基于稀疏采样的医学成像方法研究
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摘要
医学成像(medical imaging)是以图像方式显示人体内部形体与功能信息来辅助诊断和治疗疾病的科学,主要包括X线、超声、核素、CT以及磁共振成像。医学成像的发展经历了X线学(Roentgenology)、放射学(Radiology)和影像学(Imaging)三个方面。x线学与放射学的各项诊断技术均以X线作为成像源,随着科学的发展又出现了多种影像源,如超声、核素、磁共振等。
MRI(magnetic resonance imaging, MRI)及CT(computed tomography, CT)的临床应用,开创了影像诊断新纪元。磁共振成像是当今最重要的影像学手段之一,它具有组织分辨率高、可任意方向断层、空间分辨率高、对人体无放射损伤等优点。自20世纪80年代初应用于临床以来,磁共振血管成像(MR angiography, MRA),磁共振波谱成像(MR spectroscopy, MRS)、并行磁共振成像(parallel MR imaging, PMRI)等技术越来越趋于成熟,使得磁共振成像成为临床和科学研究中越来越重要的成像方法。计算机断层成像是英国工程师Godfrey Hounsfield发明的,近年来,随着多排CT、双源CT的出现,高质量的冠状动脉成像、胸痛三联诊的一次实现以及大器官灌注图像研究都已在临床中应用。
作为一种重要的临床成像方式,MRI的主要不足是它的数据采集时间较长,从而导致成像速度较慢。二十世纪90年代以来,研究者致力于通过提高静磁场的场强、研究新的快速成像序列、开发能够快速切换的梯度磁场来提高成像速度。然而,梯度磁场切换速度过快时会刺激受检者的肌肉与神经,造成人体不适。且发展到现在,硬件的发展也极大制约了速度的进一步提高,继续依赖提高梯度场切换速度来提高成像速度基本上达到了极限。所以必须寻找新的解决途径。
另一方面,CT作为近代飞跃发展的计算机技术和X线检查技术相结合的产物,为临床提供了优质的影像学信息。但是当X线穿透机体被吸收时,可使细胞组织产生抑制、损害甚至坏死,称为X线的生物作用。X线对机体的损害程度与吸收X线量的大小有关。CT在高剂量X线下可以获得更优质的影像,但是同时增加了治疗人群的总体受辐射水平。尤其是作为主要功能成像方式之一的CT灌注成像,由于需要长时间的连续曝光,导致受检者的辐射剂量增高。为了用最小的人体损伤代价获得最佳的诊断效果,低剂量CT的研究很有必要。
综上可知,当前两项技术要解决的问题分别是,MRI需要缩短采集时间,CT需要减少X线剂量。通过重建算法研究降低成像所需的数据量,即在仅获得部分成像数据的情况下,通过优化重建算法仍然获得满足临床诊断质量需求的图像,对于磁共振成像,意味着成像速度的提升,对于CT成像,意味着可以降低病人接受的X线辐射剂量。由于部分数据成像方法不依赖于硬件性能,成为快速磁共振成像与低剂量CT成像领域的研究热点之一。
当前,基于多通道采集技术的并行磁共振成像技术(PMRI)的出现对MRI产生了深远影响,它使用相控阵线圈阵列同时采集部分数据,即各个线圈在同一时间内都进行部分数据采集,数据采集时间有效减少。CT中采用的方法为采集有限角度的投影数据,可以减少每次的曝光时间,当进行灌注图像扫描时,放射剂量的减少量更加明显。
并行磁共振成像在计算机求解图像部分是利用相控阵线圈内在包含的空间信息来恢复图像信息。然而,作为一门新的技术,还没有找到一种最优的成像算法。目前并行成像算法分为三类,基于图像域的方法、基于k-空间域的方法和基于图像域和k-空间域相结合的方法。本文主要研究了基于图像域的敏感度编码(SENSE, Sensitivity Encoding)方法。当数据采样较少,即欠采样因子较大时,SENSE重建方法的信噪比严重降低,当采样数据为非笛卡尔轨迹数据时,这种现象更为明显。传统算法优化方法是在重建方程中引入范数约束或l2范数约束。本文研究提出自适应约束的SENSE重建算法,由先验图像的梯度特征并借鉴PM模型的思想决定惩罚函数,使得在梯度幅值较大区域使用各向异性扩散的l1范数约束方式,以较好地保留图像细节；在梯度幅值较小区域使用各向同性扩散的l2范数约束方式,以有效地抑制噪声。
另外,诸多稀疏角度CT图像重建算法相继提出,整体可分为两大类：一类为基于变换域的迭代-解析重建算法；另一类为基于级数展开的迭代-代数/统计重建算法。迭代重建算法对于含噪声的不完全投影数据或者投影不均匀分布于180或360之间的图像重建是一种比较有效的算法。为了提高成像的精度和分辨率,一般采用正则化方法或者增加迭代次数。2004年,Cands、Romberg、Tao和Donoho等人提出压缩感知(CS, Compressed Sensing)理论。根据压缩感知理论在图像重建中的应用,可以知道,如果待重建图像在某个变换空间中是稀疏的,那么可以利用部分采样数据重建出质量较好的图像。对于稀疏角度CT灌注成像,相对于未灌注图像,可以认为在每一个时刻获得的灌注图像中增加的灌注信息在图像域都是稀疏的。本文中提出基于投影域减影的CT灌注图像重建,利用压缩感知原理对投影域减影数据进行约束迭代重建得出灌注信息图像,然后和预扫描图像进行配准相加来得到当前时刻的灌注图像。
总之,本研究主要利用部分数据采集方式来减少MRI的成像时间和CT扫描的辐射剂量。对并行成像SENSE约束重建算法中存在的缺陷进行了分析,提出了自适应约束SENSE非笛卡尔数据重建新算法,8通道2.6倍欠采样可变密度螺旋轨迹人体动静脉畸形瘤动脉注射X线仿真成像实验表明,与平方和(SOS)重建方法、传统无约束SENSE重建方法以及TV约束SENSE重建方法相比,本文所提算法可以有效抑制部分数据成像带来的噪声和伪影,并能较好保护图像细节尤其是小细节信息,成像效果优于传统方法。另外,对稀疏角度CT灌注成像方法进行了研究,观察到每个时间序列中灌注信息的变化是较少的,所以提出基于投影域减影的约束重建方法求解各个时刻的灌注信息变化图像。Shepp—LOgan体模实验和人体脑部灌注成像实验证明了本文算法的有效性,对结构简单的Shepp—Logan体模图像,使用本文算法在[0,p]范围内仅采集18个投影就可以重建出在背景区和目标区都与原图高度符合的图像。人体脑部灌注实验证明,本文算法可以有效恢复各种细节灌注信息,且在剂量减少96.3%(36个投影)的情况下仍能恢复出可以接受的灌注信息全面的图像。
Medical Imaging is the science that assists diagnosis and treatment of diseases by displayed the human body structure and function information within image, mainly including X ray, ultrasound, radionuclide, CT and magnetic resonance imaging。The development of medical imaging through three steps:X-ray (Roentgenology)、Radiology and Imaging. X ray is the imaging source of the diagnosis and radiographic techniques. And multiple image sources appeared such as ultrasound, radionuclide, and magnetic resonance and so on.
