基于字典学习与图拉普拉斯矩阵的图像降噪

Image Denoising Based on Dictionary Learning and the Graph Laplacian Matrix

为了获得更好的图像降噪效果,本文为图拉普拉斯矩阵引入正则化项,结合一般稀疏表示降噪模型,提出一种新的图像降噪模型,模型包括数据保真项、图拉普拉斯矩阵正则化项和稀疏约束项;同时提出选取归一化的图拉普拉斯矩阵的特征向量作为字典学习的首字典.仿真实验表明:本模型有较好的降噪效果,处理图像的峰值信噪比比双边滤波(BF)和非局部均值(NLM)高,且图像呈现出更清晰的外观和细节.

In order to achieve better image denoising, a new model is proposed by introducing the graph Laplacian matrix into the regularization term and combining it with the general sparse representation denoising model. The model consists of the data fidelity term, the graph Laplaeian matrix regularization term and the sparse constraint term. Also, this paper proposes choosing the eigenvectors of the normalized graph Laplacian matrix as the initial dictionary. The experimental results show that the proposed model achieves good denoising performance, it gains higher PSNR than BF and NLM, and exhibiting clearer appearance and details.