You could use OpenGL, but this means you'll have to write a lot of shader code to do this. And since you (I assume) don't have to make it a real time program, you might as well use the CPU instead. If you are allowed to use it in course, take a look at OpenCV, which is one of the most used libraries for image processing / computer vision.

It should have at least Sobel and median filters built in, but they are really easy to implement yourself (and doing so will teach you some of the most importent basic tools and techniques in field), like simple matrix convolutions, image formats and the like.