For a given quality of image (or quality of compression), Multiple 8x8 JPEG images can have the same DCT (Discrete cosine transform) matrix, for a given quality of JPEG compression. I want to find the number of those 8 by 8 JPEG files which have different DCT codes.
I write the question in a different way:
Assume a set $A$ of images, which is initially empty. We consider all possible DCT's for 8 by 8 Jpegs one by one, and convert each one to an image. If the image already exists in the set $A$, we throw it away, otherwise, we put it in set $A$. After we are done with all possible DCT's, how many images are in the set $A$? (what is the cardinality of $A$?)
Wikipedia has the formula for the DCT conversion. But I cannot realize from that how to find what I need. I am wondering how to solve it or if that is already solved in the literature. Any idea?