基于小波及其统计特性的图像去噪方法研究
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摘要
图像在获取或传输过程中不可避免地会受到噪声污染,图像中的噪声严重影响了后续的图像处理工作,如图像分割、编码、特征提取和目标检测等。为了提高图像的质量以及后续更高层次处理的需要,对图像进行去噪就成为图像预处理中一项非常重要的工作。图像去噪的目的就是从被噪声污染的含噪图像中恢复出原始的“干净”图像,即在滤除噪声的同时尽可能的保留重要的图像特征与细节。传统图像去噪方法在降噪与保细节折中方面难以令人满意;小波变换作为一种新的时频分析方法,具有多尺度、多分辨分析的特点,为信号处理提供了一种新的、强有力的手段,在图像去噪领域得到了成功的应用。目前,基于小波的去噪方法已经成为图像去噪和恢复的重大分支,而根据图像小波系数的统计特性,研究基于模型的去噪方法,是目前图像去噪领域中的主要研究方向,无论在理论上还是在实际应用中都具有重要意义。
本文以小波分析理论为工具,对小波域图像去噪理论与方法进行了系统、深入的研究,主要工作包括以下四部分:
1、小波图像去噪方法研究综述
本文前两章作为全文的基础,对基于小波的图像去噪方法进行了全面的研究总结。首先综述了图像去噪技术的发展现状,特别是小波图像去噪方法的研究进展。针对目前小波图像去噪领域尚未有一个较全面的分类方法,本文以该领域发展的三个阶段为线索,将小波图像去噪算法进行了新的分类并划分为四类,并对每种类型中代表性的算法做了分析讨论。阈值去噪是小波去噪研究中一类非常重要的方法,对此进行了系统、深入的分析,在阈值选择这一核心问题上,对最具代表性的阈值结合具体的算法在原理与方法上做了清晰的阐述,并对这些典型算法分别在正交小波变换基和平移不变小波基下进行了全面的实验仿真和分析讨论。从实验结果和性能分析中得到了一些有意义的结论。此外,针对一维信号去噪算法仿真中的加噪信号的生成方法进行了研究,在严格的理论推导基础上,提出了一种产生高精度信噪比加噪信号的方法。
2、小波域Wiener滤波方法研究
小波域Wiener滤波方法是小波图像去噪领域中的一个很活跃的研究内容。本文定义了小波域Wiener滤波的三种形式,提出了三种新的去噪算法。首先提出了一种小波域迭代维纳滤波算法;在小波域经验Wiener滤波器基础上,采用BayesShrink阈值算法提高期望信号的估计精度,同时利用多小波基更好的捕捉到信号的某些特定特征,并实现算法的迭代,从而显著增强了算法的去噪性能。提出了一种新的图像组合滤波方法;先用BayesShrink算法对图像做预处理,再进行空域Lee滤波;算法核心在于给出了一种估计预去噪图像中残留噪声方差的近似最优公式,从而保证了两种算法之间的匹配性。提出了一种小波域局部自适应图像去噪算法;通过对LAWML算法的估计误差进行理论分析,得到了一种观测系数局部方差估计的阈值,与LAWML算法比较,新算法在客观峰值信噪比及主观视觉效果方面都有显著的改进。
3、基于小波系数统计模型的图像去噪方法研究
对基于统计模型的Bayes小波域去噪方法进行了深入研究,针对现有的两种算法的不足进行了改进:对Sendur的基于双变量模型的去噪算法,利用MAP软阈值对三个最高频子带进行局部自适应处理;对Moulin的基于拉普拉斯模型的MapShrink子带自适应算法,将小波系数建模为具有不同边缘标准差的拉普拉斯分布,利用邻域局部窗口估计模型参数,从而使得MapShrink阈值具有局部自适应性。
本文将小波系数分类技术引入到图像去噪,提出了两种新的算法。首先在高斯混合模型基础上,提出了一种随像素自适应调整的混合高斯模型,利用局部贝叶斯阈值对小波系数进行分类,通过当前系数邻域窗中两类系数的信息,对模型参数进行估计;再根据MMSE准则设计相应的Wiener滤波器。第二种方法则将一维信号的小波邻域阈值扩展并应用于二维图像,子带内的每个小波系数根据其邻域阈值的大小被划分为“大”系数或者是“小”系数;对“小”系数直接置零,对“大”系数则采用一种具有局部空间强相关性的零均值高斯模型。实验结果表明,这种算法具有计算复杂度低、去噪性能优异的特点。
4、基于小波统计模型的SAR图像相干斑抑制方法研究
作为图像去噪的具体实例,本文最后讨论了小波去噪技术在SAR图像斑点噪声抑制中的应用。回顾了SAR图像相干斑抑制方法的研究进展,重点对基于小波统计模型的SAR图像去斑方法进行了研究,提出了一种基于Bayesian MAP估计的小波域局部自适应性去斑算法。通过对含斑图像做对数变换和冗余小波分解,将斑点噪声、有用信号的小波系数分别建模为瑞利分布、拉普拉斯分布,利用MAP准则得到了一种解析的Bayesian估计表达式,并证明了其处理本质就是一种软阈值去噪,因而具有算法简洁的特点;进一步通过局部邻域窗口估计拉普拉斯参数,使算法具有局部自适应性。理论分析和实验仿真表明,该算法能有效抑制SAR图像的斑点噪声,同时较好地保持了图像的强、弱细节。
An image is often and inevitably corrupted by noise in its acquisition or transmission. The noise in an image has degraded severely the following-up image processing tasks, such as image segmentation, coding, feature extraction, and target detection. Thus noise reduction becomes a very important image pre-processing for improving the quality of image and meeting the needs of higher lever processing tasks. The goal of image denoising is to remove the noise while retaining as much as possible the important signal features and details. Generally speaking, it is difficult for traditional image denoising methods to reach a satisfactory trade-off between noise suppression and detail preserving. As an analytic way in time-frequency, wavelet transform is multi-scale and multi-resolution, and provides a new and powerful tool for signal processing. Wavelet has been successfully used in the field of image denoising in the last two decades. Wavelet based denoising has been acknowledged as an important research in image noise reduction and image restoration. Now the focus of the field is transfered to model-based denoising methods, which are mainly depend on statistical characteristics of image wavelet coefficients. The research of denoising theory and ways with respect to wavelet and its statistics is obviously of much significance for both theory and application.
