图像降噪复原算法及其应用 | |
Alternative Title | Algorithm and Application for Image Denoising and Restoration |
王智峰1,2 | |
Department | 机器人学研究室 |
Thesis Advisor | 唐延东 |
Classification | TP391.4 |
Keyword | 图像降噪 奇异值分解 各向异性扩散 偏微分方程 半盲图像复原 |
Call Number | TP391.4/W39/2008 |
Pages | 98页 |
Degree Discipline | 模式识别与智能系统 |
Degree Name | 博士 |
2008-05-30 | |
Degree Grantor | 中国科学院沈阳自动化研究所 |
Place of Conferral | 沈阳 |
Abstract | 在图像成像、复制、扫描、传输、显示等过程中，不可避免地要造成图像的降质，如图像模糊、噪声干扰等。而在许多应用领域中，又需要清晰的、高质量的图像，因此，图像复原(如去噪、去模糊等)具有重要的意义。图像复原的目的是对降质图像进行处理，使其恢复成原始图像。它是图像处理、模式识别、机器视觉的基础，因而受到广泛的研究，并在天文学、遥感成像、医学影像等领域获得广泛的应用。图像复原的传统方法主要是进行图像滤波。由于图像的大部分信息存在于图像边缘部分，因此要求图像滤波既能去除图像的模糊和噪声，同时又能保持图像的细节。由于图像细节和噪声在频带上混叠，导致图像的平滑和边缘细节的保持成为一对矛盾。传统的滤波方法难以处理这类问题。近年来发展起来的偏微分方程图像处理技术，为解决图像复原中的这一矛盾提供了新途径。本论文共分五个部分。第一部分给出了图像复原的数学模型并讨论了其发展现状，综述了图像复原问题的规整化理论及方法，阐述了图像复原的基本过程和影响因素。第二部分研究了基于奇异值分解和能量最小原则的图像自适应降噪算法。基于有界变差的能量降噪模型的代数形式，提出了一种自适应图像降噪算法。该算法通过在矩阵范数意义下求能量最小，自适应确定去噪图像重构的奇异值个数。这一算法的特点是将能量最小原则和奇异值分解结合起来，在代数空间中建立了一种自适应的图像降噪算法。与基于压缩比和奇异值分解的降噪方法相比，该算法避免了图像压缩比函数及其拐点的计算。因此求解更加简单。第三部分研究了基于各向异性扩散的图像降噪和抖动消除算法。提出了两种算法，一、提出了一个由各向异性扩散方程定义的非线性图像滤波算子。与Perona，Malik提出的算子类似，该算子能够去除噪声，而且性能稳定，处理后的自然图像看上去清晰而且对比度也得到增强。对于图像抖动产生偏移，二、提出了一种基于各向异性非线性扩散以及抖动估计的抖动消除算法。这种各向异性非线性扩散的模型由两项组成，即扩散项以及强制项。基本思想就是对于边缘点以及光滑区域的点分别进行处理，利用Newton-Raphson算法计算最小化抖动误差，估计出抖动偏移量，从而得到抖动消除之后的图像。第四部分研究了基于四阶偏微分方程和基于高斯曲率的图像降噪算法。针对低阶的非线性偏微分方程进行图像去噪，如总变差、平均曲率流等去噪模型，会产生阶梯效应这一缺陷，即易得到分段常量结果的缺陷，提出了一种基于四阶偏微分方程的图像降噪算法，并给出了实验结果。提出了一种改进的基于高斯曲率和偏微分方程的图像降噪算法。该算法能够得到一个稳态的非平凡解，从而能够避免中止时间的选取。第五部分研究了基于C-V降噪模型的图像半盲复原算法。基于C-V降噪模型，提出了一种图像半盲的复原算法，即假定图像退化的模型已知，如高斯模糊，但是高斯核的方差未知，通过构造能量函数，将能量函数的极小问题转化为一个变分极小问题，由变分原理得到相应的欧拉-拉格朗日方程。这里设计的算法将未知数的个数由Leah Bar模型的三个减少为两个，最后估计出来高斯核的方差比Leah Bar 算法更加接近于真值。 |
Other Abstract | The presence of image degradation, such as noise and blurring, is unavoidable. It may be caused by the image formation process, image recording, image scanning, image transfer, and image showing, etc. However, in many applications, the clear images are required for the correct information extraction. The image restoration technique is to restore the original image from the degraded image, which is the fundamental problem of image processing, pattern recognition, and computer vision. And it is widely used in astronomy, remote sensing, medical imaging, etc. The traditional image restoration methods rest on image filters. Since image edge contain lots of image information, and human being is sensitive to these high frequency parts. It is required that image filter technique should preserving image edges while deblurring image and suppressing the noise. Because both image edges and the noise are high frequency part of the image. Image denoising and preserving image edges during image restoration are dilemma.The traditional filter methods can not deal with this case. In recent years, variational PDEs (Partial Differential Equations) method especially nonlinear PDEs is emerging to solve this contradiction. In the first section of the paper, a framework of image restoration is presented. The regularization theory and method for image restoration is discussed.The common process and the influence factors are also discussed. The second section deals with the image denoising algorithms based on singular value decomposition and energy minimization principle. An energy model of image denoising in matrix norm is presented for restoring noisy image. With singular value decomposition and minimizing energy ,the