The basic principle is very simple. Imagine taking out just one horizontal line from the black and white image. The gray levels for the pixels in this line form a sequence of numbers between 0 and 255. In this sequence many values are very close to their neighbors - sudden jumps only occur if there was a sudden transition there in brightness (say from a light object to a dark wall) in the image. So a piece of this sequence could look like:

45 45 46 46 47 48 53 101 104 105 106 106 107 106 106 106.

If you are given any 2 numbers a and b then you completely characterize them by giving their average s = (a+b)/2 and their difference d = a-b. (Because a = s+d/2, b = s-d/2). The averages and differences for successive pairs in our sequence are:

The sequence of differences has many more really small entries than large entries, and such sequences are easy to compress. Moreover, we can now easily make a small change to the d-sequence that would make it even more compressible. For instance, if we replace in the d-sequence every entry that is a 0 or 1 or -1 by 0:

If we now recompute the original sequence (rounding off if necessary, so that we get integers) by a' = s+d'/2 , b' = s-d'/2, then we get:

45 45 46 46 47 47 53 101 104 104 106 106 106 106 106 106