In passive imaging, the spatial information acquired is strictly bandlimited. Because of this limitation, a number of postprocessing strategies have been proposed to accomplish a measure of superresolution. These strategies incorporate prior information about the image to improve resolution. We show that unless this information is shift- variant, it is unable to contribute to any superresolution. Shift-variant information about the image can be shown to be equivalent to forcing a correlation among the basis images that represent the image. We show that accomplishing superresolution from this correlation is very difficult and has fundamental limitations. Finally, we discuss the potential gains available from using prior information and propose an acquisition strategy that in some cases could improve the potential for superresolution.