山西大学学报（自然科学版）2026，Vol.49Issue(2)：272-283,12.DOI:10.13451/j.sxu.ns.2025039
低维流形正则的三重余量Wasserstein距离图像去噪模型
Triple Residual Wasserstein Distance Image Denoising Model with Low Dimensional Manifold Regularization
摘要
Abstract
With the development of modern imaging technology,an imaging device can instantly obtain multiple images containing the same content.However,these images are sometimes difficult to avoid noise during acquisition,transmission,storage,and pro-cessing.Therefore,it is a realistic and meaningful research topic to restore a clean image from multiple degraded images.In this pa-per,a triple residual Wasserstein distance optimization model with low dimensional manifold prior regularization is proposed,and the model is applied to image denoising.Firstly,the regularization term of the image denoising model is constructed by utilizing the image prior information of the low-dimensional manifold nested in the high-dimensional space.By using the Wasserstein distance derived from the optimal transmission theory,the residual distribution of the restored image is forced to approximate the reference re-sidual distribution,achieving noise estimation of degraded images.Secondly,the proposed model confirms that the regularization of low dimensional manifold in image and the constraint of residual Wasserstein distance distribution complement each other,rather than being isolated and unrelated.The clever combination of the two contributes to the improvement of image restoration perfor-mance.Finally,the alternating iterative optimization algorithm of histogram matching and weighted non local Laplacian has the char-acteristics of good image restoration effect and high algorithm efficiency.Numerical experiments show that compared with image de-noising methods in recent years,the proposed method has advantages in both subjective and objective evaluation.The results indi-cate that the algorithm proposed in this paper has improved the average Peak Signal to Noise Ratio(PSNR)by 1.23%and 0.73%re-spectively compared to Wasserstein Driven Low-Dimensional Manifold Model(W-LDMM)and Multiple Residual Wasserstein Driv-en Model(MRWM),which have excellent denoising performance.Additionally,the computation time has been reduced by 25.58%and 93.21%respectively.关键词
直方图匹配/先验信息/交替迭代/概率分布Key words
histogram matching/prior information/alternate iteration/probability distribution分类
数理科学引用本文复制引用
何瑞强,马小军,焦莉娟..低维流形正则的三重余量Wasserstein距离图像去噪模型[J].山西大学学报（自然科学版）,2026,49(2):272-283,12.基金项目
山西省基础研究计划资助项目(202303021221175 （）
202303021222208) （）
