CT图像重建关键技术研究
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摘要
CT(Computerized Tomography)技术是一项近年来快速发展多学科交叉的先进技术,除了广为人知的医学应用,还应用在工业无损检测、射电天文学、精密仪器反演等多个重要领域。CT图像重建是CT技术的核心,重建算法的优劣直接关系到对检测结果判断的准确性。重建算法中的的解析类算法以其严密的数学理论基础,相对于代数类算法有占用内存空间小、处理速度快等优点,在CT检测设备上被广泛采用。应用的需求不断地引导着技术的进步,改进经典算法、提出新式算法,进一步提高图像分辨率、不断加快图像重建速度一直是图像重建领域不懈追求与探索的方向。目前工业上的精密结构内部无损检测以及逆向工程等更高层次的应用需求对CT的各项性能指标提出了更高的要求,三维CT成为未来的发展方向。然而三维成像面临着海量数据处理及复杂数学运算等难题,一直制约着三维CT的普及应用,因此如何提高重建速度,使三维CT检测具有更强的实用性和实时性也是研究的一个热点。在某些难以采集到完整数据的场合,如何利用不完整的投影数据重建试件已越来越多地引起人们的关注,从经济实用的角度出发,此类有限数据的重建问题的研究有着很重要的现实意义,同时也是一个难点。针对以上提出的问题,本课题作了以下几个方面的研究工作。
1.滤波反投影(Filtered Backprojection,FBP)算法是二维重建中的主流算法,其中的滤波函数对算法运行结果的好坏起到举足轻重的作用,滤波计算中由于理想矩形窗的截断作用使得重建图像出现Gibbs现象,本文以无穷级数求和理论中的C-1法则为基础,提出了利用费耶核函数的一致收敛性来消除Gibbs现象的方法,通过将理想滤波器与费耶核函数相卷积得到的新滤波器对投影进行滤波,结果显示重建后图像克服了抖动现象,相比于加汉明窗和SL(Shepp-Logan)窗的平滑效果更佳。
2.在FBP算法基础上,以Radon反变换为依据推导了等距扇束的DHB(Derivate Hilbert Backproject)算法,该算法利用了360度扫描下扇形束中的冗余射线对称性,引入适当的比例因子,该比例因子反映了重建点在互为对称的两条射线投影中所作贡献的大小,并且消掉了FBP算法中随角度和位置变化的距离加权函数,避免了该权函数取低值时所造成的算法不稳定性,同时简化了算法、提高了速度。
3.为了进一步提高扇束重建速度,提出了短扫描方式下将投影数据平行重排与极坐标平面快速反投影相结合的软件加速方法。通过对扇束投影数据的冗余性分析,给出最小扫描角度范围及最小可利用数据区,结合极坐标下的多像素点同时定位方法,在数据采集和反投影这两个环节上对重建的速度进行了优化。
4.三维图像重建数据量大、运算复杂,仅从软件角度改进已不能满足重建实时性需求。本文通过对已有的各种硬件加速平台的调研,结合对三维经典重建算法FDK的特性分析,提出以FPGA作为FDK算法的加速平台的设计方案,并以Xilinx Virtex 5系列的xc5vlx110为硬件目标,设计实现了8路并行小规模体矩阵反投影电路,仿真结果表明在精度保持不变的前提下能够达到理想的加速比。
5.对如何利用不完全数据进行图像重建进行了研究,提出了一种解析类的不完全角度重建新方法,通过在首次不完全数据重建结果的基础上划定重建感兴趣区,在投影域逐点补充其对应的正弦图缺失部分,然后在此基础上进行二次重建,该方法计算量小、处理速度快。在测试目标结构较为规则的情况下,即使角度严重缺失,仍然能得到理想的重建结果。
CT (Computerized Tomography) is an advanced technique mixed several subjects developing quickly these years. Besides the medical diagoses,it is still used many important fields such as industrial non-destructive detecting, radio astronomy ,etc.CT image reconstruction play the core role in CT technique ,the performance of reconstruction algorithm is of vital importance to the judgment of detected results. Analytical algorithm was deduced based on rigorous mathematic theroys, and have the advantage such as smaller memory consumption and shorter running time compare to the ATR kinds. So the analytical algorithm is used widely on CT detection equipment. The market demand have influence on the development of technologe.with the aim of image resolution improvement, It is the unremitting developing goal to improve the classical algorithm, introduce new method.today the higher application such as inner precision non-destructive in industrial and converse engineering bring forward the higher demand to CT reconstructed performance. Three dimension imaging become the developing direction in future. But it is facing the difficulties consist of plenty of data and complex computing, which are restrict the usage of 3D CT in wider areas. So speedup the 3D reconstruction is a research hotspot. In the case of projections can not be acquired adequately under some special situations, how to reconstruct the image using the inadequate data become an attractive and hard matter.Aimming at the problem mentioned above, the paper achieve the following fruits.
