Abstract: Nonlocal Means Filtering（NLMF） method exhibits excellent performance for image denoising. However, the computational complexity of NLMF is too high, and some structure content of the original image is still visible in the residual noise. The existing NLMFs based preselection are analyzed, and it is pointed out that they all have deficiencies in terms of feature extraction from image patch, then a detail-preserving and fast NLMF algorithm is proposed via using the Singular Value Decomposition（SVD） in gradient domain to extract structure feature from image patch. The contributions to NLMF are：（1） a robust preselection approach to image patches based local structure feature; （2） to analyze relation between size of the similar sets and filtering performance, and automatic selection of similar patches; and （3） to construct the weight coefficient with structural similarity. In addition, the symmetry of Euclidean distance is considered to accelerate the proposed algorithm further. The experimental results show that the proposed algorithm can well remove the noise while preserving image details and obtains a good tradeoff between performance and running speed.

Key words: Nonlocal Means Filtering（NLMF）, Singular Value Decomposition（SVD） in gradient domain, image feature, preselection, structure similarity weight

摘要： 非局部均值滤波方法具有优异的去噪性能，但该算法计算复杂度太高，且滤波后图像有大量结构残留。研究了基于预选择的非局部均值滤波方法，并指出已有方法在提取图像子块特征方面的不足。利用梯度域奇异值分解提取图像子块的结构特征，提出一种有效保持细节特征的快速非局部滤波方法。主要贡献有：（1）基于局部结构特征的鲁棒预选择方法；（2）相似集大小与滤波性能的关系以及相似子块的自动选取；（3）结构相似权系数的构造。利用欧氏距离的对称性进一步提高运行速度。实验结果表明，该方法在去除噪声的同时能有效地保持图像细节信息，取得滤波性能与运行速度之间较好的平衡。

关键词: 非局部滤波, 梯度域奇异值分解, 图像特征, 预选择, 结构相似权系数