基于小波系数相关性的图像去噪算法研究
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中南民族大学 硕士学位论文 基于小波系数相关性的图像去噪算法研究 姓名：毛晓晖 申请学位级别：硕士 专业：通信与信息系统 指导教师：侯建华 20100419
中南民族大学硕士学位论文
摘 要
图像作为人类视觉信息传递的重要媒介， 在传输的过程中经常会受到各种噪声 的干扰和影响，这种降质图像对后续图像的处理（如分割、压缩、特征提取和模式 识别等）将产生不利的影响，因此对图像进行去噪成为图像预处理的一项非常重要 的工作。图像去噪的任务是去除噪声的同时最大程度地保留图像本身的特征和细 节。研究图像去噪的关键在于提高信噪比，突出图像的期望特征。然而传统的去噪 方法，在去噪与保细节折中方面不理想，去噪效果不佳。 随着小波分析理论的迅猛发展，人们将注意力由空域转移到了小波域，小波分 析具有多尺度、多分辨率分析特点，能有效地改善去噪效果，因此基于小波域的图 像去噪成为了图像去噪领域的重要研究课题。本文主要工作包含以下三个方面： （1）小波变换在图像去噪领域占据非常重要的地位，本文首先列举了小波变 换有利于图像分析的一系列特点；详细介绍了小波去噪的发展历史和现状；研究了 图像噪声模型，噪声方差估计方法以及图像去噪的性能评价标准；重点讨论了小波 去噪中的阈值函数选取；分析了几种经典的阈值去噪算法，并通过实验仿真得出重 要结论：正交小波变换不具有平移不变性，引入平移不变法改进经典的阈值去噪算 法，减少了边缘的伪吉布斯效应，优化了图像去噪的质量。 （2）研究了小波系数的层内相关性，提出了一种基于正态反高斯分布模型、 以及结合上下文模型进行系数分类的图像去噪新算法。 系统研究了经典的小波系数 统计模型，重点讨论了正态反高斯模型；推导出了贝叶斯（Bayes）最大后验概率 估计（MAP）的参数形式表达式；详细论述了基于上下文模型的小波系数分类法； 研究了计算模型参数的矩估计法。实验结果表明，正态反高斯模型能够全面描述系 数的统计分布规律及相关性。该算法与经典的自适应阈值去噪相比，具有更好的信 噪比和视觉效果。 （3）研究了小波系数的层间相关性，提出了一种基于矢量空间线性最小均方 误差估计的图像去噪新算法。阐述了非下采样分解方法及冗余小波变换的优点；深 入研究了矢量空间的上下文模型分类法； 研究了基于 Bayes 准则的线性最小均方误 差估计算法（LMMSE） ；重点讨论了矢量空间的基于最小均方误差估计的系数估计 新算法。新算法可以很好地解决去噪图像边缘模糊问题，与经典的自适应去噪算法 相比，在视觉和信噪比方面有较大的改善。 关键字：阈值去噪，空域自适应，平移不变，正态反高斯先验模型，上下文模型
I
基于小波系数相关性的图像去噪算法的研究
ABSTRACT
As an important medium of the human visual information transmission, image is often influenced or interrupted by a variety of noise in the course of transmission. These degraded images will have a negative impact on the following-up image processing (such as segmentation, compression, feature extraction, and pattern recognition, etc.). Therefore, the image denoising becomes a very important job for the image-preprocessing. The image denoising is to remove the noise from the noisy image, at the same time to preserve image detail and feature. The key of the research of image denoising is to improve the signal to the noise ratio, and to highlight the expectations of the image features. However, it is difficult for traditional image denoising methods to reach a ideal trade-off between noise suppression and detail preserving and to obtain good results. With the rapid development of wavelet analysis theory, people pay their attention from spatial domain to wavelet domain. Due to the characteristics of the wavelet such as： multi-scale, multi-resolution analysis, and the improved denoising effect, the image denoising method based on wavelet becomes an important research topic in the field. The main tasks in this paper include the following three respects: (1). Wavelet transform in image denoising occupies a very important position in the field. Fist of all, a series of characteristics of wavelet transform was enumerated in this paper. The development of wavelet denoising history and current situation were introduced in detail. The noise model, the noise variance estimation and the evaluation criteria of the image denoising performance were introduced. The paper focused on threshold selection in image denoising. Several classical thresholds and the corresponding algorithms were analyzed. Some important conclusions were obtained from the simulation experiments. Orthogonal wavelet transform lacks the translation invariance ， so the classical thresholding denoising algorithm could be improved through importing the shift-invariant method. This modified algorithm could reduce the pseudo-Gibbs effects of the denoised image edges, and optimize the denoising performance. (2). Based on the studies of intrascale dependencies of wavelet coefficients , the paper proposed a new image denoising algorithm using normal inverse Gaussian distribution model for the coefficient and the context model for coefficients categories. Classical statistical model of wavelet coefficients was systematically studied. The
