中文摘要：

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.

英文摘要：

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.