基于伽马范数最小化的图像去噪算法

Gamma norm minimization based image denoising algorithm

针对核范数有偏近似秩函数导致基于核范数最小化的传统去噪方法去噪性能较差的问题,基于低秩理论,提出一种基于伽马范数最小化的图像去噪算法。首先对噪声图像重叠分块,然后基于结构相似性指数自适应搜索与当前图像块最相似的若干非局部图像块以组成相似图像块矩阵,进而利用非凸伽马范数无偏近似矩阵秩函数构建低秩去噪模型,最后基于奇异值分解对所得低秩去噪优化问题求解,并将去噪图像块重组为去噪图像。仿真结果表明,与现有主流PID、NLM、BM3D、NNM、WNNM、DnCNN和FFDNet算法相比,所提算法可较显著地消除高斯噪声,且可较好地恢复原始图像细节。

Focusing on the issue of rather poor denoising performance of the traditional kernel norm minimization based method caused by the biased approximation of kernel norm to rank function,based on the low-rank theory,a gamma norm minimization based image denoising algorithm was developed.The noisy image was firstly divided into some overlapping patches via the proposed algorithm,and then several non-local image patches most similar to the current image patch were sought adaptively based on the structural similarity index to form the similar image patch matrix.Subsequently,the non-convex gamma norm could be exploited to obtain unbiased approximation of the matrix rank function such that the low-rank denoising model could be constructed.Finally,the obtained low-rank denoising optimization issue could be tackled on the basis of singular value decomposition,and therefore the denoised image patches could be re-constructed as a denoised image.Simulation results demonstrate that,compared to the existing state-of-the-art PID,NLM,BM3D,NNM,WNNM,DnCNN and FFDNet algorithms,the developed method can eliminate Gaussian noise more considerably and retrieve the original image details rather precisely.