Techniques for handling non-stationarity in signals and images have been explored in different areas; wavelet analysis in applied mathematics, multi-rate filter bank techniques in digital signal processing and multi-resolution analysis in computer vision. Recent developments have indicated the connection between these various techniques. A goal of this work is to make a thorough exploration of the connections between these three areas and present a unified view of existing problems, techniques and applications. Further, design of new regular wavelets, examination of associated computational structures and a study of the complexity of the wavelet transform are also pursued. Finally, design of non-separable multi-dimensional wavelets, new wavelet- based-sampling methods and application to image coding are attempted.
