摘要： 针对核范数降维去噪方法对强噪声去除效果不佳的问题,提出一种鲁棒核范数降维的去噪方法。该方法在核范数最小化的思想下构建图像降维的代价函数,并在代价函数中增加噪声的L1范数作为其正规化项,用以改善降维时噪声对降维的影响,提高降维的鲁棒性,通过最小化 代价函数,从高维的噪声图像中迭代求解出低秩的图像,以达到去噪的目的。实验结果表明,与核范数降维方法和三维块匹配(BM3D)方法相比,该方法能获得更好的去噪效果。

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

中图分类号: 

• TP391