新的彩色图像去噪与增强模型  

New color image denoising and enhancement model

作　　者：王贵[1] 管志成[1] 

机构地区：[1]浙江大学计算机图形与图像处理研究所

出　　处：《浙江大学学报（工学版）》2005年第9期1343-1347,共5页Journal of Zhejiang University：Engineering Science

摘　　要：为了在对彩色图像进行去噪、增强的过程中保护原彩色图像的色彩信息,提出了一个具有稳定性算法的新的泛函模型.该模型将彩色数据分离为色彩和亮度两部分.将每个像素的三个色彩通道看成是一个三维矢量,则矢量的单位方向向量和亮度分别表示像素的色彩和亮度.亮度部分用常见的发展已较完善的各向异性扩散流来处理, 针对色彩部分的处理,新模型基于求解有约束泛函的惩罚函数方法,将对色彩的单位模约束移至能量泛函中.用Leray-Schauder不动点定理证明了该泛函的梯度下降流方程组解的存在性和唯一性,并与相关的彩色图像去噪模型进行了比较.数值实验结果表明,新的模型在去噪的同时保护了原图的彩色特征,且算法稳定.A new functional model was proposed for denoising and enhancing the chromatic component of color images. This model separated the color data into chromaticity and brightness. The three color channels of each pixel were regard as 3-dimensional vector, and the unit directional vector and its magnitude represented the chromaticity and the pixel brightness separately. The brightness component was processed by the popular and well-established anisotropic diffusion flows. Considering the processing of the chromatic component, the proposed model moved the unit norm restriction on chromatic component into the new energy functional based on the penalty function approach. The existence and uniqueness of the solution to the gradient descent flow corresponding to the new functional were proved by Leray-Schauder fixed point theorem, and the new model was compared with the correlative chromatic denoising models. Numerical experimental results show that the new model can preserve the chromatic characteristics while denoising, and that the algorithm is stable.

关 键 词：去躁 增强 惩罚函数 梯度下降流 Leray—Schauder不动点定理 

分 类 号：O175.2[理学—数学] TN911.73[理学—基础数学]