基于四元数的彩色图像去噪算法研究

发布时间：2019-07-02 19:32

【摘要】：传统的彩色图像处理方法通常将彩色图像看成三幅独立的灰度图像,对三个通道分别处理,没有考虑各通道之间的关联性,难以获得较好的处理效果。因此,为彩色图像找到一种更好的表示方法,将其三个色彩通道看做一个整体,保留各通道之间的相关性具有重要的理论意义和应用价值。四元数作为最先被发现的超复数代数,为三维彩色图像信号的重构提供了实用的数学工具。基于四元数的方法模仿人类对视觉环境的感知,以一种并行的方式处理多通道信息。作为一种新的彩色图像表示工具,四元数在彩色图像复原的诸多方面取得了令人满意的效果。本文针对彩色图像处理问题,提出一种基于四元数加权核范数最小模型和求解算法。论文的主要研究工作和创新点总结如下:第一,本文对现有的图像去噪算法以及基于四元数的彩色图像处理方法做了系统概述,详述了四元数的基本运算、彩色图像的四元数表示法,深入研究了核范数最小(Nuclear Norm Minimization,NNM)和加权核范数最小(Weighted Nuclear Norm Minimization,WNNM)两种算法以及四元数矩阵的奇异值分解方法。第二,论文的创新点在于将WNNM模型推广到四元数域,提出一种新颖的基于四元数加权核范数最小(Quaternion Weighted Nuclear Norm Minimization,QWNNM)模型。根据奇异值大小在表示图像时重要程度的不同,对较大的奇异值分配较小的权重以被较小收缩,采用一种迭代重加权的算法对四元数矩阵做低秩重构,并给出了该问题具有全局最优解的证明。第三,论文以彩色图像的四元数表示法为基础,引入自然图像子块之间的非局部自相似性,建立彩色图像子块QWNNM去噪模型,讨论了在低噪声水平、高噪声水平以及未知噪声三种情况下的去噪效果。特别地,本文实现了原WNNM算法在彩色图像去噪中的应用,并且为了保持对比实验的公平性,对于WNNM算法,本文增加了高噪声水平时对原噪声图像做高斯低通滤波预处理的对比实验。大量的彩色图像去噪实验表明,与经典的K-SVD算法以及WNNM算法相比,用本文提出的方法处理后的图像,其主观视觉效果和客观评价指标都有显著的提高。在四元数空间里,矢量重构时可以完整保存彩色图像的内在结构。QWNNM方法也可用于彩色图像修复、去模糊、去马赛克等图像处理问题中。这种多维低秩矩阵重构的思想也可以扩展到彩色图像分类、机器学习和模式识别等领域,有着广泛的应用和发展前景。
[Abstract]:The traditional color image processing method usually regards the color image as three independent gray images. The three channels are processed separately without considering the correlation between the channels, so it is difficult to obtain a better processing effect. Therefore, it is of great theoretical significance and application value to find a better representation method for color image, and to regard its three color channels as a whole, and it is of great theoretical significance and application value to retain the correlation between the channels. As the first discovered supercomplex algebra, quaternion provides a practical mathematical tool for the reconstruction of 3D color image signal. The quaternion method imitates human perception of visual environment and processes multi-channel information in a parallel way. As a new color image representation tool, quaternions have achieved satisfactory results in many aspects of color image restoration. In this paper, a minimum model and algorithm based on quaternion weighted kernel norm are proposed to solve the problem of color image processing. The main research work and innovations of this paper are summarized as follows: first, the existing image denoising algorithms and color image processing methods based on quaternion are systematically summarized, the basic operation of quaternion, the quaternion representation of color image are described in detail, and the minimum kernel norm (Nuclear Norm Minimization,NNM and weighted kernel norm minimum (Weighted Nuclear Norm Minimization, are deeply studied. WNNM) two algorithms and the singular value decomposition method of quaternion matrix. Secondly, the innovation of this paper is to extend the WNNM model to quaternion domain, and to propose a novel minimum (Quaternion Weighted Nuclear Norm Minimization,QWNNM model based on quaternion weighted kernel norm. According to the difference of the importance of the singular value in the representation of the image, a small weight is assigned to the larger singular value to be reduced. An iterative reweighting algorithm is used to reconstruct the quaternion matrix with low rank, and the proof that the problem has the global optimal solution is given. Thirdly, based on the quaternion representation of color image, the non-local self-similarity between natural image sub-blocks is introduced, and the QWNNM denoising model of color image sub-block is established, and the denoising effect in the case of low noise level, high noise level and unknown noise is discussed. In particular, this paper implements the application of the original WNNM algorithm in color image denoising, and in order to maintain the fairness of the contrast experiment, for WNNM algorithm, this paper adds a comparison experiment of Gaussian low-pass filtering preprocessing for the original noise image at high noise level. A large number of color image denoising experiments show that compared with the classical K-SVD algorithm and WNNM algorithm, the subjective visual effect and objective evaluation index of the image processed by the method proposed in this paper are significantly improved. In quaternion space, the internal structure of color image can be completely preserved in vector reconstruction. QWNNM method can also be used in color image restoration, deblurring, mosaic and other image processing problems. This idea of multi-dimensional low rank matrix reconstruction can also be extended to color image classification, machine learning and pattern recognition, and has a wide range of applications and development prospects.
【学位授予单位】：五邑大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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