Taken wavelet theory as tool, this dissertation gives systematic and deep investigation to theory and approach of image noise reduction in wavelet domain. The main contributions of this thesis are given below.
1. Overview of wavelet domain image denoising
A comprehensive study in wavelet based image denoising is addressed in the first two chapters of the thesis, which plays fundamental roles for the whole dissertation. Firstly, the development of image noise suppression, particularly wavelet image denoising, is reviewed. Secondly, as there is no a better way to categorize the existing approaches in the field of wavelet denoising, to our knowledge, this dissertation presents a new classification with wide and deep insight, according to the evolvement of the field. The wavelet denoising methods are categorized into four types, and typical algorithms in each type are analyzed. Thirdly, being commonly viewed as fundamental, wavelet thresholding denoising is elaborately discussed. The threshold selection, which is the most critical issue in thresholding denoising, is clearly explained by combination with the corresponding algorithms. Comprehensive comparative simulations are conducted on various representative methods of wavelet thresholding denoising under orthonormal wavelet basis and shift-invariance wavelet basis, respectively. And some useful conclusions are drawn from the experiment results. In the last, regarding the issue of producing 1-dimension simulation signals, a new method is proposed under strict theory deduction to produce noisy signals with high SNR accuracy.
2. Wiener filtering in wavelet domain
Wiener filtering in wavelet domain is a very active branch in the field of wavelet image denoising. Three forms are defined for wavelet based Wiener filtering and correspondingly three new denoising methods are developed. The first is an iterative algorithm for Wiener filtering in wavelet domain. On the basis of empirical Wiener filter, BayesShrink method is adopted to increase accuracy of the expected signals, and multiple wavelet bases were selected properly to uniquely capture some signal characteristics. This iterative method has effectively improved the denoising performance. The second is a joint scheme, which is implemented by BayesShrink algorithm to obtain a pre-denoised image, followed by spatial Lee filtering. The crux of the joint scheme lies in the simple yet effective estimation of the nearly optimal noise variance for Lee filter, and thus the matching between two denoising algorithms in different domains is ensured. Finally, a locally adaptive wavelet domain Wiener filter is proposed. By theoretically analyzing the expected error of Mihcak’s LAWML algorithm, a threshold for local variance estimation of observed wavelet coefficients is derived. Experiment results demonstrate that compared with LAWML algorithm, the presented locally adaptive method has improved the accuracy of variance estimation, and yielded better denoising performance in terms of objective PSNR and subjective visual effect.
