图像恢复及重建模型设计和算法研究
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摘要
图像是人类获取信息的主要来源.由于航空航天、生物医学工程、工业检测、文化艺术、模式识别、军事等发展需求,图像处理越来越受到关注,已经逐步发展成为一门前景远大的新型学科.就不同的处理目的,数字图像处理主要可以分为几何处理、算术处理、图像编码、图像增强、图像复原、图像重建、图像分割和图像分析等几项内容.本论文主要研究图像复原和图像重建问题,包括图像去噪问题、CT图像重建、核磁共振图像重建和光声图像重建等工作,研究这些问题的数学模型的建立和相应快速算法的设计.
在医学成像中,非加性泊松噪声干扰居多,研究成果相对较少.Le等人设计了TV正则化下的泊松噪声移除模型,然而一阶的全变差算子产生的不可避免的“分片常数”现象引入了图像假象.而高阶模型又容易导致复原图像边缘的过度光滑.针对这些存在的问题,本论文通过引入边缘控制函数,提出了一种自适应的泊松噪声移除高阶模型,证明了这种模型解存在且唯一,设计了针对此模型的快速算法,讨论了相应算法的收敛性.
图像重建一般指的是从原始扫描数据经过计算机采用特定的算法处理最后得到能用于诊断的一幅横断面图像.本论文主要研究三种重要的图像重建技术,即基于X-ray的计算机断层成像,核磁共振成像,以及近几年新兴起的光声成像.
由于X-ray辐射对人体有害,近年来关于如何用尽可能小的X-ray辐射剂量重建适合临床应用的图像受到广泛关注.然而剂量的减少会导致伪影以及噪声等劣质的成像图像,给临床诊断带来困难.本论文本着低剂量X-ray辐射的原则,提出了一种新的自适应的小波稀疏正则化算法用于CT图像重建问题.这种自适应的小波稀疏正则化算法克服了传统的同一小波紧框架稀疏正则化算法不能适合于不同的CT图像的缺点.为了进一步提高重建质量和速度,本论文提出了一种新的自适应的tensor framelet稀疏正则化算法用于CT图像重建问题.新提出的自适应的tensor framelet稀疏正则化算法首先基于事先给定的参考图像,根据UEP条件构造一个tensor framelet,然后将新构建的自适应的tensor framelet用于CT图像重建中,新提出的方法减少了CT图像重建所需要的投影数从而减少了扫描时间降低了X-ray的摄入,另外,算法还采用了GPU并行加速,进一步提高了运算效率.
核磁共振成像是另外一个研究活跃也更为复杂的领域,而扩散加权成像作为核磁共振成像的新技术是利用MRI观察活体组织水分子弥散运动最理想的成像方法.然而核磁共振成像往往具有扫描时间过长和成像分辨率不高等缺点.为了提高重建图像质量,本文提出了一种新的基于压缩感知的扩散加权成像MRI模型,即相位约束的低秩模型,新的模型考虑了不同扩散方向的相关性.针对这种新模型本文提出了一种基于奇异值分解和部分傅里叶变换的快速算法.进一步地,为了降低采样率从而减少扫描时间,本论文还融合了序列并结合全面自动校准部分并行采集技术(GRAPPA)到新算法中,图像重建所需采样数据明显减少.
光声成像能够有效的进行生物组织和功能成像,它结合了光学成像的高对比度特性和超声成像的高穿透深度特性,可以提供高对比度和高分辨率组织成像.本文建立了多光源的光声成像(MS-QPAT)小波稀疏正则化模型.由于这种类型的问题通常为非线性、非可微的非凸模型,数值算法研究较少.本文给出了这种问题的快速数值算法和相关的收敛性分析.
Image is the main source for human to obtain information. As the devel-opment of aerospace, biomedical engineering, industrial inspection, culture and art, pattern recognition, and military etc., image processing has been paid more and more attention and has gradually become a new discipline outlook. In terms of the different processing purposes, digital image processing can be divided into geometric processing, arithmetic processing, image coding, image enhancement, image restoration, image reconstruction, image segmentation and image analysis. This paper mainly investigates image restoration and image reconstruction prob-lems, including image denoising, CT image reconstruction, magnetic resonance image reconstruction and photoacoustic tomography image reconstruction. The mathematical models of these problems are proposed and the corresponding fast algorithms are designed.
In medical imaging field, Poisson noise appears more frequently. Poisson noise is non-additive noise, fewer results for removing Poisson noise can be found at present. Le et al. proposed the Poisson noise removal TV regularization model. However, the second-order total variation regularization model suffers from "piece-wise constant" inevitably and the high order model will easily lead to the over-smooth of the image edge. To avoid these problems, by introducing edge control function, this thesis proposes the adaptive high order Poisson noise removal model and proves that the solution of the proposed adaptive model exists and is unique. In addition, a fast algorithm for this model is presented, and also the corresponding convergence of the proposed algorithm is discussed.
