基于CTA-DFT的磁共振放射状和PROPELLER采样数据快速精确重建算法研究
发布时间：2018-11-24 17:56
【摘要】：磁共振成像(Magnetic Resonance Imaging, MRI)是一种基于核磁共振现象的断层及立体成像技术,相对于其他的成像技术如X线,CT(Computed Tomography)和超声成像技术等,具有图像分辨率高、成像参数多、可任意方向断层、对人体无电离辐射伤害等优点。因此,磁共振成像得以在临床上广泛应用,并成为临床上和科学研究中越来越重要的成像方法。 磁共振非笛卡尔K-空间轨迹成像,包括螺旋形(Spiral),放射状(Radial),推进器(PROPELLER)等,具有扫描速度快,K-空间中心过采样,对流动不敏感或运动伪影校正等优点,具有重要的临床应用价值。然而,由于采样数据不是落在均匀分布的网格点上,不能直接采用快速傅里叶变换(Fast Fourier Transform, FFT)获得图像,因而其重建一直是磁共振成像领域的热点问题之一。基于直接求和的离散傅里叶变换(Direct Fourier transform, DFT),也通常被MRI领域研究者称为共轭相位(Conjugate Phase)重建算法,被认为可以较高精度的实现图像重建,通常被研究者引作参考进行重建算法精度的评价,而且在非笛卡尔采样密度补偿算法的研究中,为了避免其他算法引入的误差,通常采用DFT进行图像重建。然而,由于DFT算法计算复杂度高,很难推广应用到临床,因此研究者致力于各种各样的快速重建算法。 许多快速算法包括网格化(Gridding)算法,块均匀采样(Block Uniform Resampling (BURS)),广义快速傅里叶变换(Generalized fast Fourier transform (GFFT))一般通过插值或解线性方程组的方式将非笛卡尔数据在均匀分布的笛卡尔网格点上进行重采样,但是这些NUFFT算法均是DFT的近似估计,并不能完全等价于DFT。 本文主要研究针对非笛卡尔采样数据的DFT精确计算的快速实现算法,主要策略是根据采样轨迹的特点,将全部非笛卡尔数据分解成一系列的子数据集合(内部数据服从均匀分布),进而寻求子数据集合的快速DFT算法。非笛卡尔采样中的放射状与PROPELLER采样,虽然从整体上看属于非均匀采样,但是这两种轨迹均由直线采样构成,而且.每条直线上的数据点是等间距分布的,规律性很明显。我们从放射状与PROPELLER采样的这种内在规律出发,根据DFT算法的线性性质,将全部采样数据的DFT变换分解为先对每条K-空间线进行DFT后再把中间变换结果进行叠加,K-空间上任意直线(任意起点,任意等间隔频率)的DFT变换可以通过快速的CTA(chirp transform algorithm)算法实现。本文所提算法简称CTA-DFT算法,适用于由直线采样组成的非笛卡尔数据重建。理论分析和实验表明,在重建图像大小为2562时,CTA-DFT算法保持了DFT算法完全相同的精度,并且速度是DFT算法的二十倍,而进行GPU加速后,速度可以再提升50倍。
[Abstract]:Magnetic resonance imaging (Magnetic Resonance Imaging, MRI) is a kind of tomographic and stereoscopic imaging technology based on nuclear magnetic resonance phenomenon. Compared with other imaging techniques such as X-ray, CT (Computed Tomography) and ultrasonic imaging, MRI has high resolution and many imaging parameters. Can be any direction fault, no ionizing radiation damage to the human body and other advantages. Therefore, magnetic resonance imaging (MRI) has been widely used in clinic and become an increasingly important imaging method in clinical and scientific research. Magnetic resonance non-Cartesian K- space trajectory imaging, including spiral (Spiral), radial (Radial), propeller (PROPELLER), has the advantages of fast scanning speed, over-sampling of K- space center, insensitivity to flow or correction of motion artifacts, etc. It has important clinical application value. However, because the sampled data is not located on the uniformly distributed grid point, the fast Fourier transform (Fast Fourier Transform, FFT) can not be directly used to obtain the image, so its reconstruction has always been one of the hot issues in the field of magnetic resonance imaging. Discrete Fourier transform (Direct Fourier transform, DFT),) based on direct summation is also commonly referred to as the conjugate phase (Conjugate Phase) reconstruction algorithm by researchers in the MRI field, which is considered to be able to achieve image reconstruction with high accuracy. In order to avoid the errors introduced by other algorithms, DFT is usually used for image reconstruction in order to avoid the errors introduced by other algorithms in the research of non-Cartesian sampling density compensation algorithm. However, due to the high computational complexity of the DFT algorithm, it is difficult to be popularized to clinical applications, so researchers focus on various fast reconstruction algorithms. Many fast algorithms include gridding (Gridding), block uniformly sampled (Block Uniform Resampling (BURS), Generalized Fast Fourier transform (Generalized fast Fourier transform (GFFT) resamples non-Cartesian data on a uniformly distributed Cartesian grid by interpolation or solving linear equations, but these NUFFT algorithms are approximate estimates of DFT. Not completely equivalent to DFT. In this paper, the fast algorithm of accurate DFT calculation for non-Cartesian sampling data is studied. The main strategy is based on the characteristics of the sampling trajectory. All the non-Cartesian data are decomposed into a series of subdata sets (uniform distribution of internal data), and then the fast DFT algorithm of subdata set is sought. Although the radiative and PROPELLER sampling in non-Cartesian sampling is considered as a non-uniform sampling as a whole, these two kinds of trajectories are composed of straight line sampling. The data points on each line are equally spaced, and the regularity is obvious. According to the linear properties of the DFT algorithm, we decompose the DFT transformation of all sampled data into DFT for each K- space line and then superposition the intermediate transformation result from the inherent law of radiate sampling and PROPELLER sampling. The DFT transform of any straight line in K-space (any starting point, any equal frequency) can be realized by a fast CTA (chirp transform algorithm) algorithm. The proposed algorithm, called CTA-DFT algorithm, is suitable for non-Cartesian data reconstruction composed of straight line sampling. Theoretical analysis and experiments show that when the reconstructed image size is 2562, the CTA-DFT algorithm has the same accuracy as the DFT algorithm, and the speed is 20 times that of the DFT algorithm, and the speed can be increased by 50 times after the GPU acceleration.