3. Research on image denoising based on statistical model of wavelet coefficients
This dissertation has studied Bayesian wavelet domain denoising approach which is based on characteristics of image wavelet coefficients and improved two famous existing algorithms by pointing out some drawback of them. For Sendur’s bivariate model based denoising algorithm, the coefficients of three highest frequency sub-bands, which remain unaltered in Sendur’s original paper, are modified by MAP soft thresholding rule via locally adaptive fashion. For Moulin’s subband adaptive MapShrink algorithm, a new stochastic model is presented. In our model, each coefficient in a subband is assumed to be Laplacian with different marginal standard deviation which can be estimated from a local neighborhood. In this way, a locally adaptive MapShrink threshold is obtained.
This thesis has also developed two algorithms by introducing classification of wavelet coefficients into noise suppression. In the first method, a pixel-adaptive Gaussian mixture model is proposed. Wavelet coefficients were classified into two categories using local Bayesian threshold, and the model parameters such as large and small variances, related probabilities, could be estimated from the information of the two classified coefficients in a neighbouring window. Then Wiener filter is designed according to Minimum Mean Squared Error (MMSE) criterion. The second method extends the neighbouring threshold of wavelet coefficients from 1-D signal to 2-D image case. Each coefficient in a subband is classified as“large”or“small”category, according to its corresponding neighbouring threshold. Those“small”coefficients are set to zero, whereas those“large”coefficients are modeled as zero-mean Gaussian random variables with high local correlation. Simulation results show this algorithm has the advantages of both low computational demands and effective denoising performance.
4. Speckle reduction for SAR images using wavelet statistical model
As a practical example of image denoising, the last part of the thesis covers a specific application of wavelet denoising in SAR image despeckling. The approaches of SAR image speckle suppression, particularly those based on wavelet statistical model, are investigated firstly. A novel locally adaptive speckle filtering is proposed based on Bayesian MAP estimation in wavelet domain. In this method, logarithmically transform is applied to original speckled SAR image, followed by redundant wavelet transform. The proposed method uses the Rayleigh distribution for speckle noise and a Laplacian distribution for modelling the statistics of wavelet coefficients due to signal. A Bayesian estimator with analytical formula is derived from MAP estimation, and the resulting formula is proven to be equivalent to soft thresholding in nature which makes algorithm very simple. In order to exploit the correlation among wavelet coefficients, the parameters of Laplacian model are assumed to be spatially correlated and can be computed from the coefficients in a neighboring window, thus making our method spatially adaptive in wavelet domain. Theoretical analysis and simulation experiment results show that this proposed method can effectively suppress speckle noise in SAR images while preserving as much as possible important signal features and details.
本文以小波分析理论为工具,对小波域图像去噪理论与方法进行了系统、深入的研究,主要工作包括以下四部分:
1、小波图像去噪方法研究综述
本文前两章作为全文的基础,对基于小波的图像去噪方法进行了全面的研究总结。首先综述了图像去噪技术的发展现状,特别是小波图像去噪方法的研究进展。针对目前小波图像去噪领域尚未有一个较全面的分类方法,本文以该领域发展的三个阶段为线索,将小波图像去噪算法进行了新的分类并划分为四类,并对每种类型中代表性的算法做了分析讨论。阈值去噪是小波去噪研究中一类非常重要的方法,对此进行了系统、深入的分析,在阈值选择这一核心问题上,对最具代表性的阈值结合具体的算法在原理与方法上做了清晰的阐述,并对这些典型算法分别在正交小波变换基和平移不变小波基下进行了全面的实验仿真和分析讨论。从实验结果和性能分析中得到了一些有意义的结论。此外,针对一维信号去噪算法仿真中的加噪信号的生成方法进行了研究,在严格的理论推导基础上,提出了一种产生高精度信噪比加噪信号的方法。
2、小波域Wiener滤波方法研究
