I'm new to image processing and I'm trying learn about image AA and upsampling algorithms such as those used in game engines. Engines tend to use jitter in order to get multiple samples from the same image followed by some sort of image alignment. This can be naturally done by jittering the camera angle.
To keep things simple, I would like to get test data by starting from one ultra high-res image, e.g. an 8K picture and then sample multiple 720p images from it and then use them to try to reconstruct a high-res image, e.g. a 1440p or 4K image. What is the correct way to do the downsampling step? How should I implement downsampling of the high-res image, so that the low-res images would correspond as closely as possible with what a game engine with camera jitter would produce if it rendered the same scene multiple times at the lower resolution?
Pointers to articles that discuss this is enough (and actually preferred, since I would like to understand the math).