Applications of Multiwavelets to Image Compression

(ABSTRACT) Methods for digital image compression have been the subject of much study over the past decade. Advances in wavelet transforms and quantization methods have produced algorithms capable of surpassing the existing image compression standards like the Joint Photographic Experts Group (JPEG) algorithm. For best performance in image compression, wavelet transforms require filters that combine a number of desirable properties, such as orthogo-nality and symmetry. However, the design possibilities for wavelets are limited because they cannot simultaneously possess all of these desirable properties. The relatively new field of multiwavelets shows promise in removing some of the limitations of wavelets. Multiwavelets offer more design options and hence can combine all desirable transform features. The few previously published results of multiwavelet-based image compression have mostly fallen short of the performance enjoyed by the current wavelet algorithms. This thesis presents new multiwavelet transform methods and measurements that verify the potential benefits of multiwavelets. Using a zerotree quantization scheme modified to better match the unique decomposition properties of multiwavelets, it is shown that the latest multiwavelet filters can give performance equal to, or in many cases superior to, the current wavelet filters. The performance of multiwavelet packets is also explored for the first time and is shown to be competitive to that of wavelet packets in some cases. The wavelet and multiwavelet filter banks are tested on a much wider range of images than in the usual literature, providing a better analysis of the benefits and drawbacks of each. Acknowledgments I would like to thank my advisor, Dr. Bell. Without the technical and financial assistance she provided I could not have completed this thesis. Her suggestions and corrections for this thesis have improved it enormously. She always helped me keep sight of the " big picture " and focus on those areas that needed the most attention. My thanks also go to my wife, Kim, whose help in proofreading this thesis is much appreciated, and Dr. Brian Woerner for agreeing to serve on my committee at the last minute. I would like to thank a number of people from the Virginia Tech physics department. In particular, I am indebted to professors Dale Long, John Ficenec, and Joseph Slawny for their support and guidance in my days as a physics student. I am also grateful for the friendship and assistance provided by my colleagues in physics, Mike Kleder and Zoltan Toroczkai. Without the support of …