The clinical application of MRI and CT creates a new era in diagnostic imaging. Magnetic resonance imaging is one of the most important means of imaging technologies. Compared with other modalities of medical imaging, MRI has many advantages, such as excellent soft-tissue contrast、imaging in arbitrary plane、excellent spatial resolution and with no ionizing radiation. Since MRI was applied in clinical from the early 1980s, magnetic resonance angiography (MR angiography, MRA), magnetic resonance spectroscopy (MR spectroscopy, MRS), the parallel magnetic resonance imaging (parallel MR imaging, PMRI) and other technologies becoming more and more mature. All those advantages make MRI a very important tool for both clinical applications and scientific research. Computed tomography (computed tomography, CT) was invented by British engineer Godfrey Hounsfield。In recent years, with the emergence of multi-slice CT and dual-source CT, some difficult technique, such as high-quality imaging of the coronary arteries and major organ perfusion, have been applied in clinical.
As an important clinical imaging modalities, the main disadvantages of MRI is the long data acquisition time and thus results in the long imaging time. Since 1990, Researchers committed to improving the field strength of magnetic field、developing the new fast imaging sequence and quickly switched gradient magnetic field to increase the imaging speed. However, rapidly switched field gradient would produce neuromuscular stimulation and lead to body unease. At the same time, owing to the limitation that caused by the status of hardware development, it almost reaches the limit that rely on gradient switching speed increase to improve imaging speed.
On the other hand, as the combining of the rapid developmental modern computer technology and X-ray examination technology, CT provides high-quality information for clinical imaging. But when the X ray is absorbed through the body, it can produce inhibition of tissue damage or necrosis, referred to as X-biological effects. X ray damage to the body is proportional to the absorption of X-ray dose. CT can get better quality images at higher X-ray doses, but it also increased the overall radiation level affected by people. In particular, as one of the main functions imaging modalities, CT perfusion imaging needs a long period of continuous exposure, and oit will lead to increased radiation dose exposure. With the principle of acquire the best diagnostic results with minimal damage to the human, it is necessary to research on the low-dose CT.
To sum up, currently, the problems need to be solved of the two technologies are, MRI need to shorten the acquisition time, CT need to reduce the X-ray dose, for these two issues, all can be solved by insufficient data collecting. the main time-consuming factors of MRI imaging is the long data sampling time, insufficient data collection can reduce the acquisition time; the X-ray radiation dose of CT imaging increases with the increase in examination time, the use of insufficient data collection methods can shorten the exposure time, which can reduce the radiation dose exposure to examiners.
Currently, Parallel magnetic resonance imaging technology that based on the multi-channel acquisition had a profound impact on magnetic resonance imaging, which uses phased array coil array to collect part of the data sets simultaneously. CT can reduce the exposure each time with a limited angle projection data collection, in the perfusion image scanning, the radiation dose reduction is more evident.
