Image Compression and Kriging

Abstract

In this research paper we use a kriging-like iterative method with changing interpolation neighborhoods and we also use the data estimated in the previous iteration in order to estimate the data of the present iteration. Our method is used for image compression and it constitutes a lossy compression algorithm. Due to multicolinearity neighboring pixels carry mostly the same information. Therefore if we reduce the’ amount of information by appropriate sampling of the image then the space needed to store this information is smaller than the space required by the original image. The semivariogram of the image is estimated. Based on this we estimate the zone of influence. If ris 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 × 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 algorithm is lossy, and tests using the image of Lenna are presented. Comparison of this algorithm with JPEG show that our algorithm has graceful degradation. By graceful degradation we mean that drastic reduction on the information used to produce the image results to recognizable images whose features fade away gradually.