三维锥束CT图像重建加速技术研究
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摘要
CT技术在临床医学上的应用是20世纪医疗技术进步的重要标志。锥束CT具有扫描速度快、分辨率各向同性、射线利用率高等优点,在医学诊断和工业无损检测等领域有着广阔的应用前景,成为当今国际CT研究领域中最为活跃的前沿课题。然而锥束CT三维图像重建的运算量和数据传输量巨大,重建时间较长,只利用CPU进行计算的方案已经不能满足现代临床和工程应用的要求。因此,研究如何提高锥束CT重建算法的运算速度并找到合适的解决方案具有重要的学术价值和应用研究价值。
目前图形处理器(GPU)已经具有高度的大规模并行计算能力,并且具有良好的可编程性。因此根据FDK三维图像重建算法可并行的特点,研究了一种利用GPU统一并行计算架构(CUDA)加速图像重建过程的方法。论文的创新点在于：一是提出了一种并行FFT计算在GPU上的实现方法以加快重建算法中数据滤波的速度；二是利用CUDA技术在GPU上实现了FDK算法的加速计算,并根据GPU硬件和存储器特点,提出了优化方法。
本文首先介绍CT成像的物理和数学基础理论,对平行束投影重建算法进行分析和总结；其次,对二维扇束CT重建算法基础知识进行了概括,然后重点分析三维锥束CT图像重建算法,研究FDK及其衍生算法在计算上的特点；第三,快速傅里叶变换(FFT)是实现滤波的一个有力工具,本文研究了一种新型的适合GPU运算的FFT并行计算方法,并通过CUDA架构实现此并行FFT算法在GPU上的运算。实验结果显示本文的并行FFT方法最高可达到了46倍的加速效果；第四,本文分析了FDK三维重建算法并行计算原理,研究运用GPU技术加速FDK算法,在FDK算法的加权预处理,滤波和反投影三个阶段,分别设计了适合CUDA的并行计算方法。同时,根据GPU存储器特点,使用多种存储器,优化数据传输和访问,实现了CPU和GPU协调合作。实验结果表明,该GPU图像重建加速方法与CPU单独重建相比获得了150倍以上的加速效果,并且两者的图像质量接近,平均误差小于10-4。
CUDA的推出,使得GPU具有更好的可编程性,适合开发人员快速掌握其编程方法,缩短了程序开发周期。考虑到存储器性能(数据传输和访问)仍对算法执行速度影响较大,如果新的GPU能够提升储器的效率,那么我们在并行FFT计算和FDK重建算法加速方面将会有更好的效果。我们可以得出结论,随着CUDA架构逐步成熟和GPU性能的提高,利用GPU的三维锥束CT图像重建速度将会更快,将能满足实时准确重建的要求。
CT technology applied in clinical medicine is an important symbol of medical technology progress in 20th century. Cone-beam CT has many advantages such as fast scanning, X-ray highly-usaged and image resolution isotropic. It is widely applied in medical diagnosis and industrial nondestructive testing fields, and has become one of the advanced reaserch subjects for the international CT field. However cone-beam CT 3D images reconstruction has great amount of computation and data transmission, so that image reconstruction is time-consuming. Only using CPU is impossible to meet the requirements of 3D image reconstruction in real-time. Therefore, improve the cone-beam CT reconstruction speed and find the right solution has important academic value and application prospect.
Nowadays GPU (Graphic Processing Unit, GPU) has high level of parallelism, so this paper advances a method using GPU-based CUDA (Compute Unified Device Architecture, CUDA) technology to accelerate FDK reconstruction algorithm. There are two innovation points in this paper:on the one hand, a parallel FFT (Fast Fourier Transform, FFT) method with GPU to improve the image data filtering time is proposed; On the other hand, uses CUDA technology to realize FDK algorithm calculation, and according to the GPU hardware and memory characteristic puts forward the optimal methods.
This paper firstly introduces physical and mathematical theory of CT imaging, and analyses parallel-beam projector reconstruction algorithm; Secondly, summarizes 2D fan-beam CT basic knowledge of reconstruction algorithms, and then focuses on analysing the 3D cone-beam image reconstruction algorithms, researching characteristics of FDK algorithm and its derivative algorithms; Thirdly, studies a new kind parallel FFT method to suit GPU computing, and uses CUDA technology to realize the method. Experimental results show that this method can achieve 46 times faster than the CPU-only method; Fourthly, this paper analyses the FDK 3D reconstruction algorithm parallel computing principle, proposes using GPU technology to accelerate FDK algorithm, designs methods respectively in weighting, filtering and backprojection stage of the FDK algorithm. Meanwhile, we employ kinds of CUDA memory to optimize both data transmission and memory access. The experiments show that the GPU method proposed by this paper is 150 times faster than the CPU method, the images of two methods are similar, and the error is less than 10(?).
The CUDA technology makes the GPU programming more easily, it suitable for developers quickly grasp its programming method, and shorten the program development cycle. Considering the memory performance (data transmission and access) still influences execution speed of the algorithms greatly, the proposed parallel FFT and FDK reconstruction methods will have better effect if new kind of GPU can improve the efficiency of the memory performance. We may safely draw the conclusion that, along with CUDA architecture gradually maturing and GPU performance improvement, cone-beamCT 3D image reconstruction will be faster, and will be able to meet the requirement of real-time and accurate reconstruction.