PMI makes use of the spatial information contained in phased array to replace the usual time consuming gradient encoding steps to speed up the imaging speed. However, as a new technology, there are deficiencies in the imaging algorithm There are mainly three kinds of PMRI algorithms, which are methods based on image domain, methods based on k space domain, and methods based on both image and k space domain. We focused on the SENSE (sensitivity encoding) method which is based on image domain. When a large acceleration factor is used the SNR of SENSE is dramatically deteriorated, and it will become much worse when the non-Cartesian sampling trajectories were adopted. Regularization methods have been shown to alleviate the problem, regularization based on Tikhonov and TV is the most widely used methods. In this paper, we propose an adaptive constraint model for SENSE, which makes use of the gradient feature of the prior image to decide the penalty function to deal with non-Cartesian data from multiple coils, in regions of higher gradient, TV based constraint which is an anisotropically smoothing method is adopted, which can protect edge information better. In more ambiguous regions with lower gradient, Tikhonov regularization method is adopted which can smooth noise better.
Currently, numbers of sparse angle image reconstruction algorithm have been proposed, there are basically divided into two categories:the iterative transform-analysis reconstruction algorithm base on the transform domain; another, iterative-algebra/statistics reconstruction algorithms based on series expansion. Iterative reconstruction algorithm is an efficient image reconstruction algorithm for noisy data or incomplete projections in the uneven distribution of projection between 180 or 360. To improve the imaging accuracy and resolution, we often take measures of use regularization method or increase the number of iterations. In 2004, Cands, et al proposed the compressed sensing (CS, Compressed Sensing) theory. According to the applications in image reconstruction of CS, if the to be reconstructed image is sparse in a transform space, and then we can use the partially sampling data to acquire a high quality image use CS method. For the sparse angular CT perfusion imaging, compared with the previous scanned image, it can be considered that the perfusion information of the perfusion image series is sparse in the image domain in every moment. We proposed the sparse angular perfusion CT image reconstruction based on the subtraction in projection domain, and acquired the perfusion information images with iterative regularization constrained CS reconstruction methods.
In conclusion, this study makes use of insufficient data collection methods to reduce the time of MRI and CT scan imaging radiation dose. We analyzed on the problem of SENSE constraint reconstruction algorithm, and proposed a new algorithm for non-Cartesian parallel MRI data reconstruction with adaptive constraint based on SENSE。Experiment data were simulated using collected projection X-ray of an arterial bolus injection in a patient with an AVM using an 8-channel head coil, and the under-sampling factor is 2.6 in our experiments. Simulation Experiments show that our method can better remove the noise and artifact caused by under-sampled data, and comes up with a better image quality with well protected image edge information especially some small details than the conventional SOS、SENSE and TV constraint SENSE reconstruction methods. In addition, we researched on the CT perfusion imaging, we can know that the change of CT perfusion information in time series is relatively smaller compared with the non-perfusion image, and