一种基于L1范数及高斯平滑的图像复原方法 Alternative Title A New Image Restoration Method by Gaussian Smoothing with L1 Norm Regularization 曲光夫 Thesis Advisor 黄玉梅 2013-05-26 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 图像复原 滤波方法 正则化方法 L1范数 交替迭代法 Abstract 图像复原是图像处理中一个基本而重要的问题。滤波器方法和正则化方法是目前图像复原中被广泛采用的两种方法。滤波器方法是一类线性滤波平滑方法，它的缺点是如果滤波较强，则复原图像过于平滑，失去很多细节；如果滤波较弱，则复原图像中的有些噪声不能被滤掉，仍然存在于图像之中。图像恢复的正则化方法是通过求解一个优化问题来获得复原图像，优化函数的的建立基于图像噪声的特性和所选择的正则项，总变分正则化能很好的去除噪声并保存图像的边界信息。本文先介绍了图像复原的常用滤波方法和正则化方法，然后运用L1范数能有效去除图像中残留异常值的特性，设计了基于L1范数及高斯平滑的总变分图像复原方法，并构造了交替迭代法来求解提出的新模型。数值实验结果表明本文提出的模型是有效的图像复原方法，和高斯平滑方法相比无论是在视觉效果还是质量结果方面都极大的提高了图像的复原质量。 Other Abstract Image restoration is a fundamental and important problem in image processing. The filtering methods and regularization methods are widely used in image restoration. Filtering method is a class of linear smoothing methods. Its drawback is that if the filtering effect is strong, the restored image will be over smooth and a lot of details will be lost; if the filtering effect is weak, some outliers in the restored image can't be removed and still remain in the restored image. Regularization method for image restoration is to obtain the restored image by solving an optimization problem, the cost function is usually established based on the statistics characteristics of image noise and the choice of the regularization term. The total variation regularization can remove noise and maintain image edges well. In this thesis, we first introduce some filtering methods and regularization methods for image restoration. And then by using the good feature of L1 norm that can remove the residual outliers effectively, we design a total variation image restoration method based on L1 norm and gaussian filtering smoothing. An alternating iterative method is constructed to solve the new model. Numerical experiment results show that the proposed model is an effective image restoration method and greatly improves the quality of image restoration in both visual effect and quality results compared with gaussian smoothing method. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224418 Collection 数学与统计学院 Recommended CitationGB/T 7714 曲光夫. 一种基于L1范数及高斯平滑的图像复原方法[D]. 兰州. 兰州大学,2013.
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