||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 nal 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 denitions of the progressiveness and the optimality in the progressive transmission
here. Since we show that there are dierent possibilities to dene progressiveness, we are
going to give and prove sucient conditions that imply the dierent progressive properties.
The linear transform-based compression will be considered separately, where further sucient
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 dierent 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 rst 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 suer from blocking artefacts. There is also a
ringing artefact observable along the edges in JPEG or JPEG2000 compressed images at high
compression ratios. One way of alleviating these eects is to preprocess the image before compression.
We shall consider a previously proposed preprocessing method here, which is based
on edge-adaptive ltering. The ltering is achieved with non-linear diusion processes. The
previous results did not give a complete understanding of the underlying processes and they did
not give an analysis of the dierent parameter choices. A visual testing of the method was also
missing. We complete the analysis by proposing diusion methods that are appropriate for preprocessing.
We consider methods for adjusting the parameters for these diusion processes. We
show that they reduce the artifacts, help in preserving the edges, and that they can improve the
visual quality. However, diculties can arise when preprocessing images with highly irregular
texture. Due to visual phenomena, the visibility of artefacts is low in this case. Preprocessing
may yield a visible blur for such images and an inferior visual quality when compared to the
compression without preprocessing.
This research was supported by the Grant Sa449/8 of the German Research Foundation
(DFG). I am grateful to Professor Dietmar Saupe and to Professor Kenneth Rose for carefully
reading my thesis and giving helpful suggestions in their reviews.