the perfusion information is sparse. So we made use of compressed sensing theory to acquire the perfusion information image, and comes up with a better image quality compared with the traditional methods. Shepp-Logan Phantom experiments and human brain perfusion imaging proved the effectiveness of the proposed algorithm, the background area and Target areas of the image which was acquired with only 18 projections in [0,p] are highly consistent with the original image. Human brain perfusion experiments show that our algorithm can effectively restore detail information of the perfusion image, and we can still recover the acceptable perfusion images with a 96.3% reduction in dose (36 projection).
MRI(magnetic resonance imaging, MRI)及CT(computed tomography, CT)的临床应用,开创了影像诊断新纪元。磁共振成像是当今最重要的影像学手段之一,它具有组织分辨率高、可任意方向断层、空间分辨率高、对人体无放射损伤等优点。自20世纪80年代初应用于临床以来,磁共振血管成像(MR angiography, MRA),磁共振波谱成像(MR spectroscopy, MRS)、并行磁共振成像(parallel MR imaging, PMRI)等技术越来越趋于成熟,使得磁共振成像成为临床和科学研究中越来越重要的成像方法。计算机断层成像是英国工程师Godfrey Hounsfield发明的,近年来,随着多排CT、双源CT的出现,高质量的冠状动脉成像、胸痛三联诊的一次实现以及大器官灌注图像研究都已在临床中应用。
作为一种重要的临床成像方式,MRI的主要不足是它的数据采集时间较长,从而导致成像速度较慢。二十世纪90年代以来,研究者致力于通过提高静磁场的场强、研究新的快速成像序列、开发能够快速切换的梯度磁场来提高成像速度。然而,梯度磁场切换速度过快时会刺激受检者的肌肉与神经,造成人体不适。且发展到现在,硬件的发展也极大制约了速度的进一步提高,继续依赖提高梯度场切换速度来提高成像速度基本上达到了极限。所以必须寻找新的解决途径。
另一方面,CT作为近代飞跃发展的计算机技术和X线检查技术相结合的产物,为临床提供了优质的影像学信息。但是当X线穿透机体被吸收时,可使细胞组织产生抑制、损害甚至坏死,称为X线的生物作用。X线对机体的损害程度与吸收X线量的大小有关。CT在高剂量X线下可以获得更优质的影像,但是同时增加了治疗人群的总体受辐射水平。尤其是作为主要功能成像方式之一的CT灌注成像,由于需要长时间的连续曝光,导致受检者的辐射剂量增高。为了用最小的人体损伤代价获得最佳的诊断效果,低剂量CT的研究很有必要。
综上可知,当前两项技术要解决的问题分别是,MRI需要缩短采集时间,CT需要减少X线剂量。通过重建算法研究降低成像所需的数据量,即在仅获得部分成像数据的情况下,通过优化重建算法仍然获得满足临床诊断质量需求的图像,对于磁共振成像,意味着成像速度的提升,对于CT成像,意味着可以降低病人接受的X线辐射剂量。由于部分数据成像方法不依赖于硬件性能,成为快速磁共振成像与低剂量CT成像领域的研究热点之一。
当前,基于多通道采集技术的并行磁共振成像技术(PMRI)的出现对MRI产生了深远影响,它使用相控阵线圈阵列同时采集部分数据,即各个线圈在同一时间内都进行部分数据采集,数据采集时间有效减少。CT中采用的方法为采集有限角度的投影数据,可以减少每次的曝光时间,当进行灌注图像扫描时,放射剂量的减少量更加明显。
并行磁共振成像在计算机求解图像部分是利用相控阵线圈内在包含的空间信息来恢复图像信息。然而,作为一门新的技术,还没有找到一种最优的成像算法。目前并行成像算法分为三类,基于图像域的方法、基于k-空间域的方法和基于图像域和k-空间域相结合的方法。本文主要研究了基于图像域的敏感度编码(SENSE, Sensitivity Encoding)方法。当数据采样较少,即欠采样因子较大时,SENSE重建方法的信噪比严重降低,当采样数据为非笛卡尔轨迹数据时,这种现象更为明显。传统算法优化方法是在重建方程中引入范数约束或l2范数约束。本文研究提出自适应约束的SENSE重建算法,由先验图像的梯度特征并借鉴PM模型的思想决定惩罚函数,使得在梯度幅值较大区域使用各向异性扩散的l1范数约束方式,以较好地保留图像细节；在梯度幅值较小区域使用各向同性扩散的l2范数约束方式,以有效地抑制噪声。
另外,诸多稀疏角度CT图像重建算法相继提出,整体可分为两大类：一类为基于变换域的迭代-解析重建算法；另一类为基于级数展开的迭代-代数/统计重建算法。迭代重建算法对于含噪声的不完全投影数据或者投影不均匀分布于180或360之间的图像重建是一种比较有效的算法。为了提高成像的精度和分辨率,一般采用正则化方法或者增加迭代次数。2004年,Cands、Romberg、Tao和Donoho等人提出压缩感知(CS, Compressed Sensing)理论。根据压缩感知理论在图像重建中的应用,可以知道,如果待重建图像在某个变换空间中是稀疏的,那么可以利用部分采样数据重建出质量较好的图像。对于稀疏角度CT灌注成像,相对于未灌注图像,可以认为在每一个时刻获得的灌注图像中增加的灌注信息在图像域都是稀疏的。本文中提出基于投影域减影的CT灌注图像重建,利用压缩感知原理对投影域减影数据进行约束迭代重建得出灌注信息图像,然后和预扫描图像进行配准相加来得到当前时刻的灌注图像。
总之,本研究主要利用部分数据采集方式来减少MRI的成像时间和CT扫描的辐射剂量。对并行成像SENSE约束重建算法中存在的缺陷进行了分析,提出了自适应约束SENSE非笛卡尔数据重建新算法,8通道2.6倍欠采样可变密度螺旋轨迹人体动静脉畸形瘤动脉注射X线仿真成像实验表明,与平方和(SOS)重建方法、传统无约束SENSE重建方法以及TV约束SENSE重建方法相比,本文所提算法可以有效抑制部分数据成像带来的噪声和伪影,并能较好保护图像细节尤其是小细节信息,成像效果优于传统方法。另外,对稀疏角度CT灌注成像方法进行了研究,观察到每个时间序列中灌注信息的变化是较少的,所以提出基于投影域减影的约束重建方法求解各个时刻的灌注信息变化图像。Shepp—LOgan体模实验和人体脑部灌注成像实验证明了本文算法的有效性,对结构简单的Shepp—Logan体模图像,使用本文算法在[0,p]范围内仅采集18个投影就可以重建出在背景区和目标区都与原图高度符合的图像。人体脑部灌注实验证明,本文算法可以有效恢复各种细节灌注信息,且在剂量减少96.3%(36个投影)的情况下仍能恢复出可以接受的灌注信息全面的图像。
Medical Imaging is the science that assists diagnosis and treatment of diseases by displayed the human body structure and function information within image, mainly including X ray, ultrasound, radionuclide, CT and magnetic resonance imaging。The development of medical imaging through three steps:X-ray (Roentgenology)、Radiology and Imaging. X ray is the imaging source of the diagnosis and radiographic techniques. And multiple image sources appeared such as ultrasound, radionuclide, and magnetic resonance and so on.