【学位授予单位】：南方医科大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TP391.41;R310
本文编号：2354514
[Abstract]:Magnetic resonance imaging (Magnetic Resonance Imaging, MRI) is a kind of tomographic and stereoscopic imaging technology based on nuclear magnetic resonance phenomenon. Compared with other imaging techniques such as X-ray, CT (Computed Tomography) and ultrasonic imaging, MRI has high resolution and many imaging parameters. Can be any direction fault, no ionizing radiation damage to the human body and other advantages. Therefore, magnetic resonance imaging (MRI) has been widely used in clinic and become an increasingly important imaging method in clinical and scientific research. Magnetic resonance non-Cartesian K- space trajectory imaging, including spiral (Spiral), radial (Radial), propeller (PROPELLER), has the advantages of fast scanning speed, over-sampling of K- space center, insensitivity to flow or correction of motion artifacts, etc. It has important clinical application value. However, because the sampled data is not located on the uniformly distributed grid point, the fast Fourier transform (Fast Fourier Transform, FFT) can not be directly used to obtain the image, so its reconstruction has always been one of the hot issues in the field of magnetic resonance imaging. Discrete Fourier transform (Direct Fourier transform, DFT),) based on direct summation is also commonly referred to as the conjugate phase (Conjugate Phase) reconstruction algorithm by researchers in the MRI field, which is considered to be able to achieve image reconstruction with high accuracy. In order to avoid the errors introduced by other algorithms, DFT is usually used for image reconstruction in order to avoid the errors introduced by other algorithms in the research of non-Cartesian sampling density compensation algorithm. However, due to the high computational complexity of the DFT algorithm, it is difficult to be popularized to clinical applications, so researchers focus on various fast reconstruction algorithms. Many fast algorithms include gridding (Gridding), block uniformly sampled (Block Uniform Resampling (BURS), Generalized Fast Fourier transform (Generalized fast Fourier transform (GFFT) resamples non-Cartesian data on a uniformly distributed Cartesian grid by interpolation or solving linear equations, but these NUFFT algorithms are approximate estimates of DFT. Not completely equivalent to DFT. In this paper, the fast algorithm of accurate DFT calculation for non-Cartesian sampling data is studied. The main strategy is based on the characteristics of the sampling trajectory. All the non-Cartesian data are decomposed into a series of subdata sets (uniform distribution of internal data), and then the fast DFT algorithm of subdata set is sought. Although the radiative and PROPELLER sampling in non-Cartesian sampling is considered as a non-uniform sampling as a whole, these two kinds of trajectories are composed of straight line sampling. The data points on each line are equally spaced, and the regularity is obvious. According to the linear properties of the DFT algorithm, we decompose the DFT transformation of all sampled data into DFT for each K- space line and then superposition the intermediate transformation result from the inherent law of radiate sampling and PROPELLER sampling. The DFT transform of any straight line in K-space (any starting point, any equal frequency) can be realized by a fast CTA (chirp transform algorithm) algorithm. The proposed algorithm, called CTA-DFT algorithm, is suitable for non-Cartesian data reconstruction composed of straight line sampling. Theoretical analysis and experiments show that when the reconstructed image size is 2562, the CTA-DFT algorithm has the same accuracy as the DFT algorithm, and the speed is 20 times that of the DFT algorithm, and the speed can be increased by 50 times after the GPU acceleration.
【学位授予单位】：南方医科大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TP391.41;R310
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