目前图形处理器(GPU)已经具有高度的大规模并行计算能力,并且具有良好的可编程性。因此根据FDK三维图像重建算法可并行的特点,研究了一种利用GPU统一并行计算架构(CUDA)加速图像重建过程的方法。论文的创新点在于：一是提出了一种并行FFT计算在GPU上的实现方法以加快重建算法中数据滤波的速度；二是利用CUDA技术在GPU上实现了FDK算法的加速计算,并根据GPU硬件和存储器特点,提出了优化方法。
本文首先介绍CT成像的物理和数学基础理论,对平行束投影重建算法进行分析和总结；其次,对二维扇束CT重建算法基础知识进行了概括,然后重点分析三维锥束CT图像重建算法,研究FDK及其衍生算法在计算上的特点；第三,快速傅里叶变换(FFT)是实现滤波的一个有力工具,本文研究了一种新型的适合GPU运算的FFT并行计算方法,并通过CUDA架构实现此并行FFT算法在GPU上的运算。实验结果显示本文的并行FFT方法最高可达到了46倍的加速效果；第四,本文分析了FDK三维重建算法并行计算原理,研究运用GPU技术加速FDK算法,在FDK算法的加权预处理,滤波和反投影三个阶段,分别设计了适合CUDA的并行计算方法。同时,根据GPU存储器特点,使用多种存储器,优化数据传输和访问,实现了CPU和GPU协调合作。实验结果表明,该GPU图像重建加速方法与CPU单独重建相比获得了150倍以上的加速效果,并且两者的图像质量接近,平均误差小于10-4。
CUDA的推出,使得GPU具有更好的可编程性,适合开发人员快速掌握其编程方法,缩短了程序开发周期。考虑到存储器性能(数据传输和访问)仍对算法执行速度影响较大,如果新的GPU能够提升储器的效率,那么我们在并行FFT计算和FDK重建算法加速方面将会有更好的效果。我们可以得出结论,随着CUDA架构逐步成熟和GPU性能的提高,利用GPU的三维锥束CT图像重建速度将会更快,将能满足实时准确重建的要求。
CT technology applied in clinical medicine is an important symbol of medical technology progress in 20th century. Cone-beam CT has many advantages such as fast scanning, X-ray highly-usaged and image resolution isotropic. It is widely applied in medical diagnosis and industrial nondestructive testing fields, and has become one of the advanced reaserch subjects for the international CT field. However cone-beam CT 3D images reconstruction has great amount of computation and data transmission, so that image reconstruction is time-consuming. Only using CPU is impossible to meet the requirements of 3D image reconstruction in real-time. Therefore, improve the cone-beam CT reconstruction speed and find the right solution has important academic value and application prospect.
Nowadays GPU (Graphic Processing Unit, GPU) has high level of parallelism, so this paper advances a method using GPU-based CUDA (Compute Unified Device Architecture, CUDA) technology to accelerate FDK reconstruction algorithm. There are two innovation points in this paper:on the one hand, a parallel FFT (Fast Fourier Transform, FFT) method with GPU to improve the image data filtering time is proposed; On the other hand, uses CUDA technology to realize FDK algorithm calculation, and according to the GPU hardware and memory characteristic puts forward the optimal methods.
This paper firstly introduces physical and mathematical theory of CT imaging, and analyses parallel-beam projector reconstruction algorithm; Secondly, summarizes 2D fan-beam CT basic knowledge of reconstruction algorithms, and then focuses on analysing the 3D cone-beam image reconstruction algorithms, researching characteristics of FDK algorithm and its derivative algorithms; Thirdly, studies a new kind parallel FFT method to suit GPU computing, and uses CUDA technology to realize the method. Experimental results show that this method can achieve 46 times faster than the CPU-only method; Fourthly, this paper analyses the FDK 3D reconstruction algorithm parallel computing principle, proposes using GPU technology to accelerate FDK algorithm, designs methods respectively in weighting, filtering and backprojection stage of the FDK algorithm. Meanwhile, we employ kinds of CUDA memory to optimize both data transmission and memory access. The experiments show that the GPU method proposed by this paper is 150 times faster than the CPU method, the images of two methods are similar, and the error is less than 10(?).
The CUDA technology makes the GPU programming more easily, it suitable for developers quickly grasp its programming method, and shorten the program development cycle. Considering the memory performance (data transmission and access) still influences execution speed of the algorithms greatly, the proposed parallel FFT and FDK reconstruction methods will have better effect if new kind of GPU can improve the efficiency of the memory performance. We may safely draw the conclusion that, along with CUDA architecture gradually maturing and GPU performance improvement, cone-beamCT 3D image reconstruction will be faster, and will be able to meet the requirement of real-time and accurate reconstruction.
引文
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[13]LA Sheep, Y Vardi. Maximum likelihood reconstruction fore mission and tomography[J]. IEEE Trans on medical imaging,1982,1:113-122.
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[15]高欣.新型迭代图像重建算法的理论研究和实现[D].浙江大学博士学位论文,2004.
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