Trees, windows and tiles for wavelet image compression

We investigate the task of compressing an image by using different probability models for compressing different regions of the image. In an earlier paper, we introduced a class of probability models for images, the k-rectangular tiling of an image, which is formed by partitioning the image into k rectangular regions and generating the coefficients within each region by using a probability model selected from a finite class C of probability models. We also describe a computationally efficient sequential probability assignment algorithm that is able to code an image with a code length that is close to the code length produced by the best model in the class. In this paper, we investigate the performance of the algorithm experimentally on the task of compressing wavelet subbands. We compare the method with compression methods that aim to compress as well as the best pruning of a quadtree and compression methods that exploit the local statistics in a window around the coefficient being compressed. For a class C consisting of a small number of Laplacian distributions and the uniform distribution, we find that the best tiling method works best, but the difference in performance is significant for only a few of the images tested.