小波域Wiener滤波方法是小波图像去噪领域中的一个很活跃的研究内容。本文定义了小波域Wiener滤波的三种形式,提出了三种新的去噪算法。首先提出了一种小波域迭代维纳滤波算法;在小波域经验Wiener滤波器基础上,采用BayesShrink阈值算法提高期望信号的估计精度,同时利用多小波基更好的捕捉到信号的某些特定特征,并实现算法的迭代,从而显著增强了算法的去噪性能。提出了一种新的图像组合滤波方法;先用BayesShrink算法对图像做预处理,再进行空域Lee滤波;算法核心在于给出了一种估计预去噪图像中残留噪声方差的近似最优公式,从而保证了两种算法之间的匹配性。提出了一种小波域局部自适应图像去噪算法;通过对LAWML算法的估计误差进行理论分析,得到了一种观测系数局部方差估计的阈值,与LAWML算法比较,新算法在客观峰值信噪比及主观视觉效果方面都有显著的改进。
3、基于小波系数统计模型的图像去噪方法研究
对基于统计模型的Bayes小波域去噪方法进行了深入研究,针对现有的两种算法的不足进行了改进:对Sendur的基于双变量模型的去噪算法,利用MAP软阈值对三个最高频子带进行局部自适应处理;对Moulin的基于拉普拉斯模型的MapShrink子带自适应算法,将小波系数建模为具有不同边缘标准差的拉普拉斯分布,利用邻域局部窗口估计模型参数,从而使得MapShrink阈值具有局部自适应性。
本文将小波系数分类技术引入到图像去噪,提出了两种新的算法。首先在高斯混合模型基础上,提出了一种随像素自适应调整的混合高斯模型,利用局部贝叶斯阈值对小波系数进行分类,通过当前系数邻域窗中两类系数的信息,对模型参数进行估计;再根据MMSE准则设计相应的Wiener滤波器。第二种方法则将一维信号的小波邻域阈值扩展并应用于二维图像,子带内的每个小波系数根据其邻域阈值的大小被划分为“大”系数或者是“小”系数;对“小”系数直接置零,对“大”系数则采用一种具有局部空间强相关性的零均值高斯模型。实验结果表明,这种算法具有计算复杂度低、去噪性能优异的特点。
4、基于小波统计模型的SAR图像相干斑抑制方法研究
作为图像去噪的具体实例,本文最后讨论了小波去噪技术在SAR图像斑点噪声抑制中的应用。回顾了SAR图像相干斑抑制方法的研究进展,重点对基于小波统计模型的SAR图像去斑方法进行了研究,提出了一种基于Bayesian MAP估计的小波域局部自适应性去斑算法。通过对含斑图像做对数变换和冗余小波分解,将斑点噪声、有用信号的小波系数分别建模为瑞利分布、拉普拉斯分布,利用MAP准则得到了一种解析的Bayesian估计表达式,并证明了其处理本质就是一种软阈值去噪,因而具有算法简洁的特点;进一步通过局部邻域窗口估计拉普拉斯参数,使算法具有局部自适应性。理论分析和实验仿真表明,该算法能有效抑制SAR图像的斑点噪声,同时较好地保持了图像的强、弱细节。
An image is often and inevitably corrupted by noise in its acquisition or transmission. The noise in an image has degraded severely the following-up image processing tasks, such as image segmentation, coding, feature extraction, and target detection. Thus noise reduction becomes a very important image pre-processing for improving the quality of image and meeting the needs of higher lever processing tasks. The goal of image denoising is to remove the noise while retaining as much as possible the important signal features and details. Generally speaking, it is difficult for traditional image denoising methods to reach a satisfactory trade-off between noise suppression and detail preserving. As an analytic way in time-frequency, wavelet transform is multi-scale and multi-resolution, and provides a new and powerful tool for signal processing. Wavelet has been successfully used in the field of image denoising in the last two decades. Wavelet based denoising has been acknowledged as an important research in image noise reduction and image restoration. Now the focus of the field is transfered to model-based denoising methods, which are mainly depend on statistical characteristics of image wavelet coefficients. The research of denoising theory and ways with respect to wavelet and its statistics is obviously of much significance for both theory and application.
Taken wavelet theory as tool, this dissertation gives systematic and deep investigation to theory and approach of image noise reduction in wavelet domain. The main contributions of this thesis are given below.
1. Overview of wavelet domain image denoising
A comprehensive study in wavelet based image denoising is addressed in the first two chapters of the thesis, which plays fundamental roles for the whole dissertation. Firstly, the development of image noise suppression, particularly wavelet image denoising, is reviewed. Secondly, as there is no a better way to categorize the existing approaches in the field of wavelet denoising, to our knowledge, this dissertation presents a new classification with wide and deep insight, according to the evolvement of the field. The wavelet denoising methods are categorized into four types, and typical algorithms in each type are analyzed. Thirdly, being commonly viewed as fundamental, wavelet thresholding denoising is elaborately discussed. The threshold selection, which is the most critical issue in thresholding denoising, is clearly explained by combination with the corresponding algorithms. Comprehensive comparative simulations are conducted on various representative methods of wavelet thresholding denoising under orthonormal wavelet basis and shift-invariance wavelet basis, respectively. And some useful conclusions are drawn from the experiment results. In the last, regarding the issue of producing 1-dimension simulation signals, a new method is proposed under strict theory deduction to produce noisy signals with high SNR accuracy.
