Progressiveness and preprocessing in image compression

The recent developments in the multimedia communication technology made it necessary to provide image compression standards with a number of functionalities such as the capability of progressive transmission of the code and more conformity with the human visual perception. The general purpose still image compression standard JPEG2000 for example, incorporates many such functionalities. This thesis contributes to the improvement of these functionalities by considering two special aspects: progressive transmission and preprocessing to improve the visual quality of the compressed images. In progressive transmission, the code for the image is sent in packets. The user attempting to view the image will be shown a sequence of ”previews” that approximate the final reconstruction with increasing quality, based on the incoming packets. This allows the user to terminate the decoding at an arbitrary point and quickly browse among a large number of images. Though many practical methods use optimisation for progressive transmission, a good understanding of the progressive behaviour and the optimality in this process has not been given yet. We give formal definitions of the progressiveness and the optimality in the progressive transmission here. Since we show that there are different possibilities to define progressiveness, we are going to give and prove sufficient conditions that imply the different progressive properties. The linear transform-based compression will be considered separately, where further sufficient conditions for progressiveness are given. We use this framework to analyse the underlying optimisation procedures in existing wavelet compression schemes. Our results can help the design of progressive compression systems. In most of the image compression standards, the images are described as linear combinations of given basis elements. Lossy compression is achieved by using an incomplete description. There are however compression methods that use a different kind of description. In fractal compression, the image is partitioned into a number of regions, each of which is approximated by some appropriate part of the same image. If we start with an arbitrary image and iterate these approximation steps, this procedure will converge to an approximation of the original image. Since the above description method is not necessarily perfect, its parameters constitute a lossy compression of the image. We give an optimal progressive transmission method for the fractal compression, which is the first result of this kind. In lossy compression, various kinds of error patterns can appear on the decompressed image. For example, the images compressed with JPEG suffer from blocking artefacts. There is also a