Construction of Biorthogonal Wavelet Transform Matrices with Mirror-symmetric Boundary-extension
边界镜像对称延拓双正交小波变换矩阵的构造

Iterative decomposition and reconstruction are needed in Mallat algorithm.In order to realize perfect reconstruction,finite-length signals must be extended to some extent before they can be transformed.The algorithm based on periodic boundary-extension always can be seen in the literature.Symmetric boundary-extension has better performance than periodic method in image processing,whereas the matrix transform method based on symmetric boundary-extension is seldom mentioned in the literature.A method of constructing decomposition and reconstruction matrices with arbitrary wavelet transform depth in mirror-symmetric boundary-extension is proposed for wavelet transform in matrix-vector multiplication,and the condition for perfect reconstruction of Mallat algorithm is proved.As an example,the base vectors and base graphs of Bior3.3 wavelet were given.The application of wavelet transform matrices in the wavelet-based image processing can avoid iterative operation,simplify the calculation and meanwhile reduce the edge effect evidently.