Design Of The Bivariate Non-separable Wavelet Filters And Application

As an important part of the theory for non-separable wavelets, the design of non-separable wavelets filter banks has already became the hotspot of research on wavelet theory. Compared with separable wavelets, non-separable wavelets have more design freedom. Furthermore, they process the multi-dimensional signal as a whole, this will be more advantageous to extracting the useful information from the signal in each direction.With the foundation of the former research achievements and my research work, this thesis proposes a new method for designing two-dimensional non-separable wavelet filter based on the tensor products of polynomial vector. By this method, we only need to solve some equations to construct the wavelet filter, which largely simplifies the construction process. The main content of this paper includes five parts as follows:In chapter 1, we simply introduce the developing history and present research situation of the wavelets and the non-separable wavelets.In chapter 2, we discuss the fundamental theories of designing two-dimensional wavelets filter banks in detail.Chapter 3 is the most important contents of this paper. Firstly, we introduce some basic notions and assumptions that are essential to prove the main theorems. Secondly, we give a detailed proof of these theorems. At last we present parametric expressions for orthogonal non-separable wavelets filter banks.In chapter 4, we mainly studied the application of non-separable wavelets in face recognition. At first we propose a new algorithm for face recognition. And then,we can find the advantage of using this approach in facial feature extraction through the analysis of related experiment results.In chapter 5, we give the summary and forecast of this paper.