The clinical application of MRI and CT creates a new era in diagnostic imaging. Magnetic resonance imaging is one of the most important means of imaging technologies. Compared with other modalities of medical imaging, MRI has many advantages, such as excellent soft-tissue contrast、imaging in arbitrary plane、excellent spatial resolution and with no ionizing radiation. Since MRI was applied in clinical from the early 1980s, magnetic resonance angiography (MR angiography, MRA), magnetic resonance spectroscopy (MR spectroscopy, MRS), the parallel magnetic resonance imaging (parallel MR imaging, PMRI) and other technologies becoming more and more mature. All those advantages make MRI a very important tool for both clinical applications and scientific research. Computed tomography (computed tomography, CT) was invented by British engineer Godfrey Hounsfield。In recent years, with the emergence of multi-slice CT and dual-source CT, some difficult technique, such as high-quality imaging of the coronary arteries and major organ perfusion, have been applied in clinical.
As an important clinical imaging modalities, the main disadvantages of MRI is the long data acquisition time and thus results in the long imaging time. Since 1990, Researchers committed to improving the field strength of magnetic field、developing the new fast imaging sequence and quickly switched gradient magnetic field to increase the imaging speed. However, rapidly switched field gradient would produce neuromuscular stimulation and lead to body unease. At the same time, owing to the limitation that caused by the status of hardware development, it almost reaches the limit that rely on gradient switching speed increase to improve imaging speed.
On the other hand, as the combining of the rapid developmental modern computer technology and X-ray examination technology, CT provides high-quality information for clinical imaging. But when the X ray is absorbed through the body, it can produce inhibition of tissue damage or necrosis, referred to as X-biological effects. X ray damage to the body is proportional to the absorption of X-ray dose. CT can get better quality images at higher X-ray doses, but it also increased the overall radiation level affected by people. In particular, as one of the main functions imaging modalities, CT perfusion imaging needs a long period of continuous exposure, and oit will lead to increased radiation dose exposure. With the principle of acquire the best diagnostic results with minimal damage to the human, it is necessary to research on the low-dose CT.
To sum up, currently, the problems need to be solved of the two technologies are, MRI need to shorten the acquisition time, CT need to reduce the X-ray dose, for these two issues, all can be solved by insufficient data collecting. the main time-consuming factors of MRI imaging is the long data sampling time, insufficient data collection can reduce the acquisition time; the X-ray radiation dose of CT imaging increases with the increase in examination time, the use of insufficient data collection methods can shorten the exposure time, which can reduce the radiation dose exposure to examiners.
Currently, Parallel magnetic resonance imaging technology that based on the multi-channel acquisition had a profound impact on magnetic resonance imaging, which uses phased array coil array to collect part of the data sets simultaneously. CT can reduce the exposure each time with a limited angle projection data collection, in the perfusion image scanning, the radiation dose reduction is more evident.
PMI makes use of the spatial information contained in phased array to replace the usual time consuming gradient encoding steps to speed up the imaging speed. However, as a new technology, there are deficiencies in the imaging algorithm There are mainly three kinds of PMRI algorithms, which are methods based on image domain, methods based on k space domain, and methods based on both image and k space domain. We focused on the SENSE (sensitivity encoding) method which is based on image domain. When a large acceleration factor is used the SNR of SENSE is dramatically deteriorated, and it will become much worse when the non-Cartesian sampling trajectories were adopted. Regularization methods have been shown to alleviate the problem, regularization based on Tikhonov and TV is the most widely used methods. In this paper, we propose an adaptive constraint model for SENSE, which makes use of the gradient feature of the prior image to decide the penalty function to deal with non-Cartesian data from multiple coils, in regions of higher gradient, TV based constraint which is an anisotropically smoothing method is adopted, which can protect edge information better. In more ambiguous regions with lower gradient, Tikhonov regularization method is adopted which can smooth noise better.
Currently, numbers of sparse angle image reconstruction algorithm have been proposed, there are basically divided into two categories:the iterative transform-analysis reconstruction algorithm base on the transform domain; another, iterative-algebra/statistics reconstruction algorithms based on series expansion. Iterative reconstruction algorithm is an efficient image reconstruction algorithm for noisy data or incomplete projections in the uneven distribution of projection between 180 or 360. To improve the imaging accuracy and resolution, we often take measures of use regularization method or increase the number of iterations. In 2004, Cands, et al proposed the compressed sensing (CS, Compressed Sensing) theory. According to the applications in image reconstruction of CS, if the to be reconstructed image is sparse in a transform space, and then we can use the partially sampling data to acquire a high quality image use CS method. For the sparse angular CT perfusion imaging, compared with the previous scanned image, it can be considered that the perfusion information of the perfusion image series is sparse in the image domain in every moment. We proposed the sparse angular perfusion CT image reconstruction based on the subtraction in projection domain, and acquired the perfusion information images with iterative regularization constrained CS reconstruction methods.
