基于量子力学的图像处理方法研究
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摘要
量子力学是二十世纪物理学最重要的科学成就之一,具有划时代意义。量子力学中的规律不仅支配着微观世界,而且也支配着宏观世界。信号作为自然界中客观存在的物理实体,它在物理上也受量子力学原理约束。本文借鉴并利用量子力学的基本概念与基本原理,充分发挥量子特性优势,在经典计算机上,提出了解决基于量子力学原理的图像处理新方法或改进方法。这些方法不依赖于量子级物理设备,实现了量子力学理论与图像处理技术的相互渗透与有机结合,不仅取得了较好的图像处理效果,而且为图像处理技术引入了一种新的理论工具。
本论文从实际图像处理应用背景出发,结合量子力学的基本概念、原理,围绕图像去斑、图像增强、图像分割三个关键图像处理技术,展开了如下研究工作：
首先,在系统分析各种图像去斑方法的基础上,从医学超声图像去斑方法研究出发,借鉴量子力学的基本理论,利用双树复小波变换,提出了两种量子衍生图像去斑方法。在这两种方法中,首先提出了两种带可调参数的改进信号模型。改进信号模型较传统的信号模型自适应更强,能适合各种不同概率分布的信号,可调参数的拟合过程简单有效。然后,考虑到小波系数的尺度间相关性,根据父-子代小波系数的归一化乘积,在高频子带中引入量子衍生信号与噪声出现概率。随后,利用贝叶斯估计理论,提出了一种基于量子衍生收缩因子的图像去斑方法和一种基于量子衍生阈值的图像去斑方法。这两种方法通过采用局部自适应的量子衍生参数,较好地解决了抑斑平滑与保持细节之间的矛盾。本论文提出的两种图像去斑方法计算复杂度低,自适应性强和鲁棒性好,不仅能有效地抑制斑点噪声,而且能更好地保持图像细节。此外,这两种方法具有一定普遍适用性,不仅对医学超声图像的去斑非常有效,而且对SAR图像相干斑抑制同样有效,具有很好的推广应用前景。
其次,结合医学图像的特点,本论文提出了一种基于量子概率统计的图像增强方法。该方法首先利用量子力学基本原理,定义了两种不同的像素量子比特表达形式；然后,结合3×3邻域像素灰度关联性,提出了一种基于量子概率统计的图像增强算子。为了优化图像增强的效果,本算子的灰度阂值参数可根据子采样图像信息熵自适应确定。本论文提出的图像增强方法,综合考虑了图像全局与局部信息,较传统方法能更有效地提高图像成像质量,不仅增强图像细节信息与图像对比度,而且较好地保持了图像的基本信息。此外,本论文提出的方法计算复杂度低,具有一定的普适性,不仅能有效增强医学图像,而且能有效改善其它非医学图像的视觉效果。
最后,定义了一种自适应隶属度函数,提出了一种基于自适应最大模糊熵的多阈值图像分割方法。为了提高多阈值的求解效率,本论文将量子遗传算法应用于图像分割方法中,并对已有的量子遗传算法进行了一些有益的改进,提高了多阈值图像分割结果准确性、稳定性以及算法的实时处理能力。结合本论文提出的自适应最大模糊熵评价函数,本论文提出了一种基于改进量子遗传算法的多阈值图像分割方法。实验结果表明本论文提出的方法具有稳定的求解性能和更好的图像分割效果。
Quantum mechanics is one of the most important scientific achievements of physics in the twentieth century. Microscopic world is not only dominated by the laws of quantum mechanics, but also the macroscopic world is also done. As an objective physical entity in nature, the Image signal is also affected by the physical constraints of quantum mechanics. With the principle, the basic concepts of quantum mechanics and the advantages of quantum properties, the novel methods of image processing are proposed for the solution of some specific problems in the classical computer, which don't depend on the quantum level of physical equipment. It promotes the realization of the combination and mutual penetration between quantum mechanics and image processing technology. Not only the better image processing results are achieved, but also a new theoretical tool is introduced into the image processing theory.
From practical applications of image processing, three key image processing techniques are studied with the basic concept and principle of quantum mechanics in this thesis which focus on the image despeckling, image enhancement and image segmentation. The main work of this thesis is summarized as follows.
