The semivariogram of the image is estimated. Based on this we estimate the zone of influence. If r is the zone of influence of the semivariogram function of the picture, then we sample the picture using a square sampling design with side length equal to a X r, where a is a factor less than one. A kriging estimator is used to estimate the pixels not included in the sample. Under the assumptions of the process being wide sense stationary this kriging estimator is best linear unbiased. The mean square error is calculated, and we prove that as a goes to zero the decompressed image converges to the original. The convergence is with probability one (convergence in probability). The algorithm is lossy, and tests using popular images are presented. Comparison of this algorithm with other popular image compression algorithms are made. The comparisons include compression ratio, and a measure of distance between the original image, and the decompressed image.
Evangelos A. Yfantis,
Matthew Y. Au,
"Image compression algorithm based on kriging", Proc. SPIE 1903, Image and Video Processing, (8 April 1993); doi: 10.1117/12.143130; https://doi.org/10.1117/12.143130