2. Wiener filtering in wavelet domain
Wiener filtering in wavelet domain is a very active branch in the field of wavelet image denoising. Three forms are defined for wavelet based Wiener filtering and correspondingly three new denoising methods are developed. The first is an iterative algorithm for Wiener filtering in wavelet domain. On the basis of empirical Wiener filter, BayesShrink method is adopted to increase accuracy of the expected signals, and multiple wavelet bases were selected properly to uniquely capture some signal characteristics. This iterative method has effectively improved the denoising performance. The second is a joint scheme, which is implemented by BayesShrink algorithm to obtain a pre-denoised image, followed by spatial Lee filtering. The crux of the joint scheme lies in the simple yet effective estimation of the nearly optimal noise variance for Lee filter, and thus the matching between two denoising algorithms in different domains is ensured. Finally, a locally adaptive wavelet domain Wiener filter is proposed. By theoretically analyzing the expected error of Mihcak’s LAWML algorithm, a threshold for local variance estimation of observed wavelet coefficients is derived. Experiment results demonstrate that compared with LAWML algorithm, the presented locally adaptive method has improved the accuracy of variance estimation, and yielded better denoising performance in terms of objective PSNR and subjective visual effect.
3. Research on image denoising based on statistical model of wavelet coefficients
This dissertation has studied Bayesian wavelet domain denoising approach which is based on characteristics of image wavelet coefficients and improved two famous existing algorithms by pointing out some drawback of them. For Sendur’s bivariate model based denoising algorithm, the coefficients of three highest frequency sub-bands, which remain unaltered in Sendur’s original paper, are modified by MAP soft thresholding rule via locally adaptive fashion. For Moulin’s subband adaptive MapShrink algorithm, a new stochastic model is presented. In our model, each coefficient in a subband is assumed to be Laplacian with different marginal standard deviation which can be estimated from a local neighborhood. In this way, a locally adaptive MapShrink threshold is obtained.
This thesis has also developed two algorithms by introducing classification of wavelet coefficients into noise suppression. In the first method, a pixel-adaptive Gaussian mixture model is proposed. Wavelet coefficients were classified into two categories using local Bayesian threshold, and the model parameters such as large and small variances, related probabilities, could be estimated from the information of the two classified coefficients in a neighbouring window. Then Wiener filter is designed according to Minimum Mean Squared Error (MMSE) criterion. The second method extends the neighbouring threshold of wavelet coefficients from 1-D signal to 2-D image case. Each coefficient in a subband is classified as“large”or“small”category, according to its corresponding neighbouring threshold. Those“small”coefficients are set to zero, whereas those“large”coefficients are modeled as zero-mean Gaussian random variables with high local correlation. Simulation results show this algorithm has the advantages of both low computational demands and effective denoising performance.
4. Speckle reduction for SAR images using wavelet statistical model
As a practical example of image denoising, the last part of the thesis covers a specific application of wavelet denoising in SAR image despeckling. The approaches of SAR image speckle suppression, particularly those based on wavelet statistical model, are investigated firstly. A novel locally adaptive speckle filtering is proposed based on Bayesian MAP estimation in wavelet domain. In this method, logarithmically transform is applied to original speckled SAR image, followed by redundant wavelet transform. The proposed method uses the Rayleigh distribution for speckle noise and a Laplacian distribution for modelling the statistics of wavelet coefficients due to signal. A Bayesian estimator with analytical formula is derived from MAP estimation, and the resulting formula is proven to be equivalent to soft thresholding in nature which makes algorithm very simple. In order to exploit the correlation among wavelet coefficients, the parameters of Laplacian model are assumed to be spatially correlated and can be computed from the coefficients in a neighboring window, thus making our method spatially adaptive in wavelet domain. Theoretical analysis and simulation experiment results show that this proposed method can effectively suppress speckle noise in SAR images while preserving as much as possible important signal features and details.
引文
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