In conclusion, this study makes use of insufficient data collection methods to reduce the time of MRI and CT scan imaging radiation dose. We analyzed on the problem of SENSE constraint reconstruction algorithm, and proposed a new algorithm for non-Cartesian parallel MRI data reconstruction with adaptive constraint based on SENSE。Experiment data were simulated using collected projection X-ray of an arterial bolus injection in a patient with an AVM using an 8-channel head coil, and the under-sampling factor is 2.6 in our experiments. Simulation Experiments show that our method can better remove the noise and artifact caused by under-sampled data, and comes up with a better image quality with well protected image edge information especially some small details than the conventional SOS、SENSE and TV constraint SENSE reconstruction methods. In addition, we researched on the CT perfusion imaging, we can know that the change of CT perfusion information in time series is relatively smaller compared with the non-perfusion image, and the perfusion information is sparse. So we made use of compressed sensing theory to acquire the perfusion information image, and comes up with a better image quality compared with the traditional methods. Shepp-Logan Phantom experiments and human brain perfusion imaging proved the effectiveness of the proposed algorithm, the background area and Target areas of the image which was acquired with only 18 projections in [0,p] are highly consistent with the original image. Human brain perfusion experiments show that our algorithm can effectively restore detail information of the perfusion image, and we can still recover the acceptable perfusion images with a 96.3% reduction in dose (36 projection).
引文
[1]. Carlson JW. An algorithm for NMR imaging reconstruction based on multiple RF receiver coils [J]. J Magn Reson,1987,74:376-380.
[2]. Ra JB, Rim CY. Fast imaging using sub-encoding data sets from multiple detectors [J]. Magn Reson Med,1993,30(1):142-145.
[3]. Blaimer M, Breuer F, Mueller M, et al. SMASH, SENSE, PILS, GRAPPA:How to choose the optimal method [J].Top Magn Reson Imaging,2004,15:223-236.
[4]. Sodickson DK, Manning WJ. Simultaneous acquisition of spatial harmonics (SMASH):fast imaging with radiofrequency coil arrays [J]. Magn Reson Med, 1997,38 (4):591-603.
[5]. Jakob PM, Griswold MA, Edelman RR, et al. AUTO-SMASH:a self-calibrating technique for SMASH imaging [J]. MAGMA,1998,7:42-54.
[6]. Heidemann RM, Griswold MA, Haase A, et al. VD-AUTO-SMASH imaging [J]. Magn Reson Med,2001,45(6):1066-1074.
[7]. Griswold MA, Jakob PM, Heidemann RM, et al. Generalized autocalibrating partially parallel acquisitions (GRAPPA) [J]. Magn Reson Med,2002,47 (6):1202-1210.
[8]. Bydder M, Larkman DJ, Hajnal JV. Generalized SMASH imaging [J]. Magn Reson Med,2002,47 (1):160-170.
[9]. Pruessmann KP, Weiger M, Scheidegger MB, et al. Sensitivity encoding for fast MRI [J]. Magn Reson Med,1999,42(5):952-962.
[10]. Griswold MA, Jakob PM, Nittka M, et al. Partially parallel imaging with localized sensitivities (PILS) [J]. Magn Reson Med,2000,44:602-609.
[11]. Wang J, Kluge T, Nittka M, et al. Parallel acquisition techniques with modified SENSE reconstruction mSENSE[A]. In:Proceedings of the First Wurzburg Workshop on Parallel Imaging Basics and Clinical Applications[C]. Germany,2001.89.
[12]. Kyriakos WE, Panych LP, Kacher DF, et al. Sensitivity profiles from an array of coils for encoding and reconstruction in parallel (SPACE RIP) [J]. Magn Reson Med,2000,44:301-308.
[13]. Kellman P, Epstein FH, McVeigh ER. Adaptive sensitivity encoding incorporating temporal filtering (TSENSE) [J]. Magn Reson Me,2001,45(5):846-852.
[14]. Breuer F, Kellman P, Griswold MA, et al. Dynamic Autocalibrated Parallel Imaging using TGRAPPA [A]. In:Proc. Eleventh Scientific Meeting Intl. Soc. Magn Reson Med[C].2003,2330.
[15]. Tsao J, Boesiger P, Pruessmann KP. K-t BLAST and k-t SENSE:dynamic MRI with high frame rate exploiting spatiotemporal correlations [J]. Magn Reson Med,2003,50:1031-1042.
[16]. Huang F, Cheng H. k-t GRAPPA [A]. In:Proceedings of the Second International Workshop on Parallel MRI [C]. ETH Zurich,2004.
[17]. Xu D, Wiener E, Ying L, et al. Integrating parallel imaging with generalized series for accelerated dynamic imaging [A]. In: Proceedings of the 2005 IEEE 27th EMBC [C]. Shanghai,2005.
[18]. Weiger M, Pruessmann KP, Boesiger P.2D SENSE for faster 3D MRI [J]. MAGMA.2002,14 (1):10-19.
[19]. Martin Blaimer, Felix Breuer, Matthias Mueller, Robin M. Heidemann, Mark A. Griswold, and Peter M. JakobSMASH, SENSE, PILS, GRAPPA How to Choose the Optimal Method [J]. Top Magn Reson Imaging,2004,15(4).
[20]. vaardingerbroek MT, Boer JA. Magnetic resonance imaging:theory and practice [M].1999,55-91.
[21]. Haacke EM, Brown RW, ThomPson MR, et al. Magnetic resonance imaging: physical principles and sequence design [M].2002,51-62.
[22]. 赵喜平.磁共振成像系统的原理及其应用[M].2002,20-139.
[23]. 高元桂,磁共振成像诊断学[M].北京：人民军医出版社,2004
[24]. 李月卿,李萌.医学影像成像原理[M].2002,151-181.
