基于小世界模型和图论的图像去噪  

Image denoising based on graph theory and small world

作　　者：刘国金[1] 曾孝平[1] 田逢春[1] 刘刈[1] 

机构地区：[1]重庆大学通信工程学院,重庆400030

出　　处：《光电子．激光》2010年第1期149-153,共5页Journal of Optoelectronics·Laser

基　　金：教育部高等学校博士学科点科研基金资助项目(20070611013);重庆市自然科学基金资助项目(CSTC;2009BB2358;2008BB2164);重庆大学研究生创新基金资助项目(200909C1015;200911A1A0030319)

摘　　要：提出了一种基于图论的偏微分方程(PDE)图像去噪方法。在构造图的拓扑结构过程中,引入了小世界模型,降低图的直径,加快算法的收敛速度。同时,评估了图的权重函数中最优参数的选取。最后,用图的拉普拉斯矩阵和图上的热扩散方程实现图像的去噪。仿真实验结果表明,本文提出的方法能够有效去除高斯噪声,较完整地保持图像中的边缘等细节信息,在去噪性能和算法收敛速率上优于其它的PDE去噪方法。A novel partial differential equation method for image denoising is proposed based on graph theory.In the process of constructing graph,the small world model is introduced into the graph topology to decrease the diameter of graph,which speeds up the denoisng algorithm.Meanwhile,the optimal parameter selection in graph weighting function is studied.After that,the heat diffusion equation and Lapician matrix on the graph are used to filter the noisy image.Experiments illustrate that compared with some existing methods,the proposed method can effectively reduce Gaussian noise and preserve details such as borders in the image;larger speedup and better performance are achieved than other partial differential equation methods when these graph topologies and weighting function are utilized.

关 键 词：小世界模型 图论 图像去噪 热扩散方程 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]