II
中南民族大学硕士学位论文
ห้องสมุดไป่ตู้
paper focused on the normal inverse Gaussian model. The parameters formula of Bayes maximum posteriori estimate were derived. The classification of wavelet coefficients based on context model was discussed in detail. The paper researched on the moment estimation for parameter estimation. The statistical model introduced in this algorithm could comprehensively describe the intrascale dependencies of wavelet coefficients. The classification method based on context modeling could also embodiment the the intrascale dependencies of wavelet coefficients, with which the shrinkage function became more adaptive and the denoising result was improved. (3). Based on research of the interscale dependencies of wavelet coefficients, the paper proposed a linear minimum mean square error estimation of image denoising in vector space. Decomposition method based on Nonsubsampled and the advantages of redundant wavelet transform was expounded. Context classification model applied to the vector space was deeply studied. The LMMSE algorithm based on Bayes criteria was introduced. The paper focused on a new algorithm based on the LMMSE algorithm applied to the vector space. The new algorithm could resolve the fuzzy edge denoising, and it had greater improvement in the vision and signal to noise ratio than the use of intrascale correlation.
中南民族大学硕士学位论文
摘 要
图像作为人类视觉信息传递的重要媒介， 在传输的过程中经常会受到各种噪声 的干扰和影响，这种降质图像对后续图像的处理（如分割、压缩、特征提取和模式 识别等）将产生不利的影响，因此对图像进行去噪成为图像预处理的一项非常重要 的工作。图像去噪的任务是去除噪声的同时最大程度地保留图像本身的特征和细 节。研究图像去噪的关键在于提高信噪比，突出图像的期望特征。然而传统的去噪 方法，在去噪与保细节折中方面不理想，去噪效果不佳。 随着小波分析理论的迅猛发展，人们将注意力由空域转移到了小波域，小波分 析具有多尺度、多分辨率分析特点，能有效地改善去噪效果，因此基于小波域的图 像去噪成为了图像去噪领域的重要研究课题。本文主要工作包含以下三个方面： （1）小波变换在图像去噪领域占据非常重要的地位，本文首先列举了小波变 换有利于图像分析的一系列特点；详细介绍了小波去噪的发展历史和现状；研究了 图像噪声模型，噪声方差估计方法以及图像去噪的性能评价标准；重点讨论了小波 去噪中的阈值函数选取；分析了几种经典的阈值去噪算法，并通过实验仿真得出重 要结论：正交小波变换不具有平移不变性，引入平移不变法改进经典的阈值去噪算 法，减少了边缘的伪吉布斯效应，优化了图像去噪的质量。 （2）研究了小波系数的层内相关性，提出了一种基于正态反高斯分布模型、 以及结合上下文模型进行系数分类的图像去噪新算法。 系统研究了经典的小波系数 统计模型，重点讨论了正态反高斯模型；推导出了贝叶斯（Bayes）最大后验概率 估计（MAP）的参数形式表达式；详细论述了基于上下文模型的小波系数分类法； 研究了计算模型参数的矩估计法。实验结果表明，正态反高斯模型能够全面描述系 数的统计分布规律及相关性。该算法与经典的自适应阈值去噪相比，具有更好的信 噪比和视觉效果。 （3）研究了小波系数的层间相关性，提出了一种基于矢量空间线性最小均方 误差估计的图像去噪新算法。阐述了非下采样分解方法及冗余小波变换的优点；深 入研究了矢量空间的上下文模型分类法； 研究了基于 Bayes 准则的线性最小均方误 差估计算法（LMMSE） ；重点讨论了矢量空间的基于最小均方误差估计的系数估计 新算法。新算法可以很好地解决去噪图像边缘模糊问题，与经典的自适应去噪算法 相比，在视觉和信噪比方面有较大的改善。 关键字：阈值去噪，空域自适应，平移不变，正态反高斯先验模型，上下文模型
I
基于小波系数相关性的图像去噪算法的研究
ABSTRACT
As an important medium of the human visual information transmission, image is often influenced or interrupted by a variety of noise in the course of transmission. These degraded images will have a negative impact on the following-up image processing (such as segmentation, compression, feature extraction, and pattern recognition, etc.). Therefore, the image denoising becomes a very important job for the image-preprocessing. The image denoising is to remove the noise from the noisy image, at the same time to preserve image detail and feature. The