal".
The story of every PhD student is of course different, but should there be some researcher who finds that his snow flake resembles mine, he might find this post useful.
In some cases the professor gives clear guidance and strictly decides on what the PhD student should work on. If this is your case, you can skip my post.
Sometimes in a more "free" PhD the student has to find by himself in which field to do research in and the professor's role resembles more that of an (very) experienced coworker and advisor.
In this case, I found that, one good move, especially when starting out, is to read PhD thesises of previous graduates and if possible ask them personally what could be worth exploring and in which areas their work could be extended.
Don't be too arrogant only because you A'ced all the courses. People who have spent at least 4 years of their life in the lab you are going to stay, surely have some good advise.
Now another thought is should you jump into a flashy new field, in signal processing and machine learning nowaways this could be 'compressed sensing', 'Gaussian processes' or 'deep neural networks' ?
Of course I believe the most important thing is to choose something you like, but assuming you are a curious person who loves different fields, I believe that it can be more rewarding to work in a new field, where there might be still low hanging fruits and many things to discover ;-)
If you go for a very mature field, let's say adaptive filter theory or Kalman filtering you most likely will end up rediscovering stuff from the 60's or so.
Surely, deriving some old algorithms with a modern perspective, e.g. Kalman filtering from a Bayesian and Graphical model perspective compared to the original least squares is a contribution, but at least in my opinion, less rewarding than discovering something new which possibly pushes the limits further.
Well, if you have read the post up to here and listened to my opinion, I'd be glad to hear yours in the comment section!
