"Eigen images" for categorical data

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I have a sequence of categorical images. For a two category image, each image pixel can have one of two values. I would like to analyze these images using a technique like eigen images. The goal is to express each image as a linear combination of some basis vectors. Is there a mathematical technique/transform that could do this ? I think eigen image methodology won't work as the data is discrete and not continuous. If anyone can point me in the right direction, that would be great!

Thanks!