An exploration of various ways of computing wavelet transforms over integers.

摘要

Wavelet transforms have been used in a variety of applications, including image data compression. Building invertible integer wavelet transforms is one approach to achieve lossless coding. In this thesis, we explore various ways of computing wavelet transforms over integers. The theories behind these explorations are studied. Design methodologies to generate integer wavelet transforms over finite integer rings and Galois fields are presented. The method of constructing invertible integer wavelet transforms using lifting steps is also examined. Experiments regarding potential applications of these wavelet transforms in image data compression as well as still image watermarking are conducted. The results and some observations are presented in this thesis. Finally, we give some recommendations of other potential applications of these integer wavelet transforms.