Image reconstruction generally means to obtain a cross-sectional image for diagnosis by some specific algorithms based on the raw scanning data. This pa-per mainly studies three kinds of important image reconstruction techniques, i.e. Computed tomography based on X-ray (CT), magnetic resonance imaging (MRI), and photoacoustic tomography (PAT).
Since the X-ray radiation is harmful to the human body, how to reconstruct images used for clinical application with less X-ray dose are paid more and more attention. However, dose reduction will result in poor quality image such as image artifacts and noise etc., which will bring clinical diagnosis difficult. Based on reduc-ing X-ray radiation, a new adaptive wavelet sparse regularization algorithm for CT reconstruction is introduced. The proposed adaptive wavelet sparse regularization algorithm overcomes the problem that the traditional wavelet tight frame sparse regularization algorithm is not suitable for all the different CT images with differ-ent structures and details. In order to further improve the image reconstruction quality and speed, a new adaptive tensor framelet sparse regularization algorithm for CT image reconstruction is presented. In the new adaptive algorithm, adaptive tensor framelet is constructed based on the UEP condition according to the given reference image in advance, then the tensor framelet constructed by the first step is used to reconstruct CT images. The proposed adaptive algorithms reduce the number of projections, which means reducing the scan time so as to reduce X-ray radiation. The new algorithms are accelerated by GPU parallel technology, so the efficiency of algorithms are further enhanced.
Magnetic resonance imaging is another active research and also more complex. Diffusion-weighted imaging as a new technology for magnetic resonance imaging is the most ideal method to observe the water molecular diffusion in vivo tissue. However, magnetic resonance imaging often suffers from too long scanning time and low imaging resolution. In order to improve the quality of image reconstruc-tion, this thesis presents a new diffusion weighted imaging MRI model based on Compressive Sensing, i.e. phase-constrained low-rank (PCLR) model. Different from the traditional low rank model, the new proposed model takes into account the correlation of different diffusion directions. An efficient and easy-to-implement image reconstruction algorithm, mainly consisting of partial Fourier update and singular value decomposition, was developed for solving PCLR. Further more, generalized autocalibrating partially parallel acquisitions (GRAPPA) was incorpo-rated for better phase estimation while allowing higher undersampling factor. The required sample data for image reconstruction significantly reduced.
Photoacoustic imaging can be performed effectively for biological tissue and functional imaging. This imaging method combines with the high penetration characteristics of optical imaging and high contrast characteristics of ultrasonic imaging, can provide high contrast and high resolution imaging of tissue. The research results for photoacoustic imaging sparse regularization are less, especially the photoacoustic imaging with multi-source and multi-spectrum. The photoa-coustic imaging multiple light sources (MS-QPAT) wavelet sparse regularization model is established. Since this type of problem is generally non-convex, non-linear and non-differentiable, many existing numerical algorithm can not used for it. So, further studies of fast numerical algorithms and convergence results are established.
在医学成像中,非加性泊松噪声干扰居多,研究成果相对较少.Le等人设计了TV正则化下的泊松噪声移除模型,然而一阶的全变差算子产生的不可避免的“分片常数”现象引入了图像假象.而高阶模型又容易导致复原图像边缘的过度光滑.针对这些存在的问题,本论文通过引入边缘控制函数,提出了一种自适应的泊松噪声移除高阶模型,证明了这种模型解存在且唯一,设计了针对此模型的快速算法,讨论了相应算法的收敛性.
图像重建一般指的是从原始扫描数据经过计算机采用特定的算法处理最后得到能用于诊断的一幅横断面图像.本论文主要研究三种重要的图像重建技术,即基于X-ray的计算机断层成像,核磁共振成像,以及近几年新兴起的光声成像.
由于X-ray辐射对人体有害,近年来关于如何用尽可能小的X-ray辐射剂量重建适合临床应用的图像受到广泛关注.然而剂量的减少会导致伪影以及噪声等劣质的成像图像,给临床诊断带来困难.本论文本着低剂量X-ray辐射的原则,提出了一种新的自适应的小波稀疏正则化算法用于CT图像重建问题.这种自适应的小波稀疏正则化算法克服了传统的同一小波紧框架稀疏正则化算法不能适合于不同的CT图像的缺点.为了进一步提高重建质量和速度,本论文提出了一种新的自适应的tensor framelet稀疏正则化算法用于CT图像重建问题.新提出的自适应的tensor framelet稀疏正则化算法首先基于事先给定的参考图像,根据UEP条件构造一个tensor framelet,然后将新构建的自适应的tensor framelet用于CT图像重建中,新提出的方法减少了CT图像重建所需要的投影数从而减少了扫描时间降低了X-ray的摄入,另外,算法还采用了GPU并行加速,进一步提高了运算效率.
