Construction of Wavelet Transform Matrices with Symmetric Boundary-Extension

In order to realize perfect reconstruction, finite-length signals must be extended in some way before they can be transformed. This paper first proposes a method of constructing wavelets decomposition and reconstruction matrices of wavelet coefficient without iterative calculation with symmetric boundary-extension of finite length signal, and correspondingly gives the base vectors and base graphs of 9/7 wavelet as an example. While the edge effect can be evidently reduced compared with the periodic boundary-extension method, the matrices constructed with symmetric boundary-extension of signal in this paper have better performance and can be widely used for image-partition processing based on wavelet method