Firstly, through analyzing and comparing various image despeckling methods, two quantum-inspired despeckling methods for medical ultrasound images are proposed by combining the dual-tree complex wavelet transform (DTCWT) with the basic theory of quantum mechanics. In the two proposed methods, two improved signal models with an adjustable parameter are built up for the log-transformed images wavelet coefficients firstly. Both the improved signal models have much better adaptability than the traditional signal models which can suit different probability distribution signals and the fitting procedure of adjustable parameter is simple and effective. And then, considering the inter-scale dependency of coefficients, the quantum-inspired probability of signal and noise is firstly introduced based on the normalized products of the coefficients and their parents. Finally, using the Bayesian estimation theory, two image despeckling methods are proposed, where one is based on a quantum-inspired shrinkage factor and the other is based on quantum-inspired threshold. By adopting different local adaptive quantum-inspired parameters, both methods can notably reduce speckle noise and preserve image details effectively, which have low computational complexity, strong adaptability and robustness. In addtion, both methods have universal applicability to some degree, which can effectively suppress speckle noise not only for medical ultrasound images but also Synthetic Aperture Radar (SAR) images, which have good generalization and application.
Secondly, two different mathematics expressions of pixel quantum bit are given first according to the basic principle of quantum mechanics. Then, aiming at the characteristics of medical images and combining with gray correlative characteristics of pixels in 3x3 neighborhoods, an image enhancement operator is proposed based on quantum probability statistics. In order to optimize the effect of image enhancement, the gray threshold parameter of the operator is adaptively chosen based on the sub-sampling image entropy. The proposed image enhancement method considers both global and local image information and can improve images quality effectively. In addtion, it has low computational complexity and universal applicability to some degree, which can not only enhance medical images effectively, but also improve vision effect of nonmedical images.
Finally, an adaptive membership function is defined and a method of multi-threshold image segmentation is proposed based on the adaptive maximum fuzzy entropy. In order to improve searching efficiency of multi-threshold, quantum genetic algorithm is applied to image segmentation and some improvements of existed quantum genetic algorithm are made which can not only increase accuracy and stablility for the results of multi-threshold image segmentation but also improve the real-time dealing ability. In this thesis, a method of multi-threshold image segmentation is proposed based on an improved quantum genetic algorithm, which combines with the evaluation function of adaptive maximum fuzzy entropy. Experimental results demonstrated that the proposed method had a more stable performance of solution and can achieve much better image segmentation effect.
本论文从实际图像处理应用背景出发,结合量子力学的基本概念、原理,围绕图像去斑、图像增强、图像分割三个关键图像处理技术,展开了如下研究工作：
首先,在系统分析各种图像去斑方法的基础上,从医学超声图像去斑方法研究出发,借鉴量子力学的基本理论,利用双树复小波变换,提出了两种量子衍生图像去斑方法。在这两种方法中,首先提出了两种带可调参数的改进信号模型。改进信号模型较传统的信号模型自适应更强,能适合各种不同概率分布的信号,可调参数的拟合过程简单有效。然后,考虑到小波系数的尺度间相关性,根据父-子代小波系数的归一化乘积,在高频子带中引入量子衍生信号与噪声出现概率。随后,利用贝叶斯估计理论,提出了一种基于量子衍生收缩因子的图像去斑方法和一种基于量子衍生阈值的图像去斑方法。这两种方法通过采用局部自适应的量子衍生参数,较好地解决了抑斑平滑与保持细节之间的矛盾。本论文提出的两种图像去斑方法计算复杂度低,自适应性强和鲁棒性好,不仅能有效地抑制斑点噪声,而且能更好地保持图像细节。此外,这两种方法具有一定普遍适用性,不仅对医学超声图像的去斑非常有效,而且对SAR图像相干斑抑制同样有效,具有很好的推广应用前景。
其次,结合医学图像的特点,本论文提出了一种基于量子概率统计的图像增强方法。该方法首先利用量子力学基本原理,定义了两种不同的像素量子比特表达形式；然后,结合3×3邻域像素灰度关联性,提出了一种基于量子概率统计的图像增强算子。为了优化图像增强的效果,本算子的灰度阂值参数可根据子采样图像信息熵自适应确定。本论文提出的图像增强方法,综合考虑了图像全局与局部信息,较传统方法能更有效地提高图像成像质量,不仅增强图像细节信息与图像对比度,而且较好地保持了图像的基本信息。此外,本论文提出的方法计算复杂度低,具有一定的普适性,不仅能有效增强医学图像,而且能有效改善其它非医学图像的视觉效果。
最后,定义了一种自适应隶属度函数,提出了一种基于自适应最大模糊熵的多阈值图像分割方法。为了提高多阈值的求解效率,本论文将量子遗传算法应用于图像分割方法中,并对已有的量子遗传算法进行了一些有益的改进,提高了多阈值图像分割结果准确性、稳定性以及算法的实时处理能力。结合本论文提出的自适应最大模糊熵评价函数,本论文提出了一种基于改进量子遗传算法的多阈值图像分割方法。实验结果表明本论文提出的方法具有稳定的求解性能和更好的图像分割效果。
