基于谱特征参数的图像稀疏降噪

Image Denoising via Sparse Representation with Spectral Parameter

提出一种基于谱特征参数的图像稀疏降噪算法。其采用稀疏重构理论为图像降噪框架,并将图论中的谱特征参数作为一约束条件,以有效克服传统稀疏重构中稀疏解不稳定的问题。该降噪算法将噪声图像块作为基础元素进行关系图构建,进而得到邻接矩阵。然后,求解该邻接矩阵对应的拉普拉斯矩阵,并对其进行特征分解,得到对应的特征向量,即谱特征参数。最后,将图像块矩阵与一定数目该高频谱特征参数所组成矩阵的乘积作为稀疏模型的正则项形成提出的算法模型。实验结果表明,与基于K-SVD的稀疏表示降噪算法相比,在相同参数的情况下提出的算法在多种类型噪声下对多幅图像的降噪效果都有着显著的提高。

An image denoising algorithm via sparse representation with spectral parameter is proposed.The theory of sparse reconstruction is adopted as the frame of image denoising,and spectral parameter is considered as a constraint condition to overcome the problem of sparse solution to be unstable.In the denoising algorithm,noisy image patches are treated as elements to construct relational graph,and,then the adjacent matrix is obtained.After that,the laplacian matrix corresponding to the adjacent matrix is deduced and relevant eigenvectors of the laplacian matrix,namely the spectral parameter,is solved by eigendecomposition.Finally,the product of image patches matrix and the matrix consisting of certain high frequency spectral parameter,as a regular term,is introduced into the sparse modle,which forms this algorithm modle.Experiments demonstrate that the denoising result of the proposed algorithm compared with that of sparse model of K-SVD leads to better performance on several images under four sorts of noise and the same conditon.