Edge Structure Preserving 2-D and 3-D Image Denoising by

I would like to express my sincere gratitude, and appreciation to my adviser Prof. Peihua Qiu, for his guidance, encouragement, and support to complete my PhD research. During a course on smoothing techniques and image processing, that I took in my first year of PhD program, he introduced me to some of the research areas on the application of statistics in image processing. Since then, he spent an enormous amount of time in training me, so that I can do well in research. I also want to express my appreciation to the other members of my committee, Prof. Douglas M. Hawkins, Prof. Hui Zou, and Prof. Sudipto Banerjee for their thought-provoking comments, encouragement, and support. Also, I would like to thank the School of Statistics for providing me an opportunity to carry out and complete my PhD research. i Image denoising is often used for pre-processing images so that subsequent image analyses are more reliable. Many existing methods can not preserve complicate