计算小波变换的Mallat算法需要进行逐级分解和重构，对于有限长信号的小波变换来说，为了保证其完全重构，有必要对其进行边界延拓。基于边界周期延拓的小波变换算法极易实现，也常见于文献，而边界对称延拓较周期延拓则更适合用于信号和图像的处理，但基于边界对称延拓的小波变换矩阵实现方法却很少出现在文献中。为了用矩阵-向量乘积实现信号的小波变换，给出了一种在信号镜像对称延拓方式下，任意深度小波变换矩阵的构造方法，并证明了该延拓方式下实现Mallat算法的完全重构条件。作为实例，绘出了Bior3.3小波的分解和重构矩阵的基向量及波形图。将构造的变换矩阵用于基于小波的图像处理中，不仅可以避免逐级迭代，大大简化运算量，而且边界效应也明显减少。

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.