Experiments have shown that we can only memorize images up to a certain complexity level, after which, instead of memorizing the image itself, we, sort of, memorize a probability distribution in terms of which this image is "random" (in the intuitive sense of this word), and next time, we reproduce a "random" sample from this distribution. This random sample may be different from the original image, but since it belongs to the same distribution, it, hopefully, correctly reproduces the statistical characteristics of the original image.
The reason why a complex image cannot be accurately memorized is, probably, that our memory is limited. If storing the image itself exhausts this memory, we store its probability distribution instead. With this limitation in mind, we conclude that we cannot store arbitrary probability distributions either, only sufficient simple ones.
In this paper, we show that an arbitrary image is indeed either itself simple, or it can be generated by a simple probability distribution. This result provides a mathematical foundations for the above theoretical explanation of the randomized-memorization phenomena.