基于K-SVD和残差比的低信噪比图像稀疏表示去噪算法

Low SNR image denoising via sparse and redundant representations over K-SVD algorithm and residual ratio iteration termination

针对低信噪比图像去噪问题,提出了一种基于K-SVD(Singular Value Decomposition)和残差比(Residual Ratio Iteration Termination)的正交匹配追踪(Orthogonal Matching Pursuit,OMP)图像稀疏分解去噪算法。该算法利用K-SVD算法将离散余弦变换(Discrete cosine transform,DCT)框架产生的冗余字典训练成能够有效反映图像结构特征的超完备字典,以实现图像的有效表示。然后以残差比作为OMP算法迭代的终止条件来实现图像的去噪。实验表明,该算法相对于传统基于Symlets小波图像去噪、基于Contourlet变换的图像去噪,以及基于DCT冗余字典的稀疏表示图像去噪,能够更加有效地滤除低信噪比图像中的高斯白噪声,保留原图像的有用信息。

For the low SNR(Signal to Noise Ratio) images denoising,a new algorithm is proposed based on K-SVD and residual ratio iteration termination.Firstly,an initial redundant dictionary is produced under the DCT framework and the dictionary is trained by K-SVD algorithm through the noisy image.A new dictionary that reflects the structure of the image effectively is produced.Then,the residual ratio is used as the iteration termination of OMP algorithm to remove the zero-mean white and homogeneous Gaussian additive noise from a given image.Different kinds of images with different noise levels are used to test the algorithm.The results show that the algorithm has strong robustness and performs better than the image denoising algorithm using Symlets wavelet,Contourlet and sparse representation based on DCT redundant dictionary.