核磁共振成像是另外一个研究活跃也更为复杂的领域,而扩散加权成像作为核磁共振成像的新技术是利用MRI观察活体组织水分子弥散运动最理想的成像方法.然而核磁共振成像往往具有扫描时间过长和成像分辨率不高等缺点.为了提高重建图像质量,本文提出了一种新的基于压缩感知的扩散加权成像MRI模型,即相位约束的低秩模型,新的模型考虑了不同扩散方向的相关性.针对这种新模型本文提出了一种基于奇异值分解和部分傅里叶变换的快速算法.进一步地,为了降低采样率从而减少扫描时间,本论文还融合了序列并结合全面自动校准部分并行采集技术(GRAPPA)到新算法中,图像重建所需采样数据明显减少.
光声成像能够有效的进行生物组织和功能成像,它结合了光学成像的高对比度特性和超声成像的高穿透深度特性,可以提供高对比度和高分辨率组织成像.本文建立了多光源的光声成像(MS-QPAT)小波稀疏正则化模型.由于这种类型的问题通常为非线性、非可微的非凸模型,数值算法研究较少.本文给出了这种问题的快速数值算法和相关的收敛性分析.
Image is the main source for human to obtain information. As the devel-opment of aerospace, biomedical engineering, industrial inspection, culture and art, pattern recognition, and military etc., image processing has been paid more and more attention and has gradually become a new discipline outlook. In terms of the different processing purposes, digital image processing can be divided into geometric processing, arithmetic processing, image coding, image enhancement, image restoration, image reconstruction, image segmentation and image analysis. This paper mainly investigates image restoration and image reconstruction prob-lems, including image denoising, CT image reconstruction, magnetic resonance image reconstruction and photoacoustic tomography image reconstruction. The mathematical models of these problems are proposed and the corresponding fast algorithms are designed.
In medical imaging field, Poisson noise appears more frequently. Poisson noise is non-additive noise, fewer results for removing Poisson noise can be found at present. Le et al. proposed the Poisson noise removal TV regularization model. However, the second-order total variation regularization model suffers from "piece-wise constant" inevitably and the high order model will easily lead to the over-smooth of the image edge. To avoid these problems, by introducing edge control function, this thesis proposes the adaptive high order Poisson noise removal model and proves that the solution of the proposed adaptive model exists and is unique. In addition, a fast algorithm for this model is presented, and also the corresponding convergence of the proposed algorithm is discussed.
Image reconstruction generally means to obtain a cross-sectional image for diagnosis by some specific algorithms based on the raw scanning data. This pa-per mainly studies three kinds of important image reconstruction techniques, i.e. Computed tomography based on X-ray (CT), magnetic resonance imaging (MRI), and photoacoustic tomography (PAT).
Since the X-ray radiation is harmful to the human body, how to reconstruct images used for clinical application with less X-ray dose are paid more and more attention. However, dose reduction will result in poor quality image such as image artifacts and noise etc., which will bring clinical diagnosis difficult. Based on reduc-ing X-ray radiation, a new adaptive wavelet sparse regularization algorithm for CT reconstruction is introduced. The proposed adaptive wavelet sparse regularization algorithm overcomes the problem that the traditional wavelet tight frame sparse regularization algorithm is not suitable for all the different CT images with differ-ent structures and details. In order to further improve the image reconstruction quality and speed, a new adaptive tensor framelet sparse regularization algorithm for CT image reconstruction is presented. In the new adaptive algorithm, adaptive tensor framelet is constructed based on the UEP condition according to the given reference image in advance, then the tensor framelet constructed by the first step is used to reconstruct CT images. The proposed adaptive algorithms reduce the number of projections, which means reducing the scan time so as to reduce X-ray radiation. The new algorithms are accelerated by GPU parallel technology, so the efficiency of algorithms are further enhanced.
Magnetic resonance imaging is another active research and also more complex. Diffusion-weighted imaging as a new technology for magnetic resonance imaging is the most ideal method to observe the water molecular diffusion in vivo tissue. However, magnetic resonance imaging often suffers from too long scanning time and low imaging resolution. In order to improve the quality of image reconstruc-tion, this thesis presents a new diffusion weighted imaging MRI model based on Compressive Sensing, i.e. phase-constrained low-rank (PCLR) model. Different from the traditional low rank model, the new proposed model takes into account the correlation of different diffusion directions. An efficient and easy-to-implement image reconstruction algorithm, mainly consisting of partial Fourier update and singular value decomposition, was developed for solving PCLR. Further more, generalized autocalibrating partially parallel acquisitions (GRAPPA) was incorpo-rated for better phase estimation while allowing higher undersampling factor. The required sample data for image reconstruction significantly reduced.
Photoacoustic imaging can be performed effectively for biological tissue and functional imaging. This imaging method combines with the high penetration characteristics of optical imaging and high contrast characteristics of ultrasonic imaging, can provide high contrast and high resolution imaging of tissue. The research results for photoacoustic imaging sparse regularization are less, especially the photoacoustic imaging with multi-source and multi-spectrum. The photoa-coustic imaging multiple light sources (MS-QPAT) wavelet sparse regularization model is established. Since this type of problem is generally non-convex, non-linear and non-differentiable, many existing numerical algorithm can not used for it. So, further studies of fast numerical algorithms and convergence results are established.
引文
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