I got my degree in EE and applied for software jobs and got one. I worked on side programming projects and taught myself basic programming (C++ at the time). When I interviewed I was able to 1) show that I understood concepts like polymorphism and object-oriented development, and 2) cared enough to work on software projects in my own time.
I did get burned on a few interviews where I claimed to know C and then they asked some difficult pointer questions that were out of my depth. Truth was I had done C++ and a little bit of C in one class but not much. So you need to be able to pass a verbal interview and a coding interview.
If I were you I would also suggest not trying to get a job in one of those sub-fields right away, but instead look for any decent software job, get some experience, then look to move into a niche area.
I did get burned on a few interviews where I claimed to know C and then they asked some difficult pointer questions that were out of my depth. Truth was I had done C++ and a little bit of C in one class but not much. So you need to be able to pass a verbal interview and a coding interview.
If I were you I would also suggest not trying to get a job in one of those sub-fields right away, but instead look for any decent software job, get some experience, then look to move into a niche area.