基于四元数表示的彩色图像泊松噪声去噪

Poisson noise removal for color images using quaternion representation

为了整体处理彩色图像,提出了一种基于四元数的去除泊松噪声的加权平均滤波器.首先,基于彩色图像四元数表示法,将一幅彩色图像表示为一个纯四元数矩阵,并利用四元数代数理论定义了重建图像和原始图像之间的四元数均方误差;然后,结合非局部均值滤波的基本思想,采用拉格朗日乘数法推导出使QMSE紧上界最小的加权系数;最后,基于这些最优加权系数,对四元数表示的像素值进行加权平均,构造出四元数最优权值非局部均值滤波器,并将其应用于彩色图像泊松噪声去噪.针对常用标准图像的对比实验结果表明,所提的滤波器优于现有的四元数滤波器以及传统的基于向量方法的滤波器和基于分量独立处理方法的滤波器.

In order to process color images holistically,a quaternion weighted mean filter for Poisson noise removal in color images is presented.First,a color image is represented by a pure quaternion matrix by using the quaternion representation of color images.After that,the quaternion mean square error（QMSE） betw een the restored color image and the original one is defined based on the algebra of quaternions.Then,combining w ith the essential idea of the non-local means filter,the optimal w eights for minimizing the tight bound of QMSE are obtained by using the method of Lagrange multipliers.Finally,the w eighted average of the observed quaternion representation is obtained,and a quaternion optimal w eights non-local means filter（QOWNLMF） for Poisson noise removal for color image is constructed by using the optimal w eights.The comparative experiment results of commonly used standard images demonstrate that the proposed filter performs better than the existing quaternion filters and the conventional vector-based filter and component-w ise filter.