[25]. 何斌,马天予,王运坚等.Visual C++数字图像处理[M].2001,213-215
[26]. 俎栋林.核磁共振成像学[M].2004,507-529
[27]. Pruessmann KP, Weiger. M. SENSE:Sensitivity Encoding for fast MRI [J]. Magnetic Resonance in Medicine,1999,42(5):952-962.
[28]. Liu B, King K. Regularized sensitivity encoding (SENSE) reconstruction using bregman iterations [J]. Magnetic Resonance in Medicine,2009,61(1): 145-152.
[29]. 陈武凡.并行磁共振成像的回顾、现状与发展前景[J].中国生物医学工程学报,2005,24(6)：649-654.
[30]. Vijayakumar S, Duensing R, Huang F. G-factor and gradient weighted denoising with edge restoration (g-denoiser) for SENSE reconstruction MR images [C]//Christophe J, Marin O, eds.2008 5th IEEE International Symposium on Biomedical Imaging: from Nano to Macro. Paris: IEEE,2008: 472-475.
[31]. Perona P, Malik J. Scale space and edge detection using anisotropic diffusion [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(7): 629-639.
[32]. Lustig M, Donoho D, Pauly JM. Sparse MRI:the application of compressed sensing for rapid MR imaging [J]. Magnetic Resonance in Medicine,2007,58(6): 1182-1195.
[33]. Pruessmann KP, Weiger M. Advances in sensitivity encoding with arbitrary k-space trajectories [J]. Magnetic Resonance in Medicine,2001,46(4):638-651.
[34]. Rasche V, Proksa R, Sinkus R, et al. Resampling of data between arbitrary grids using convolution interpolation [J]. IEEE Trans Med Imaging,1999,18(5): 385-392.
[35]. Jackson JI, Meyer CH, Nishimura DG. Selection of a convolution function for fourier inversion using gridding [J]. IEEE Trans Med Imaging,1991,10(3): 473-478.
[36]. Osulllivan J. A fast sine function gridding algorithm for fourier inversion in computed tomography [J]. IEEE Trans Med Imaging,1985,4(4):200-207.
[37]. Cukur T, Santos JM, Nishimura DG, et al. Varying kernel-extent gridding reconstruction for undersampled variable-density spirals [J]. Magnetic Resonance in Medicine,2008,59(1):196-201.
[38]. Hoge RD, Kwan RKS, Pike GB. Density compensation functions for spiral MRI [J]. MRM,1997,38(1):117-128.
[39]. Beatty PJ, Nishimura DG. Rapid gridding reconstruction with a minimal oversampling ratio [J]. IEEE Trans Med Imaging,2005,24(6):799-808.
[40]. Osher S, Burger M, Goldfarb D. An iterative regularization method for total variation-based image restoration [J]. Multiscale Model Simul,2005,4(2): 460-489.
[41]. Huang F, Chen YM, Duensing GR. Application of partial differential equation-based inpainting on sensitivity maps [J]. Magnetic Resonance in Medicine,2005,53(2):388-397.
[42]. Rudin LI, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms [J]. Physica,1992,60(1-4):259-268.
[43]. Block KT, Uecker M, Frahm J. Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint [J]. Magnetic Resonance in Medicine,2007,57(6):1086-1098.
[44]. Larsson EG, Erdogmus D, Yan R, et al. SNR-optimality of sum-of-squares reconstruction for phased-array magnetic resonance imaging [J]. Journal of Magnetic Resonance,2003,163(1):121-123
[45]. G.T. Herman, image reconstruction from projections, Academic, New York,1980.
[46]. Jiang H. Computed tomography: principle, design, artifacts and recent advances [M]. NewYork:International Society for Optical Engineering,2003.
[47]. F.Natter, The mathematics of computerized tomography, J. Wiley & Sons, New York,1986.
[48]. Yu L, Liu X, Leng S, et al. Radiation dose reduction in computed tomography techniques and future perspective [J]. Imaging in Medicine,2009, 1(1):65-84.
[49]. Fricke E, Fricke H, Weise R, et al. Attenuation correction of myocardial SPECT perfusion images with low-dose CT:evaluation of the method by comparison with perfusion PET [J]. J Nucl Med,2005,46(5):736-744.
[50]. Kajander S, Ukkonen H, Sipila H, et al. Low radiation dose imaging of myocardial perfusion and coronary angiography with a hybrid PET/CT scanner [J]. Clin Physiol Funct Imaging,2009,29(1):81-88.
[51]. O'Halloran R L, Wen Z, Holmes J H, et al. Iterative projection reconstruction of time-resolved images using highly-constrained back-projection (HYPR)[J]. Magn Reson Med,2008,59(1):132-139.
[52]. Jakobs T F, Becker C R, Ohnesorge B, et al. Multislice helical CT of the heart with retrospective ECG gating:reduction of radiation exposure by ECG-controlled tube current modulation [J]. Eur Radiol,2002,12(5):1081-1086.
