传统连续图像信号的采样过程采用的是矩形点阵结构。当连续图像信号的频带处于一个圆形区域之内时，正六边形点阵结构的采样密度比矩形点阵结构的采样密度要降低13．4％。但目前图像输入输出设备只支持矩形点阵结构的数字图像，所以首先讨论了满足Nyquist采样定理的正六边形点阵结构的采样矩阵(空间采样间隔)，及矩形点阵结构数字图像和正六边形点阵结构数字图像之间的转换。另一方面由于正六边形点阵结构的数字图像是不可分离信号，这给图像处理造成许多的不便。为此提出了一种基于可分离滤波器阵列的图像分解方法，降低了计算复杂度，得到类似矩形图像小波变换所得的多尺度分解结构，并给出重构图像的实验结果。

Traditionally, the most commonly used sampling lattice in image processing systems is the rectangular sampling lattice. However, when the signal is a circularly band-limited, the minimum sampling density for a hexagonal sampling lattice is 13.4% less than that for a rectangular sampling lattice. This result is one of the most attractive reasons for considering the hexagonal sampling lattice as an alternative to the rectangular lattice. Almost all the input/output devices only support the rectangular sampled digital images, so the transformation between the hexagonal sampling lattice and the rectangular sampling lattice is discussed in this paper, and the hexagonal sampling matrix satisfied Nyquist Sampling Theorem is given. Moreover hexagonal sampled digital images are non-separable signals. It is difficult to process a non-separable signal directly. In this paper, a multiresolution decomposition of hexagonal sampled images based on a separable filter bank is proposed. A multi-scale decomposition structure is obtained with low computation complexity, and the reconstructed image is presented.