Image to sub-image

Firstly, the image is divided into many 8 * 8 sub images, each sub image is FFT, and 64 coefficients in each sub image are sorted according to the variance of each coefficient. After that, the small transformation coefficients are removed, only 16 coefficients are retained, and the 4:1 image compression is realized.

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

64 coefficients in each sub image are sorted according to the variance of each coefficient

Variance relative to what? Variance is a statistical property, not a property of individual numbers.

[KALYAN ACHARJYA]

As per my understanding-

1. Image subdivided to 8x8, let say total nxn blocks having 8x8 individual image block size
2. Replace with variance of individual blocks

Result will be nxn having variances of individual blocks sizes,right?

[Image Analyst]

For each 8 pixel-by-8 pixel block (of the n*n blocks total that cover the entire image) they do a fft2() to get real and imaginary 8x8 arrays (that's TWO arrays). So there are 2x8x8 or 128 coefficients - 64 real ones and 64 imaginary ones. Of those 64 they are (I guess) taking the variance of all the coefficients, like the variance of the n^2 (1,1) elements (upper left corner), the variance of the n^2 (1,2) elements, and so on down to the lower right corner, the (8,8) element. So now we'd have an 8x8 image where each element is the variance of the n^2 blocks. Then they sort and keep only 16 of the 64 coefficients and save those 2 * n^2 * 16 coefficients somehow in a file. The data will be reduced from the amount of data originally used to save the original image, thus leading to compression.