key of the research of image denoising is to improve the signal to the noise ratio, and to highlight the expectations of the image features. However, it is difficult for traditional image denoising methods to reach a ideal trade-off between noise suppression and detail preserving and to obtain good results. With the rapid development of wavelet analysis theory, people pay their attention from spatial domain to wavelet domain. Due to the characteristics of the wavelet such as： multi-scale, multi-resolution analysis, and the improved denoising effect, the image denoising method based on wavelet becomes an important research topic in the field. The main tasks in this paper include the following three respects: (1). Wavelet transform in image denoising occupies a very important position in the field. Fist of all, a series of characteristics of wavelet transform was enumerated in this paper. The development of wavelet denoising history and current situation were introduced in detail. The noise model, the noise variance estimation and the evaluation criteria of the image denoising performance were introduced. The paper focused on threshold selection in image denoising. Several classical thresholds and the corresponding algorithms were analyzed. Some important conclusions were obtained from the simulation experiments. Orthogonal wavelet transform lacks the translation invariance ， so the classical thresholding denoising algorithm could be improved through importing the shift-invariant method. This modified algorithm could reduce the pseudo-Gibbs effects of the denoised image edges, and optimize the denoising performance. (2). Based on the studies of intrascale dependencies of wavelet coefficients , the paper proposed a new image denoising algorithm using normal inverse Gaussian distribution model for the coefficient and the context model for coefficients categories. Classical statistical model of wavelet coefficients was systematically studied. The
II
中南民族大学硕士学位论文
ห้องสมุดไป่ตู้
paper focused on the normal inverse Gaussian model. The parameters formula of Bayes maximum posteriori estimate were derived. The classification of wavelet coefficients based on context model was discussed in detail. The paper researched on the moment estimation for parameter estimation. The statistical model introduced in this algorithm could comprehensively describe the intrascale dependencies of wavelet coefficients. The classification method based on context modeling could also embodiment the the intrascale dependencies of wavelet coefficients, with which the shrinkage function became more adaptive and the denoising result was improved. (3). Based on research of the interscale dependencies of wavelet coefficients, the paper proposed a linear minimum mean square error estimation of image denoising in vector space. Decomposition method based on Nonsubsampled and the advantages of redundant wavelet transform was expounded. Context classification model applied to the vector space was deeply studied. The LMMSE algorithm based on Bayes criteria was introduced. The paper focused on a new algorithm based on the LMMSE algorithm applied to the vector space. The new algorithm could resolve the fuzzy edge denoising, and it had greater improvement in the vision and signal to noise ratio than the use of intrascale correlation.