数字脊波变换的实现与一种改进方法

脊波变换作为一种新的连续空间中函数的多尺度表示方法，其离散变换形式仍然有许多问题有待解决.目前大多将离散脊波变换形式看做Radon变换与小波变换的复合变换形式，进而对其分步进行处理.利用计算机图形学中的Bresenham算法思想，使得在实现Radon变换的过程中提高了变换的效率.与先前的最近邻方法相比，快速准确，并可完全重构.数值实验显示，与Z+2-p方法实现的脊波变换相比较，利用此方法生成的图像重构、压缩、去噪效果都有显著提高，为进一步的研究工作奠定了基础.

Implementation of Digital Ridgelet Transform and a New Method

Although the ridgelet transform is introduced as a new multiscale representation for functions on continuous spaces, discrete versions of the ridgelet transform that lead to algorithmic implementations remains to be solved. In this paper, approximate digital implementation is described by using a new method. As an important tool, Bresenham algorithm is used to offer exact reconstruction. Compared with the nearest-neighbor interpolation method, the new method has better performance such as stability against perturbations, low computation complexity and easy implementation. Compared with the ridgelet transform based on the Zp^2 method, the numerical results show that the new transform is more effective in reconstruction, compression and denoising images with straight edges, which lays a solid foundation for further research.