基于回归分析和主成分分析的噪声方差估计方法  

Noise Variance Estimation Method Based on Regression Analysis and Principal Component Analysis

作　　者：吴疆[1] 尤飞[1] 蒋平 WU Jiang;YOU Fei;JIANG Ping(College of Information Engineering,Yulin University,Yulin 719000,China;School of Computer Science and Technology,Xidian University,Xi’an 710071,China)

机构地区：[1]榆林学院信息工程学院,榆林719000 [2]西安电子科技大学计算机学院,西安710071

出　　处：《电子与信息学报》2018年第5期1195-1201,共7页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(11641002);榆林市科技计划项目(Gy13-12);陕西省教育厅科研项目(11JK0636)~~

摘　　要：准确可靠的噪声强度估计是数字图像处理领域中一个重要的研究课题。噪声估计的难点在于如何提取用于估计的纯噪声信息,近几年,许多算法采用主成分分析技术来避免图像纹理信息的干扰,用最小特征值来估计噪声方差,可以有效地减少图像纹理信息对估计结果的影响,所以这类方法对于高频图像(丰富纹理图像)效果很好。由于图像块数量有限,最小特征值实际上比真实噪声方差小,而且图像块数量越少,偏差越大。如果直接把最小特征值作为估计方差,则容易低估计高噪声。该文通过回归分析确定最小特征值跟真实噪声方差的比值和图像块数量呈幂函数关系,因此可以通过最小特征值和幂函数关系得到真实的噪声方差。实验表明该文方法既能处理高频图像,又适合各种噪声水平,同时也能处理乘性高斯噪声。Accurate and reliable blind noise estimation is an important research topic of digital image processing. The main challenge is how to extract pure noise information for estimating. In recent years, many algorithms use principal component analysis technology to exclude the interference of image textures information, and estimate noise level by using the minimal eigenvalue. So that, the image textures have smallest effect on the minimal eigenvalue, thus this kind of methods performs well for high frequency image （image with abundant textures）. The minimal eigenvalue is actually smaller than the true noise variance because of limited image blocks, and the bias is the bigger if the number of image patches is the smaller. If the noise level is estimated as the smallest eigenvalue, the final result will be underestimated. It is found that the relation between the ratio of estimated result to real noise variance and the number of image blocks is power function by using regression analysis, thus the true noise level can be computed by using the minimal eigenvalue and the power function. The experiment results show that the proposed algorithm works well over a large range of visual content and noise conditions, and can process multiply Gaussian noise too.

关 键 词：噪声图像 高斯噪声 噪声估计 主成分分析 回归分析 

分 类 号：TN911.7[电子电信—通信与信息系统]