基于偏微分方程理论的图像复原技术研究

发布时间：2018-05-17 07:49

本文选题：图像复原 + 图像去噪　；参考：《中国矿业大学》2012年博士论文

【摘要】：现代社会中，信息产业发展迅速，技术日新月异，人们对信息的需求也不断增加，图像是人类获取、传递信息的重要媒介。然而图像在成像、复制、传输以及显示等过程中，受某些因素干扰，不可避免的会产生降质，如图像信息缺损或收受噪声污染，而在很多领域中又需要清晰的、高质量的图像，因此图像复原技术具有非常重要的意义。本文内容为数字图像复原技术的研究，采用的方法为偏微分方程理论。偏微分方程是一种重要的数学分析工具，具有良好的各项异性扩散性能，能够很好地用于图像处理。所谓图像复原技术，是指由图像中已知信息来修复缺损信息或者去除噪声信息，属于贝叶斯先验概率问题，在内容上可以分为图像修复和图像去噪。由于图像中所含信息非常复杂，既有纹理细节也有结构轮廓，一种复原方法不可能解决所有类型的图像问题，故根据所采用的已知信息在待复原图像中的范围，可以将本文工作分为基于局域以及全局信息的图像复原研究，主要内容包括以下几个方面：一、从数学角度出发，在局部坐标系中分析了全变分修复模型的缺陷，提出了一种基于自适应全变分理论的修复模型，该模型能够根据图像特征灵活地扩散图像信息，有效地避免了图像阶梯效应的产生；提出了一种基于泊松方程的梯度域图像修复模型，该算法改进了基于曲率扩散的模型，首先修复图像的梯度域，然后对图像的梯度域求解泊松方程，最终得到完整的复原图像。二、对经典全变分去噪模型中的相关参数进行了详细解析，得出了正则项及忠诚项在模型中各自的功能，通过对模型中相关参数的改进，从而大大提高了经典模型的去噪能力以及收敛速度；依据去噪模型中正则项的特性，对先前比较有名的模型进行了分析，提出了一个统一的变分去噪模型框架，该框架有助于推进变分理论在图像去噪中的应用；在四阶偏微分方程去噪模型的基础上，通过引入新的耦合算子及尺度因子，提出了一个全变分模型与四阶模型的耦合模型，该模型具有边缘保护好、收敛速度快的特点。三、提出了基于样块的偏微分方程约束的图像修复方法。本算法对图像块的采样、匹配等关键技术进行了改进，能够依据图像的特征很好地修复受损图，可以用于结构、纹理较复杂的大区域图像修复；引入了一种非局域算子，该算子涵盖了偏微分方程中的梯度、散度等算子，并将其应用到了图像全局范围，，提出了基于非局域算子的全变分复原模型，该模型在复原过程中可以遍历整幅图像寻找可用信息，对于纹理图像具有较好的修复效果；提出了两种不同忠诚约束项的非局域全变分模型，实验对比了两者的纹理提取效果，最终得到了一种更加适合于纹理图像复原的模型。本文第一、二项内容为基于局域信息的图像修复和图像去噪技术，分别针对图像中的细小结构缺损以及噪声问题，提出了相应的解决方案；第三项内容为基于图像全局信息的复原技术，对于含纹理细节较丰富的图像具有很好的复原效果。
[Abstract]:In modern society, the information industry is developing rapidly, technology is changing and the demand for information is increasing. Image is an important medium for people to obtain and transmit information. However, images are interfered by some factors in the process of imaging, replication, transmission and display, which can not be avoided, such as the defect of image information or the reception of noise. Pollution, however, requires clear and high-quality images in many areas. Therefore, image restoration technology is of great significance.
In this paper, the research of digital image restoration technology is the partial differential equation theory. Partial differential equation is an important mathematical analysis tool. It has good heterosexual diffusion performance and can be used in image processing well. The so-called image restoration technology refers to the repair of defect information from the known information in the image or The removal of noise information, which belongs to the Bias priori probability problem, can be divided into image restoration and image denoising. As the information contained in the image is very complex, there are both texture details and structural outlines, and a restoration method can not solve all types of image problems, so the known information is used in the image to be restored. We can divide the work into image restoration based on local and global information. The main contents are as follows:
First, from the mathematical point of view, the defect of the fully variational repair model is analyzed in the local coordinate system, and a repair model based on the adaptive full variational theory is proposed. The model can flexibly diffuse the image information according to the image features, effectively avoid the generation of the image step effect, and propose a gradient based on the Poisson equation. In the domain image restoration model, the algorithm improves the model based on the curvature diffusion. Firstly, the gradient domain of the image is repaired. Then the Poisson equation is solved in the gradient domain of the image, and the complete restoration image is finally obtained.
Two, the relevant parameters in the classical total variational denoising model are analyzed in detail, and the functions of regular term and loyalty item in the model are obtained. By improving the relevant parameters in the model, the denoising ability and convergence speed of the classical model are greatly improved. The model of the name is analyzed, and a unified variational denoising model is proposed. The framework helps to promote the application of the variational theory in image denoising. On the basis of the four order partial differential equation de-noising model, a new coupling operator and the scale factor are introduced, and a coupling model of the full variation model and the four order model is proposed. The model has the advantages of good edge protection and fast convergence.
Three, the image restoration method based on partial differential equation constraint based on sample block is proposed. This algorithm improves the key techniques such as sampling and matching of image blocks. It can repair the damaged graph well according to the features of the image. It can be used in the reconstruction of large area with complex structure and texture, and a non local operator is introduced. The operator covers the image. The gradient, divergence and other operators in the partial differential equation are applied to the global range of the image. A full variational restoration model based on the non local operator is proposed. In the restoration process, the whole image can be traversed to find the available information, and the restoration effect is better for the texture image. Two different loyalty constraints are proposed. Finally, a model which is more suitable for texture image restoration is obtained.
The first, second contents of this paper are image restoration and image denoising based on local information. The corresponding solutions are proposed for the small structure defects and noise problems in the images. The third content is a restoration technique based on the global information of the image, which has a good recovery effect for the images with rich texture details. Fruit.
【学位授予单位】：中国矿业大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：TP391.41

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