中文摘要：

低秩表示算法是通过最小化矩阵核范数来求解低秩表示系数,然而待求解的低秩表示系数的稀疏性低的要求导致求解不稳定的情况。针对这个问题,在基本的图像低秩表示算法中引入一个约束条件来保证系数的最稀疏性,在特征提取过程中来获取图像数据在各个空间中的整体几何结构。通过对不同的加噪图像进行去噪恢复和分类识别,并与现有算法对比,证明改进算法的低秩特性更具有效性和判别性。在ORL库和Yale B库人脸库上的实验结果证明,改进的算法比原算法在图像去噪效果上更有效,具有较高的识别率。

英文摘要：

Low rank representation is achieved by minimizing the nuclear matrix norm to obtain the coefficient of low rank representation,however,an unstable situation can be obtained due to the requirements for the low sparse sex of the coefficient of low rank representation.Aiming at this problem,by introducing a constraint conditions in the basic low rank algorithm to ensure the most sparse coefficient,then the overall geometry of the image data from various space in the process of feature extraction was obtained.To verify the efficient and discrimination of low rank characteristics,some different noise images are used to restore the noise and classification using the presented method compared with the existing algorithm.The experimental results on ORL and Yale B database show that the improved algorithm is more effective than the original algorithm on image denoising,and has a higher recognition rate.