基于稀疏表示与加权核范数最小化的图像去噪算法

Image Denoising Using Sparse Representation and Weighted Nuclear Norm Minimization

为解决一部分纹理数据在运用加权核范数最小化处理低秩矩阵逼近时出现丢失的问题,提出一种基于稀疏表示与加权核范数最小化的图像去噪算法。稀疏表示用于辅助重构清晰图像,加权核范数最小化用于图像块样本的低秩矩阵逼近。通过分析纹理数据找出熵较大的非平滑块,运用一种奇异值维纳滤波,从其差异矩阵中找出丢失的部分纹理信息,并将其与低秩去噪结果融合。实验结果表明,该算法能够保持图像的细小纹理,去噪效果更好,具有良好的鲁棒性与泛化性。

To solve the problem that some texture structures will be lost when weighted nuclear norm minimization is used to deal with low rank approximation,an image denoising algorithm based on sparse representation and weighted nuclear norm minimization is pro-posed. Sparse representation is used to reconstruct the clear image. Weighted nuclear norm minimization is used to low rank matrix ap-proximation of image. Smooth patches which have larger entropy can be found by analyzing texture of patches. Missing texture of the im-age was obtained by using the proposed Wiener filter based singular value from the difference matrix of non-smooth patches to have the integration and result of low rank denoising. Experimental results show that the proposed algorithm can maintain the fine texture of the image and have better effect of denoising and robustness and generalization performances.