FBP (Filtered Backprojection)is the main algorithm in two dimension image reconstruction. It is filter function that has a close relationship with the quality of image reconstruction. The Gibbs phenomena will emerges when the filter function truncated by ideal rectangle window. The paper introduces a method to eliminate Gibbs by Fejer core function based on C-1 principle in infinite series sum theory. The experiment result shows the method is more efficient comparing with the ways of adding RL window and hamming window. The paper deduces a DHB algorithm based on FBP and Radon reverse transform. The algorithm uses the symmetrical property of X-ray in fan-beam under 360 scanning to eliminate the distant weighting function which has the relationship with the change of scanning angle and pixel location by bring in a ratio factor reflecting the value of pixel contributing .The algorithm avoid the instability when the weighting function has a small value. At the same time, the formula becomes simple which make it possible to speedup the computing speedup the reconstruction much more, the paper proposes a software method .The way is arrange the fan-beam projections to parallel projections, and then backproject in polar coordinate. The minimum scanning scope and the minimum available data are given after analysis of projection redundance, so a short scanning mode can be done to save the scanning time. When backproject in polar coordinate, we use a method called MSBP to decrease the compute time of pixel location .here are plenty of projections and complex calculations in 3D reconstruction. It is hardware solution that can be efficient to satisfy the real-time demand. The paper considers that FPGA is the most appropriate hardware on which the FDK algorithm run following the compare with others hardware such as GPU, workstation.Cell and so on. We design a circuit to implement FDK backprojection in eight path synchronously using Xilinx xc5vlx110.The simulation result shows the speedup ratio arrive at 252.
Aiming at the problem of limited-view reconstruction, the paper makes a primary research. A new method belong to analytical kind is proposed. Following the original reconstruction, the FOI (field of interesting) is located, and then fill the missing projection on sinogram according to the acquired projections, finilly reconstruct the last image utilizing the whole projections. The method is simple to realize compare with iterative kind, and the image reconstructed is good when inner structure of detected object is regular.
1.滤波反投影(Filtered Backprojection,FBP)算法是二维重建中的主流算法,其中的滤波函数对算法运行结果的好坏起到举足轻重的作用,滤波计算中由于理想矩形窗的截断作用使得重建图像出现Gibbs现象,本文以无穷级数求和理论中的C-1法则为基础,提出了利用费耶核函数的一致收敛性来消除Gibbs现象的方法,通过将理想滤波器与费耶核函数相卷积得到的新滤波器对投影进行滤波,结果显示重建后图像克服了抖动现象,相比于加汉明窗和SL(Shepp-Logan)窗的平滑效果更佳。
2.在FBP算法基础上,以Radon反变换为依据推导了等距扇束的DHB(Derivate Hilbert Backproject)算法,该算法利用了360度扫描下扇形束中的冗余射线对称性,引入适当的比例因子,该比例因子反映了重建点在互为对称的两条射线投影中所作贡献的大小,并且消掉了FBP算法中随角度和位置变化的距离加权函数,避免了该权函数取低值时所造成的算法不稳定性,同时简化了算法、提高了速度。
3.为了进一步提高扇束重建速度,提出了短扫描方式下将投影数据平行重排与极坐标平面快速反投影相结合的软件加速方法。通过对扇束投影数据的冗余性分析,给出最小扫描角度范围及最小可利用数据区,结合极坐标下的多像素点同时定位方法,在数据采集和反投影这两个环节上对重建的速度进行了优化。
4.三维图像重建数据量大、运算复杂,仅从软件角度改进已不能满足重建实时性需求。本文通过对已有的各种硬件加速平台的调研,结合对三维经典重建算法FDK的特性分析,提出以FPGA作为FDK算法的加速平台的设计方案,并以Xilinx Virtex 5系列的xc5vlx110为硬件目标,设计实现了8路并行小规模体矩阵反投影电路,仿真结果表明在精度保持不变的前提下能够达到理想的加速比。
5.对如何利用不完全数据进行图像重建进行了研究,提出了一种解析类的不完全角度重建新方法,通过在首次不完全数据重建结果的基础上划定重建感兴趣区,在投影域逐点补充其对应的正弦图缺失部分,然后在此基础上进行二次重建,该方法计算量小、处理速度快。在测试目标结构较为规则的情况下,即使角度严重缺失,仍然能得到理想的重建结果。
CT (Computerized Tomography) is an advanced technique mixed several subjects developing quickly these years. Besides the medical diagoses,it is still used many important fields such as industrial non-destructive detecting, radio astronomy ,etc.CT image reconstruction play the core role in CT technique ,the performance of reconstruction algorithm is of vital importance to the judgment of detected results. Analytical algorithm was deduced based on rigorous mathematic theroys, and have the advantage such as smaller memory consumption and shorter running time compare to the ATR kinds. So the analytical algorithm is used widely on CT detection equipment. The market demand have influence on the development of technologe.with the aim of image resolution improvement, It is the unremitting developing goal to improve the classical algorithm, introduce new method.today the higher application such as inner precision non-destructive in industrial and converse engineering bring forward the higher demand to CT reconstructed performance. Three dimension imaging become the developing direction in future. But it is facing the difficulties consist of plenty of data and complex computing, which are restrict the usage of 3D CT in wider areas. So speedup the 3D reconstruction is a research hotspot. In the case of projections can not be acquired adequately under some special situations, how to reconstruct the image using the inadequate data become an attractive and hard matter.Aimming at the problem mentioned above, the paper achieve the following fruits.
FBP (Filtered Backprojection)is the main algorithm in two dimension image reconstruction. It is filter function that has a close relationship with the quality of image reconstruction. The Gibbs phenomena will emerges when the filter function truncated by ideal rectangle window. The paper introduces a method to eliminate Gibbs by Fejer core function based on C-1 principle in infinite series sum theory. The experiment result shows the method is more efficient comparing with the ways of adding RL window and hamming window. The paper deduces a DHB algorithm based on FBP and Radon reverse transform. The algorithm uses the symmetrical property of X-ray in fan-beam under 360 scanning to eliminate the distant weighting function which has the relationship with the change of scanning angle and pixel location by bring in a ratio factor reflecting the value of pixel contributing .The algorithm avoid the instability when the weighting function has a small value. At the same time, the formula becomes simple which make it possible to speedup the computing speedup the reconstruction much more, the paper proposes a software method .The way is arrange the fan-beam projections to parallel projections, and then backproject in polar coordinate. The minimum scanning scope and the minimum available data are given after analysis of projection redundance, so a short scanning mode can be done to save the scanning time. When backproject in polar coordinate, we use a method called MSBP to decrease the compute time of pixel location .here are plenty of projections and complex calculations in 3D reconstruction. It is hardware solution that can be efficient to satisfy the real-time demand. The paper considers that FPGA is the most appropriate hardware on which the FDK algorithm run following the compare with others hardware such as GPU, workstation.Cell and so on. We design a circuit to implement FDK backprojection in eight path synchronously using Xilinx xc5vlx110.The simulation result shows the speedup ratio arrive at 252.
Aiming at the problem of limited-view reconstruction, the paper makes a primary research. A new method belong to analytical kind is proposed. Following the original reconstruction, the FOI (field of interesting) is located, and then fill the missing projection on sinogram according to the acquired projections, finilly reconstruct the last image utilizing the whole projections. The method is simple to realize compare with iterative kind, and the image reconstructed is good when inner structure of detected object is regular.
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