基于压缩感知的CT系统图像重建算法研究

发布时间：2018-02-24 12:16

本文关键词： 计算机断层成像压缩感知图像重建正则化参数稀疏约束优化算法　出处：《中国科学院研究生院(长春光学精密机械与物理研究所)》2016年博士论文　论文类型：学位论文

【摘要】：为了减轻X射线辐射对人体和周边环境的危害,用于医学诊断的计算机断层成像(Computed Tomography,CT)扫描系统的设计需要考虑降低辐射剂量的问题。降低采样率,缩短扫描时间是一个直接有效的方法。然而传统的图像重建算法受到香农柰奎斯特采样定理的限制,其投影采样的频率必须达到重建目标最高频率的两倍以上,才能精确重建图像,否则会导致混叠伪影的出现,无法满足医学CT检查对成像质量的要求。近年来提出的压缩感知(Compressed Sensing,CS)理论能够有效提取图像的稀疏性,从而利用其稀疏性作为先验知识来进行断层图像重建,与传统的滤波反投影(Filtered Back-projection,FBP)算法相比可以明显改进重建图像质量。因此,结合CT扫描系统的特点,研究设计快速稳定的CS算法,有效的重建CT图像,使基于CS理论的CT系统图像重建算法由理论向实际应用转化,就是本研究的意义和预期目标。目前已提出的基于CS理论的欠采样重建算法分别以TV最小化和字典学习正则项为稀疏约束,其中基于TV最小化约束的重建算法已比较成熟。基于字典学习正则项的重建算法还存在一些待解决的问题,比如:1.正则化参数的确定。2.重建图像中软组织区域边缘细节信息的保留。3.扫描数据采样率进一步下降条件下高质量重建图像的问题。针对这些问题,本文提出了相应的模型和改进方法,主要创新性工作包括:(1)针对字典学习重建算法中正则化参数无法有效选取的问题,建立正则化参数取值模型。正则化参数的大小与原始扫描数据的噪声水平,扫描几何等关系密切,该模型首先通过计算找到能够反映当前扫描数据特点的相关参量,并通过函数拟合建立其与最佳正则化参数的函数关系。正则化参数选取模型的建立,免除了通过大量重复实验挑选合理正则化参数的步骤,提高了重建效率,也为进一步的字典学习重建算法研究打下基础。(2)为了使重建图像能够保留更多的软组织边缘细节信息,提出一种加权字典学习重建算法。基于字典学习正则项的重建算法从待重建图像中抽取出所有大小相同且互相重叠的小图像块,每个小图像块都可以用待训练的过完备字典稀疏表示,以此稀疏表示作为正则约束,在迭代过程中使结果图像收敛到合理的可行解域中。加权字典学习重建算法根据每个图像块包含细节的多少给予不同的稀疏约束权重,更好了保留了重建图像的细节信息。实验结果表明,与改进前的算法相比,重建图像归一化平均绝对偏差更小,对于图像中的细节部分和低对比度信息的分辨率提高,更有利于医生的临床诊断。(3)为了改进基于字典学习的重建算法,使其能够适应更低采样率的扫描数据,提出一种基于L1稀疏约束的字典学习重建算法。该算法用L1范数下的约束项代替原算法中的L2稀疏约束项,利用L1约束项更高的稀疏性适应采样率的进一步降低。实验结果表明该算法在降低采样率的条件下依然能保持较高的图像质量。与改进前的字典学习算法对比,L1稀疏约束项也进一步提高了同等采样条件下图像的空间分辨率,降低了重建图像与真实图像的偏差,提高了重建质量。
[Abstract]:In order to reduce the X ray radiation on the human body and the surrounding environment, computerized tomography for medical diagnosis (Computed Tomography CT) scanning system needs to be considered in the design to reduce the radiation dose. To reduce the sampling rate, shorten the scan time is a direct and effective method. However, the traditional image reconstruction algorithm by Shannon Nai queis special sampling limit, the projection of the sampling frequency must reach the goal of reconstruction of the highest frequency of more than two times, in order to accurately reconstruct the image, otherwise it will cause aliasing artifacts, unable to meet the medical CT check on the quality of imaging requirements. Compressed sensing proposed in recent years (Compressed, Sensing, CS) theory to sparse effective extraction of the image, and use its sparsity as a prior knowledge to carry out fault image reconstruction, and the conventional filtered backprojection (Filtered Back-projection FBP) algorithm Compared with can improve the quality of image reconstruction. Therefore, combined with the characteristics of CT scanning system, CS algorithm design fast and stable, the reconstruction of CT image effectively, the CT image reconstruction algorithm based on CS theory from theory to practical application, is the significance of this study and the expected goal. The CS theory under sampling reconstruction algorithm using TV minimization and regularization for dictionary learning based on sparse constraint have been proposed, including TV reconstruction algorithm based on constrained minimization has been relatively mature. Dictionary learning regularization reconstruction algorithm has some problems to be solved, such as: 1. based on the determination of the regularization parameter preserving.3. scan data.2. reconstruction images of soft tissue regional edge information sampling rate to decline further high quality of image reconstruction conditions. To solve these problems, this paper puts forward the corresponding model and the improved method, the main To the innovative work include: (1) according to the dictionary learning regular reconstruction algorithm parameters can not be effectively selected, establishing regularization parameter model. The noise level of the regularization parameter and the size of the original scan data, scan geometry relationship, the model is first calculated to find relevant parameters of the current scan data characteristics. To reflect, and through function fitting to establish the function relationship and the optimal regularization parameter. The model of choosing the regularization parameter, from the large number of repeated experiments through selecting the reasonable regularization parameter step, improve the efficiency of the reconstruction, but also for further study to lay the foundation for the study of dictionary reconstruction algorithm. (2) in order to make the image reconstruction soft tissue can retain more edge details, we propose a weighted dictionary learning algorithm. Dictionary learning regularization reconstruction algorithm based on image reconstruction from To extract all the same size and overlapping small image blocks, each image block can be used to be trained overcomplete dictionaries for sparse, the sparse representation as regular constraints in the iterative process of the image converges to the reasonable feasible solution domain. The weighted dictionary learning algorithm according to the reconstruction of each image block contains many the details of the given sparse constraint different weights, the better retaining details of the reconstructed image. The experimental results show that compared with the former algorithm, the reconstructed image normalized mean absolute deviation is smaller, the image details and low contrast information to improve the resolution, more conducive to clinical diagnosis (3) to the doctor. The improved reconstruction algorithm based on dictionary learning, which can adapt to the lower sampling rate of scan data, proposes a learning L1 reconstruction algorithm for sparse constraint based on the dictionary. By using the method of L1 norm constraint instead of the original algorithm L2 sparse constraint, L1 constraint using higher sparsity to further reduce the sampling rate. The experimental results show that the algorithm can still maintain high image quality at lower sampling rate conditions. Compared with the improved learning algorithm of dictionary, L1 the sparsity constraints can further improve the spatial resolution of the image of the same sampling condition, reduce the reconstruction image and real image deviation, the reconstruction quality is improved.

【学位授予单位】：中国科学院研究生院(长春光学精密机械与物理研究所)
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.41

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