Can we make a picture bigger without the jaggies and blurriness?
Essentially we take a lame interpolation (bilinear or bicubic) and futz with it using an approximation of the sensor that created (or could have created) the image and some differential geometry that lets us push the isophotes around to clean up the jaggies and blurriness.
The tricks are in the details of when you use certain differential geometric functions and how you balance them. The contribution I am most proud of was the development of a function that would stop us from over-smoothing the image, given the tricks we were playing. One of the things that still bothers me is a degree of over sharpening. Some of the sharpening looks good, other bits unnecessary.
The "generalized" comes in because interpolation is used in more than enlargement. Any kind of image warping will have some kind of interpolation.
Let's talk about what I can do for you (demo reel on request).