singular values for denoising image are adaptively determined. Comparing with the adaptive denoising algorithm based on compression ratio and SVD, it avoids calculating the function of image compression ratio and its knee point. Furthermore, it avoids solving nonlinear partial differential equation numerically comparing with the energy minimization denoising model of bounded variation, it can’t lead to local minimum in general In the third section, the anisotropic diffusion image denoising and image dejittering algorithms are studied. The first one, a nonlinear image processing operator defined by an anisotropic diffusion equation is presented. Similar to the operators proposed by Perona, Malik and Catte et al, it can remove noise and perform stably. It can also enhance step-like edges and keep the locality of them. What is different is that it is capable of keeping stronger peaks and thin edges. Due to these characteristics, the denoised images look much more clear and smooth, while keep the details. For displacement on image jitter, a new method based on an anisotropic nonlinear diffusion and jitter estimation is proposed in this paper. This anisotropic nonlinear diffusion model has two terms: the diffusion and the forcing term. The basic idea is that boundary points and interior points of the objects that make up the image are treated differently. Using Newton-Raphson algorithm, jitter displacement is estimated by minimizing jitter error. In the fourth section, the fourth-order partial differential equation and the Gauss curvature image denoising algorithms are proposed respectively. Second order nonlinear partial differential equation such as total variation minimization and mean curvature flow will lead to staircase effect, in other words,will obtain a piecewise constant image. A fourth-order PDE is presented, the responding experiment results are given. The second one, Geometric properties of images are incorporated in noise-removal PDEs by regarding the intensity image as a two-dimensional surface in a three-dimensional space. An improved noise-removal algorithm is presented based on Gauss curvature to preserve image feature. It has the advantage of having a nontrivial steady state, therefore eliminating the problem of choosing a stopping time. In the fifth section, the semi-blind image restoration algorithm based on C-V denoising model is proposed.A semi-blind image restoration algorithm is proposed based on C-V denoising model, compared with C-V denoising model, the fidelity term is modified and a term on point spread function. Is added The functional depends on two variables, so the problems consist in solving a system with two coupled equations. Compared with Leah Bar semi-blind image restoration model, our method only need to solve two equations, but Leah Bar method must be solved three couple equations. Furthermore, the estimation of Gauss kernel derivation by our algorithm is superior to Leah Bar’s algorithm. |
Language | 中文 |
Contribution Rank | 1 |
Document Type | 学位论文 |
Identifier | http://ir.sia.cn/handle/173321/414 |
Collection | 机器人学研究室 |
Affiliation | 1.中国科学院沈阳自动化研究所 2.中国科学院研究生院 |
Recommended Citation GB/T 7714 | 王智峰. 图像降噪复原算法及其应用[D]. 沈阳. 中国科学院沈阳自动化研究所,2008. |
Files in This Item: | ||||||
File Name/Size | DocType | Version | Access | License | ||
LWWZF01.pdf（3634KB） | 开放获取 | -- | Application Full Text |
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment