Wasserstein距离驱动的低维流形图像修复  

Low-dimensional Manifold Image Inpainting Driven by Wasserstein Distance

作　　者：何瑞强[1] 王立志[1] 王彩云[1] HE Ruiqiang;WANG Lizhi;WANG Caiyun(Department of Mathematics,Xinzhou Teachers University,Xinzhou 034000,China)

机构地区：[1]忻州师范学院数学系,山西忻州034000

出　　处：《山西大学学报（自然科学版）》2021年第5期897-906,共10页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(61772389,61941111);山西省应用基础研究青年科技研究基金(201801D221033);忻州师范学院科研基金(2019KY07)。

摘　　要：针对含噪图像修复问题,提出一种新的Wasserstein距离驱动的低维流形模型,该模型巧妙组合噪声Wasser‐stein距离正则和图像低维流形约束。首先,Wasserstein距离将被估计噪声直方图和参照噪声直方图之间的差异最小化,进而提升噪声估计准确性。其次,基于自然图像块流形的低维结构,将图像块流形维数作为图像修复模型的数据项。最后,利用直方图匹配和加权非局部Laplace求解优化模型,并设计出Wasserstein距离驱动的低维流形图像修复算法。所提方法将Wasserstein距离噪声正则和低维流形图像约束相互融合,数值实验表明,与近年来几种图像修复方法相比,提出的方法在定量性能和视觉效果两方面都有优势。在两类测试图像上,文章算法比块一致的离散余弦变换算法(Patch Consensus-Discrete Cosine Transformation,PACO-DCT)算法在平均PSNR方面分别提高了1.97%和0.94%,同时用时缩短了10.6%。Aiming at the problem of noisy image inpainting, a new Wasserstein distance driven low-dimensional manifold model was proposed, and the model cleverly combined the noise Wasserstein distance regularization and the image low-dimensional manifold constraint. First, the Wasserstein distance minimized the difference between the estimated noise histogram and the reference noise histogram, thereby improving the accuracy of noise estimation. Second, based on the low-dimensional structure of the natural image block manifold, the dimension of the image block manifold was utilized as the data item of the image inpainting model. Finally, histogram matching and weighted non-local Laplace were used to solve the optimization model, and a Wasserstein distance-driven lowdimensional manifold image inpainting algorithm was designed. The key idea of the proposed method was that the Wasserstein distance noise regularization and the low-dimensional manifold image constraint were complementary to each other, rather than in isolation. The numerical experiments show that compared with several image inpainting methods, the proposed method has advantages in both quantitative performance and visual effect. On the two types of test images, compared with the existing excellent Patch Consensus-Discrete Cosine Transformation(PACO-DCT) algorithm, the algorithm in this paper improves the average PSNR by 1. 97%and 0. 94%, and reduces the time by 10. 6%.

关 键 词：Wasserstein距离 低维流形 图像修复 直方图匹配 噪声估计 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]