Assume that I have samples from an image, but the samples aren't on a grid, but instead there are multiple lowres versions of the original where the sampling locations are slightly jittered, so the pixels in the lowres images haven't been sampled from the exact same location (i.e. the lowres images aren't identical, however assume I now the precise sampling location for each pixel in the lowres images). What methods exist for reconstructing the original image?
The most general case of this is assume you have random samples from the image (making the assumption here that the image is a continuous signal). Are there optimal algorithms for reconstruction? For example, this assumes that the sampling density can vary spatially in the image, so that some regions have very few samples while others are densely sampled.
My DSP books seem to concentrate on methods where some signal has been sampled at fixed periodic intervals, so they don't seem to be of much use.
EDIT: Pointers to literature that discusses this would be great, even knowing what such reconstruction problems are called!