关键词: 降维, 核范数, 代价函数, 低秩矩阵逼近, 鲁棒性

Abstract: In consideration of problems of image denoising by Nuclear Norm Minimization(NNM) for strong noise-submerged images,a robust NNM method is proposed for image denoising.Based on inspiration of original NNM,the proposed denoising method constructs a cost function for dimensionality reduction.But in order to be robust to the influence of noises during dimensionality reduction and to improve the ability of de-noising,the cost function adds the L1 norm of noises as its regularization term.And then,a low-rank image of the high dimension noisy image is iteratively recovered by minimizing the cost function to reach the purpose of denoising.Experimental results show that the proposed method has good performance compared with the NNM method and Block Method of 3-Dimension(BM3D).

Key words: dimension reduction, nuclear norm, cost function, low-rank matrix approximation, robustness