基于最小方差估计的图像低秩去噪  

Low-rank Image Denoising Based on Minimum Variance Estimator

作　　者：郭强[1,2,3] 张彩明[2,3] 张云峰[1,3] 刘慧[1,3] 沈晓红[1,3] 

机构地区：[1]山东财经大学计算机科学与技术学院,济南250014 [2]山东大学计算机科学与技术学院,济南250101 [3]山东省数字媒体技术重点实验室,济南250014

出　　处：《计算机辅助设计与图形学学报》2015年第12期2237-2246,共10页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61202150;61202151;61272245;61472220);中国博士后科学基金(2013M531600);山东省科技发展计划(2014GGX101037;2015GGX101004);山东省高校优秀科研创新团队资助项目

摘　　要：自然图像通常表现出一定的自相似性,这种相似性意味着由相似图像块所构成的图像矩阵具有低秩性.基于图像的这种低秩性和最小方差估计理论,提出一种有效的迭代去噪方法.该方法通过构造图像相似块矩阵将图像去噪问题转化为低秩矩阵估计问题,并由最小方差估计理论导出低秩矩阵的估计值;在此基础上,对图像块的估计值进行加权平均即可重构出去噪后的图像;针对少量噪声残留问题,将去噪方法与反向投影方法相结合实现图像的迭代去噪,进一步抑制图像中残留的噪声.实验结果表明,采用文中方法产生的去噪图像不仅具有较高的峰值信噪比和特征相似度均值,而且具有很好的视觉效果.Natural images always exhibit a certain nonlocal self-similarity property, which implies that the patch matrix formed by similar image patches is low-rank. Based on the low-rank approximation and the minimum variance estimate theory, this paper proposes an efficient iterative denoising method. The proposed method trans-lates the image denoising issue into the estimate of some low-rank matrices by constructing similar patch matrices. The minimum variance estimator is exploited to yield the estimates of these matrices, and a denoised image is achieved by aggregating all denoised image patches. In order to further reduce the residual noise in the denoised image, an iterative version of the proposed method based on back-projection process is introduced. Experimental results show that the proposed method obtains not only higher peak signal-to-noise ratio and feature structural si-milarity values but also better visual quality.

关 键 词：图像去噪 奇异值分解 最小方差估计 低秩性 自相似性 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]