| 一类基于鲁棒统计的噪声抑制变分模型与算法 |
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| 引用本文： | 肖亮,韦志辉. 一类基于鲁棒统计的噪声抑制变分模型与算法[J]. 系统仿真学报, 2007, 19(21): 4884-4888 |
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| 作者姓名： | 肖亮 韦志辉 |
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| 作者单位： | 南京理工大学计算机科学与技术学院,南京,210094 |
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| 基金项目： | 国家自然科学基金;中国博士后科学基金;江苏省自然科学基金;江苏省博士后科学基金;南京理工大学校科研和教改项目 |
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| 摘 要： | 从最大后验概率估计和马尔科夫随机场出发,将图像梯度场的分布建模为混合加权的容许密度类,利用鲁棒统计学中的Hubber定理,导出了一类鲁棒性密度。建立了一类由L2范数或L1范数数据保真约束和鲁棒意义下的图像正则化项组成的噪声抑制变分模型。提出了该类模型的基于梯度最速下降的有限差分算法。在Matlab集成环境下进行了六组不同噪声抑制变分模型的仿真实验,通过计算峰值信噪比和结构化相似指标给出了性能评价结果。
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| 关 键 词： | 变分方法 偏微分方程 图像去噪 鲁棒统计 建模与仿真 |
| 文章编号： | 1004-731X（2007）21-4884-05 |
| 收稿时间： | 2006-08-28 |
| 修稿时间： | 2007-04-09 |
A Class of Image De-noising Variational Models and Algorithms Based on Robust Statistics |
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| XIAO Liang,WEI Zhi-hui. A Class of Image De-noising Variational Models and Algorithms Based on Robust Statistics[J]. Journal of System Simulation, 2007, 19(21): 4884-4888 |
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| Authors: | XIAO Liang WEI Zhi-hui |
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| Affiliation: | School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 210094, China |
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| Abstract: | Assuming that the gradient of images is a member of a class of hybrid weighted probability distribution,a class of least favorable distribution was obtained based on the Hubber theorem.Then a class variational functional for image de-noising was set up in the form of robustness regularized term under constraint of data fidelity with L1 norm or L2 norm.A gradient descent flow for image denoising with a iterative finite difference algorithm was proposed.Simulated experiments were implemented for six de-noising models with respect to Gaussian noise and Laplace noise,and the performance evaluation was given through computing the PSNR(Peak Signal Noise Ratio) and SSIM(Structural Similarity Index Method). |
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| Keywords: | Variatioanl approach partial differential equation image de-noising robust statistics modeling and simulation |
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