引入耦合梯度保真项的非线性扩散图像去噪方法  

Nonlinear Diffusion based Image Denoising Coupling Gradient Fidelity Term

作　　者：朱立新[1] 王平安[2] 夏德深[1] 

机构地区：[1]南京理工大学计算机科学与技术学院,南京210094 [2]香港中文大学计算机科学与工程学系

出　　处：《计算机研究与发展》2007年第8期1390-1398,共9页Journal of Computer Research and Development

基　　金：香港特别行政区政府研究资助局基金项目(CUHK/1/00C);江苏省自然科学基金项目(BK2006704-2)

摘　　要：利用二阶的非线性扩散方程进行图像去噪易产生具有"阶越效应"的去噪结果,也即使分段光滑的图像变为分段常量的.针对低阶非线性扩散去噪方法的不足,通过在原有的扩散方程中引入从梯度保真约束项导出的Euler-Lagrange方程,提出了耦合梯度保真项的非线性扩散图像去噪方法.由于梯度保真约束项考虑了去噪前后图像梯度的相似度,利用该模型能够在保持边缘的同时得到分段光滑的结果,使视觉效果更自然.证明了新模型是一个凸函数,从而保证了最优解的存在性和惟一性.还分析了从噪声图像估计梯度时引入空间正则化对最终结果的影响,并且从理论和实验两个角度分析了合理选择正则化参数的重要性.模型在有界变差函数空间中可积,使得新方法克服了高阶非线性扩散去噪方法易造成边界泄漏以及破坏图像中纹理等高频成分的不足.实验结果表明,通过耦合梯度保真项能够很好地防止"阶越效应"的产生,同时保持图像中的边缘、纹理等结构信息.Image denoising with second order non-linear diffusion PDEs often leads to an undesirable staircase effect, namely, the transformation of smooth regions into piecewise constant ones. In this paper, these nonlinear diffusion models are improved by adding the Euler-Lagrange equation derived from the gradient fidelity term which describes the similarity in gradient between the noise images and the restored ones. After coupling the new restriction equation derived from the gradient fidelity term, the classical second order PDE-based denoising models will produce piecewise smooth results, while preserving sharp jump discontinuities in images. The convexity of the proposed model is proved and the existence and uniqueness of optimal solution is ensured. The influence of introducing spatial regularization on the gradient estimation is also analyzed and the importance of proper regularization parameter selection to the final results is emphasized theoretically and experimentally. In addition, the gradient fidelity term is integrable in bounded variation function space which makes the models outperform fourth order nonlinear PDEs based denoising methods suffering from the leakage problems and the sensitivity to high frequency components in images. Experimental results show that the new model alleviates the staircase effect to some extent and preserves the image features well, such as textures and edges.

关 键 词：阶越效应 梯度保真项 偏微分方程 非线性扩散 图像去噪 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]