多尺度变换域图像反卷积理论研究
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摘要
在实际应用中,数字图像往往会在诸多模糊和噪声因素的影响下变成质量下降的退化图像。而在许多应用领域中,需要的是清晰、高质量的图像,因此,如何提高退化图像的质量是一项具有重要意义的研究。图像反卷积技术作为这一领域众多研究方向中(如图像复原、超分辨率重建等)的一项核心技术,具有重要的科学意义和应用价值。
目前,图像反卷积技术研究的重点是如何在克服问题病态性的同时获得清晰的边缘和细节信息。图像在变换域中往往表现出其在空间域所无法获得的特性。在反卷积问题中利用这些特性,可以获得优于传统方法的结果。本文对多尺度变换域中的图像反卷积技术进行了深入的研究,主要工作如下:
1.在基于小波域统计模型的图像反卷积算法方面,针对目前基于小波域隐Markov树(HMT)模型的图像反卷积算法模型训练不准确以及运算效率较低的问题,提出了一种改进算法。该算法使用Fourier-平稳小波规整化对退化图像进行预处理,并在预处理图像基础上建立统计模型,将其作为原始图像的先验知识,通过MAP方法对图像进行反卷积,无需循环地进行训练。另外,提出使用小波域背景隐Markov树(CHMT)模型代替原模型,加强了尺度内小波系数的相关性描述,以进一步提高了先验知识的精确程度,从而加强了反卷积算法对图像边缘的复原能力。
2.对基于Hopfield神经网络的图像反卷积算法进行了研究,针对目前该类算法对图像细节复原能力不足的问题,将小波域统计模型引入到神经网络框架下,使两者的优点相结合,利用Hopfield神经网络自身的优化能力完成反卷积。并且针对网络权值矩阵求取困难的问题,提出一种高度并行的权值矩阵求取算法,仅通过快速Fourier变换和小波变换算法即可实现,具有较高的运算效率。
3.在利用小波变换表示二维图像时,其对图像中方向性信息的表现能力有限,在小波域进行图像反卷积时同样面临着这样的问题。因此,本文在其它变换域对图像反卷积问题进行了研究,提出一种Contourlet域的图像反卷积算法。Contourlet变换是一种同时具有多尺度性多方向性的图像变换方法,与传统的二维可分离小波变换相比,Contourlet变换能够更有效地表示图像中的轮廓和纹理。该算法以边界优化算法为基础,在Contourlet域迭代进行,对图像轮廓和纹理的恢复能力要优于同类小波域算法。
In the practical applications, the digital images are always degraded by many blurred and noisy factors. But in many situations, the clear and high-quality images are required, so how to improve the quality of degraded images is an important research. The technology of image deconvolution is the key technology of this research area (such as image restoration, super-resolution reconstruction).
At present, the focus of the research of image deconvolution technology is how to overcome the ill-posedness and obtain clear edge and detail information at the same time. Images always exhibit special properties in transform domain, which can’t be obtained in spatial domain. These properties can be utilized to get better results than the traditional methods in image deconvolution problem. In this paper, we mainly research and develop three kinds of image deconvolution algorithms in the multi-scale transform domain.
1. Image deconvolution algorithms based on wavelet domain statistical model. Aiming at the problems that the results of image deconvolution algorithms based on the wavelet domain hidden Markov tree model is not good enough caused by the unprecise of the model training and the computational efficiency is low, an improved algorithm is proposed. The proposed algorithm employs the modified Fourier-wavelet regularized algorithm to pre-process the degraded image, and generate a sample image, which can be used to be the foundation of the model, the prior knowledge of the original image, and the deconvolution is finished under the MAP framework. In addition, the contextual hidden Markov tree model is adopted to substitute the original model, the description of relationship of the wavelet coefficients in the same scale is reinforced, so the image quality is improved further.
2. Research image deconvolution algorithms based on Hopfield neural network, aiming at the poor ability of detail recovery of this kind of algorithms at present, the wavelet domain hidden Markov tree model is introduced into the framework of neural network, and combines the advantages of these two methods, utilize the convergence property of Hopfield network to complete the deconvolution. In this algorithm, the computation of the weight value matrix is a difficult problem.So we propose a method to solve this problem, only the fast Fourier transform and fast wavelet transform are used, and it can be run in parallel on several processor simultaneously, so the efficiency is high.
3. When the image is presented by the wavelet transform, the description ability of the directional information in the image is insufficient inherently, it is also a problem in the wavelet domain image deconvolution. So in this paper, based on the research of other wavelet domain deconvolution algorithms, a new algorithm in contourlet domain is proposed. Contourlet transform is a multi-scale and multi-direction image transform, compared with the traditional separatable 2D wavelet transform, contourlet can express the edge and texture of images more efficiently. The proposed algorithm is based on the bounded optimize algorithm, and proceeds in the contourlet domain iteratively. The proposed algorithm is better to recovery the contour and texture of images, compared with the similar algorithms in wavelet domain.
