I'm afraid I'm not that closely involved in the field to predict the future of image processing. I think generally the more interesting and difficult issues will need specialized hardware (graphics controllers) for some time, if only to reduce the power requirements of the computations. Learning good software techniques especially for mathematical algorithms is always a good idea. Even hardware engineering is mostly software any more -- using Verilog, Perl, TCL, etc. to run the design tools and synthesis. In the broad view, image processing is about one thing -- presenting information in the best possible way to the human's highest bandwidth input device, his eyes. This need will not be diminished, but our computers are doing a pretty fair job of it now with large multiple hi-res screens available for any PC. The one thing we lack is hi-res large format output for handheld devices (cell phones). Best wishes for your success in whatever you do!
To understand image compression techniques, start with the JPEG standard which is freely available and go on from there. There was an effort & book called JPEG 2000 which never seemed to go anywhere but which I believe was pushing for 3D compression, adding the time dimension for video. Open source software for compression is generally available and good. Further research in this area is IMO of limited benefit - because you are hitting the asymptotic limit of the information content.
Today the bigger image processing effort is in with comb filters, etc. for hi-def TV arena, and streaming for web TV, . Compare the various standards and schemes which differ between the Americas, Europe, and Asia. Attempts to gain real-time support for audio/video streaming at the low level internet access are a big portion of the upcoming new web version.
Expect many more changes in these areas in the future as the internet evolves.