Quantum mechanics is one of the most important scientific achievements of physics in the twentieth century. Microscopic world is not only dominated by the laws of quantum mechanics, but also the macroscopic world is also done. As an objective physical entity in nature, the Image signal is also affected by the physical constraints of quantum mechanics. With the principle, the basic concepts of quantum mechanics and the advantages of quantum properties, the novel methods of image processing are proposed for the solution of some specific problems in the classical computer, which don't depend on the quantum level of physical equipment. It promotes the realization of the combination and mutual penetration between quantum mechanics and image processing technology. Not only the better image processing results are achieved, but also a new theoretical tool is introduced into the image processing theory.
From practical applications of image processing, three key image processing techniques are studied with the basic concept and principle of quantum mechanics in this thesis which focus on the image despeckling, image enhancement and image segmentation. The main work of this thesis is summarized as follows.
Firstly, through analyzing and comparing various image despeckling methods, two quantum-inspired despeckling methods for medical ultrasound images are proposed by combining the dual-tree complex wavelet transform (DTCWT) with the basic theory of quantum mechanics. In the two proposed methods, two improved signal models with an adjustable parameter are built up for the log-transformed images wavelet coefficients firstly. Both the improved signal models have much better adaptability than the traditional signal models which can suit different probability distribution signals and the fitting procedure of adjustable parameter is simple and effective. And then, considering the inter-scale dependency of coefficients, the quantum-inspired probability of signal and noise is firstly introduced based on the normalized products of the coefficients and their parents. Finally, using the Bayesian estimation theory, two image despeckling methods are proposed, where one is based on a quantum-inspired shrinkage factor and the other is based on quantum-inspired threshold. By adopting different local adaptive quantum-inspired parameters, both methods can notably reduce speckle noise and preserve image details effectively, which have low computational complexity, strong adaptability and robustness. In addtion, both methods have universal applicability to some degree, which can effectively suppress speckle noise not only for medical ultrasound images but also Synthetic Aperture Radar (SAR) images, which have good generalization and application.
Secondly, two different mathematics expressions of pixel quantum bit are given first according to the basic principle of quantum mechanics. Then, aiming at the characteristics of medical images and combining with gray correlative characteristics of pixels in 3x3 neighborhoods, an image enhancement operator is proposed based on quantum probability statistics. In order to optimize the effect of image enhancement, the gray threshold parameter of the operator is adaptively chosen based on the sub-sampling image entropy. The proposed image enhancement method considers both global and local image information and can improve images quality effectively. In addtion, it has low computational complexity and universal applicability to some degree, which can not only enhance medical images effectively, but also improve vision effect of nonmedical images.
Finally, an adaptive membership function is defined and a method of multi-threshold image segmentation is proposed based on the adaptive maximum fuzzy entropy. In order to improve searching efficiency of multi-threshold, quantum genetic algorithm is applied to image segmentation and some improvements of existed quantum genetic algorithm are made which can not only increase accuracy and stablility for the results of multi-threshold image segmentation but also improve the real-time dealing ability. In this thesis, a method of multi-threshold image segmentation is proposed based on an improved quantum genetic algorithm, which combines with the evaluation function of adaptive maximum fuzzy entropy. Experimental results demonstrated that the proposed method had a more stable performance of solution and can achieve much better image segmentation effect.
引文
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