基于分数阶偏微分方程的彩色图像去噪新方法  

Novel color image denoising method based on fractional-order partial differential equation

作　　者：张富平[1] 周尚波[1] 赵灿 

机构地区：[1]重庆大学计算机学院,重庆400044 [2]昆山华恒焊接股份有限公司,江苏昆山215300

出　　处：《计算机应用研究》2013年第3期946-949,共4页Application Research of Computers

基　　金：国家自然科学基金资助项目(61004112)

摘　　要：为了克服现有彩色图像去噪方法不能有效抑制边缘噪声和保持纹理信息的缺点,提出了一种结合了离散四元数傅里叶变换(DQFT)和分数阶微分理论的彩色图像去噪改进方法。算法采用四元数矩阵表示一幅彩色图像,首先对该四元数矩阵进行离散傅里叶变换;然后将其代入基于分数阶微分的能量泛函极小值求解过程中,利用变分原理求解并推导出去噪模型,并与两种传统彩色图像去噪模型进行实验比较。实验结果表明,提出的模型在去噪效果和纹理保护方面都有更好的表现。The traditional methods for color image denoising usually can＇ t smooth the edge noise effectively and can＇ t protect the texture information Well. To overcome these shortcomings, this paper proposed a novel method for color image denoising which combined DQFT with the theory of fractional order differentiation. The method used a quaternion matrix to represent a color image, and it was carried out by following procedures. Firstly, transformed the quaternion matrix to the DQFI＂ domain. Secondly, applied it to the process of a fractional-order-differentiation-based energy function to seek its minimum, used the variational principle, to solve this minimization problem and then inferred the proposed method. Finally, compared the method with two traditional methods for color image denoising to evaluate its superiority. The experimental results show that the pro- posed method has better performance in denoising and protection of the details.

关 键 词：彩色图像去噪 四元数 离散四元数傅里叶变换 分数阶微分 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]