中文摘要：

利用矩阵值函数空间的多分辨分析理论研究了四元数多分辨分析理论，给出了四元数尺度函数与小波的构造．这种设计为我们提供了丰富的选择参数．此外给出了系数矩阵的一般表达式．

英文摘要：

In this paper we study quaternion-valued multi-resolution analysis by the theory of multi- resolution in vector-valued function space. We give the construction of quaternion-valued scaling functions and wavelets. It includes the presence of negative indices to two-scale coefficient of both scaling functions and wavelets. It has variable parameters providing rich classes of designs. Moreover, we give the more general expression of coefficient matrices.