中文摘要：

目的去除彩色图像噪声。方法采用RGB灰度中心的彩色空间，使用四元数极表示的各向异性扩散方程给出彩色图像去噪的应用实例。结果使用非线性四元数扩散方程，可以有效地递减阶梯效应。结论基于四元数极表示，提出一个线性扩散方程和3个非线性扩散方程及它们的离散算法，其理论分析结果紧凑，容易应用。

英文摘要：

Objective--To remove noise from color images. Methods--Gray-centered RGB color space is adopted and application examples are shown by using anisotropic diffusion equations expressed in quaternion polar form. Results--The nonlinear quaternion diffusion process can reduce noise over the ramp and avoid the staircase effect. Conclusion--Based on quaternion polar, this paper presents a linear diffusion equation, three nonlinear diffusion equations and their discrete algorithms. The theo- retical analysis results are closed and easy to apply.