基于CTA-DFT的磁共振放射狀和PROPELLER采樣數(shù)據(jù)快速精確重建算法研究
發(fā)布時間：2018-11-24 17:56
【摘要】：磁共振成像(Magnetic Resonance Imaging, MRI)是一種基于核磁共振現(xiàn)象的斷層及立體成像技術,相對于其他的成像技術如X線,CT(Computed Tomography)和超聲成像技術等,具有圖像分辨率高、成像參數(shù)多、可任意方向斷層、對人體無電離輻射傷害等優(yōu)點。因此,磁共振成像得以在臨床上廣泛應用,并成為臨床上和科學研究中越來越重要的成像方法。 磁共振非笛卡爾K-空間軌跡成像,包括螺旋形(Spiral),放射狀(Radial),推進器(PROPELLER)等,具有掃描速度快,K-空間中心過采樣,對流動不敏感或運動偽影校正等優(yōu)點,具有重要的臨床應用價值。然而,由于采樣數(shù)據(jù)不是落在均勻分布的網(wǎng)格點上,不能直接采用快速傅里葉變換(Fast Fourier Transform, FFT)獲得圖像,因而其重建一直是磁共振成像領域的熱點問題之一�；谥苯忧蠛偷碾x散傅里葉變換(Direct Fourier transform, DFT),也通常被MRI領域研究者稱為共軛相位(Conjugate Phase)重建算法,被認為可以較高精度的實現(xiàn)圖像重建,通常被研究者引作參考進行重建算法精度的評價,而且在非笛卡爾采樣密度補償算法的研究中,為了避免其他算法引入的誤差,通常采用DFT進行圖像重建。然而,由于DFT算法計算復雜度高,很難推廣應用到臨床,因此研究者致力于各種各樣的快速重建算法。 許多快速算法包括網(wǎng)格化(Gridding)算法,塊均勻采樣(Block Uniform Resampling (BURS)),廣義快速傅里葉變換(Generalized fast Fourier transform (GFFT))一般通過插值或解線性方程組的方式將非笛卡爾數(shù)據(jù)在均勻分布的笛卡爾網(wǎng)格點上進行重采樣,但是這些NUFFT算法均是DFT的近似估計,并不能完全等價于DFT。 本文主要研究針對非笛卡爾采樣數(shù)據(jù)的DFT精確計算的快速實現(xiàn)算法,主要策略是根據(jù)采樣軌跡的特點,將全部非笛卡爾數(shù)據(jù)分解成一系列的子數(shù)據(jù)集合(內部數(shù)據(jù)服從均勻分布),進而尋求子數(shù)據(jù)集合的快速DFT算法。非笛卡爾采樣中的放射狀與PROPELLER采樣,雖然從整體上看屬于非均勻采樣,但是這兩種軌跡均由直線采樣構成,而且.每條直線上的數(shù)據(jù)點是等間距分布的,規(guī)律性很明顯。我們從放射狀與PROPELLER采樣的這種內在規(guī)律出發(fā),根據(jù)DFT算法的線性性質,將全部采樣數(shù)據(jù)的DFT變換分解為先對每條K-空間線進行DFT后再把中間變換結果進行疊加,K-空間上任意直線(任意起點,任意等間隔頻率)的DFT變換可以通過快速的CTA(chirp transform algorithm)算法實現(xiàn)。本文所提算法簡稱CTA-DFT算法,適用于由直線采樣組成的非笛卡爾數(shù)據(jù)重建。理論分析和實驗表明,在重建圖像大小為2562時,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,而進行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.
【學位授予單位】：南方醫(yī)科大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：TP391.41;R310
本文編號：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.
【學位授予單位】：南方醫(yī)科大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：TP391.41;R310
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