目前,图像反卷积技术研究的重点是如何在克服问题病态性的同时获得清晰的边缘和细节信息。图像在变换域中往往表现出其在空间域所无法获得的特性。在反卷积问题中利用这些特性,可以获得优于传统方法的结果。本文对多尺度变换域中的图像反卷积技术进行了深入的研究,主要工作如下:
1.在基于小波域统计模型的图像反卷积算法方面,针对目前基于小波域隐Markov树(HMT)模型的图像反卷积算法模型训练不准确以及运算效率较低的问题,提出了一种改进算法。该算法使用Fourier-平稳小波规整化对退化图像进行预处理,并在预处理图像基础上建立统计模型,将其作为原始图像的先验知识,通过MAP方法对图像进行反卷积,无需循环地进行训练。另外,提出使用小波域背景隐Markov树(CHMT)模型代替原模型,加强了尺度内小波系数的相关性描述,以进一步提高了先验知识的精确程度,从而加强了反卷积算法对图像边缘的复原能力。
2.对基于Hopfield神经网络的图像反卷积算法进行了研究,针对目前该类算法对图像细节复原能力不足的问题,将小波域统计模型引入到神经网络框架下,使两者的优点相结合,利用Hopfield神经网络自身的优化能力完成反卷积。并且针对网络权值矩阵求取困难的问题,提出一种高度并行的权值矩阵求取算法,仅通过快速Fourier变换和小波变换算法即可实现,具有较高的运算效率。
3.在利用小波变换表示二维图像时,其对图像中方向性信息的表现能力有限,在小波域进行图像反卷积时同样面临着这样的问题。因此,本文在其它变换域对图像反卷积问题进行了研究,提出一种Contourlet域的图像反卷积算法。Contourlet变换是一种同时具有多尺度性多方向性的图像变换方法,与传统的二维可分离小波变换相比,Contourlet变换能够更有效地表示图像中的轮廓和纹理。该算法以边界优化算法为基础,在Contourlet域迭代进行,对图像轮廓和纹理的恢复能力要优于同类小波域算法。
In the practical applications, the digital images are always degraded by many blurred and noisy factors. But in many situations, the clear and high-quality images are required, so how to improve the quality of degraded images is an important research. The technology of image deconvolution is the key technology of this research area (such as image restoration, super-resolution reconstruction).
At present, the focus of the research of image deconvolution technology is how to overcome the ill-posedness and obtain clear edge and detail information at the same time. Images always exhibit special properties in transform domain, which can’t be obtained in spatial domain. These properties can be utilized to get better results than the traditional methods in image deconvolution problem. In this paper, we mainly research and develop three kinds of image deconvolution algorithms in the multi-scale transform domain.
1. Image deconvolution algorithms based on wavelet domain statistical model. Aiming at the problems that the results of image deconvolution algorithms based on the wavelet domain hidden Markov tree model is not good enough caused by the unprecise of the model training and the computational efficiency is low, an improved algorithm is proposed. The proposed algorithm employs the modified Fourier-wavelet regularized algorithm to pre-process the degraded image, and generate a sample image, which can be used to be the foundation of the model, the prior knowledge of the original image, and the deconvolution is finished under the MAP framework. In addition, the contextual hidden Markov tree model is adopted to substitute the original model, the description of relationship of the wavelet coefficients in the same scale is reinforced, so the image quality is improved further.
2. Research image deconvolution algorithms based on Hopfield neural network, aiming at the poor ability of detail recovery of this kind of algorithms at present, the wavelet domain hidden Markov tree model is introduced into the framework of neural network, and combines the advantages of these two methods, utilize the convergence property of Hopfield network to complete the deconvolution. In this algorithm, the computation of the weight value matrix is a difficult problem.So we propose a method to solve this problem, only the fast Fourier transform and fast wavelet transform are used, and it can be run in parallel on several processor simultaneously, so the efficiency is high.
3. When the image is presented by the wavelet transform, the description ability of the directional information in the image is insufficient inherently, it is also a problem in the wavelet domain image deconvolution. So in this paper, based on the research of other wavelet domain deconvolution algorithms, a new algorithm in contourlet domain is proposed. Contourlet transform is a multi-scale and multi-direction image transform, compared with the traditional separatable 2D wavelet transform, contourlet can express the edge and texture of images more efficiently. The proposed algorithm is based on the bounded optimize algorithm, and proceeds in the contourlet domain iteratively. The proposed algorithm is better to recovery the contour and texture of images, compared with the similar algorithms in wavelet domain.
引文
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