图像去噪的加权核范数正则化方法研究 Alternative Title The Study of Weighted Nuclear Norm Minimization for Image Denoising 黄摇 Subtype 学士 Thesis Advisor 黄玉梅 2016-05-17 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 学士 Keyword 图像去噪 低秩矩阵最小化 加权核范数 奇异值分解 峰值信噪比 Abstract 图像去噪是图像处理中最基本的问题，是各种图像处理问题的基础。图像在形成或传输的过程中，不可避免的要受到图像系统或者外界的干扰而产生噪声，图像去噪就是采用一定方法去除所记录图像中的噪声，从而获得和原始清晰图像尽可能接近的图像。物理上，图像去噪方法常见的有空间域滤波法，变换域滤波法。数学上，因为图像去噪是一个高度病态问题，常见方法是最小化一个含有正则项的能量函数。非局部方法在图像去噪中也有着广泛的应用。这种方法是利用图像的非局部自相似性达到去噪目的。近年来，低秩矩阵的最小化方法得到了大量研究，利用这种方法能很好的去除图像中的噪声。在实际应用中，用矩阵的核范数去近似矩阵的秩，前者是凸函数，而后者是非凸的。矩阵核范数最小化通过矩阵的奇异值分解来实现。在本文中，我们研究了加权核范数最小化问题，即对于不同的奇异值附以不同的权值。在图像的非局部相似块的匹配下，我们将提出的加权值的确定方法用于核范数最小化算法中进行图像的去噪。实验结果表明，算法与经典非局部方法和核范数去噪算法相比，复杂度更低，去噪效果更好。 Other Abstract Image denoising is the basic problem of different image processing problems.In the process of image formation or transmission,noises are inevitably generated because of properties of imaging systems or external interference.The task of image denoising is to remove noise in the observed image and obtain a clear image as closely as possible to the original image.Physically, image noises could be removed by filters such as spatial domain filter, transform domain filtering method.Mathematically, since the image denoising is a highly ill-posed problem,the common method is to minimize an energy function which contains a regularization term. Non-local denoising method also has wide applications.This method uses the nonlocal self-similarity of image to recover images.In recent years,low-rank matrix minimization method has been wildly studied,as well as this method is applied to remove noises in images.In practice,the nuclear norm of a matrix is used to approximate its rank,the former is convex,while the latter is non-convex.nuclear norm minimization problem is usually solved through singular value decomposition of the matrix.In this paper,we study the weighted nuclear norm minimization problem,that is different weights are attached to different singular values.Under the assumptions of nonlocal self-similarity of an image,our proposed weight value is used in weighted nuclear norm minimization algorithm then which is applied to image denoising. Experimental results show that, comparing with the classical algorithm for image noise removal and nuclear norm minimization, the improved algorithm we proposed has less computation complexities and better denoising effects. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224615 Collection 数学与统计学院 Recommended CitationGB/T 7714 黄摇. 图像去噪的加权核范数正则化方法研究[D]. 兰州. 兰州大学,2016.
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