[53]. Yu H, Zhao S, Hoffman E A, et al. Ultra-low dose lung CT perfusion regularized by a previous scan[J]. Acad Radiol,2009,16(3):363-373
[54]. Yu L, Liu X, Leng S, et al. Radiation dose reduction in computed tomography techniques and future perspective [J]. Imaging in Medicine,2009, 1(1):65-84.
[55]. Gutte H, Mortensen J, Jensen C V, et al. Detection of pulmonary embolism with combined ventilation-perfusion SPECT and low-dose CT:head-to-head comparison with multidetector CT angiography [J]. J Nucl Med,2009, 50(12):1987-1992.
[56]. Saito N, Kudo K, Sasaki T, et al. Realization of reliable cerebral-blood-flow maps from low-dose CT perfusion images by statistical noise reduction using nonlinear diffusion filtering[J]. Radiol Phys Technol,2008, 1(1):62-74.
[57]. Verhoeven D. Limited-data computed tomography algorithms for the physical sciences [J]. Appl Opt,1993,32(20):3736-3754.
[58]. Hsieh J, Wei Y, Wang G. Fractional scan algorithms for low-dose perfusion CT [J]. Med Phys,2004,31(5):1254-1257.
[59]. Nassi M, Brody W R, Medoff B P, et al. Iterative reconstruction reprojection: an algorithm for limited data cardiac-computed tomography [J]. IEEE Trans Biomed Eng,1982,29(5):333-341.
[60]. Papoulis A. A new algorithm in spectral analysis and bandlimited singal extrapolation [J]. Circ Sys,1975(32):735-742.
[61]. Emamnuel J, Candes. Compressive Sampling [Z]. Madrid Spain:2006, 1433-1452.
[62]. Candes EJ, Justin Romberg.Robust uncertainty principles Exact signal reconstruction from highly incomplete frequency information [J]. IEEE Trans on Information Theory,2006,52(2):489-509.
[63]. Lustig M, Donoho D, Pauly J M. Sparse MRI: The application of compressed sensing for rapid MR imaging [J]. Magn Reson Med,2007, 58(6):1182-1195.
[64]. D L Donoho Y T. Extensions of compressed sensing [J]. Signal Process, 2006,86(3):533-548.
[2]. Ra JB, Rim CY. Fast imaging using sub-encoding data sets from multiple detectors [J]. Magn Reson Med,1993,30(1):142-145.
[3]. Blaimer M, Breuer F, Mueller M, et al. SMASH, SENSE, PILS, GRAPPA:How to choose the optimal method [J].Top Magn Reson Imaging,2004,15:223-236.
[4]. Sodickson DK, Manning WJ. Simultaneous acquisition of spatial harmonics (SMASH):fast imaging with radiofrequency coil arrays [J]. Magn Reson Med, 1997,38 (4):591-603.
[5]. Jakob PM, Griswold MA, Edelman RR, et al. AUTO-SMASH:a self-calibrating technique for SMASH imaging [J]. MAGMA,1998,7:42-54.
[6]. Heidemann RM, Griswold MA, Haase A, et al. VD-AUTO-SMASH imaging [J]. Magn Reson Med,2001,45(6):1066-1074.
[7]. Griswold MA, Jakob PM, Heidemann RM, et al. Generalized autocalibrating partially parallel acquisitions (GRAPPA) [J]. Magn Reson Med,2002,47 (6):1202-1210.
[8]. Bydder M, Larkman DJ, Hajnal JV. Generalized SMASH imaging [J]. Magn Reson Med,2002,47 (1):160-170.
[9]. Pruessmann KP, Weiger M, Scheidegger MB, et al. Sensitivity encoding for fast MRI [J]. Magn Reson Med,1999,42(5):952-962.
[10]. Griswold MA, Jakob PM, Nittka M, et al. Partially parallel imaging with localized sensitivities (PILS) [J]. Magn Reson Med,2000,44:602-609.
[11]. Wang J, Kluge T, Nittka M, et al. Parallel acquisition techniques with modified SENSE reconstruction mSENSE[A]. In:Proceedings of the First Wurzburg Workshop on Parallel Imaging Basics and Clinical Applications[C]. Germany,2001.89.
[12]. Kyriakos WE, Panych LP, Kacher DF, et al. Sensitivity profiles from an array of coils for encoding and reconstruction in parallel (SPACE RIP) [J]. Magn Reson Med,2000,44:301-308.
[13]. Kellman P, Epstein FH, McVeigh ER. Adaptive sensitivity encoding incorporating temporal filtering (TSENSE) [J]. Magn Reson Me,2001,45(5):846-852.
[14]. Breuer F, Kellman P, Griswold MA, et al. Dynamic Autocalibrated Parallel Imaging using TGRAPPA [A]. In:Proc. Eleventh Scientific Meeting Intl. Soc. Magn Reson Med[C].2003,2330.
[15]. Tsao J, Boesiger P, Pruessmann KP. K-t BLAST and k-t SENSE:dynamic MRI with high frame rate exploiting spatiotemporal correlations [J]. Magn Reson Med,2003,50:1031-1042.
[16]. Huang F, Cheng H. k-t GRAPPA [A]. In:Proceedings of the Second International Workshop on Parallel MRI [C]. ETH Zurich,2004.
[17]. Xu D, Wiener E, Ying L, et al. Integrating parallel imaging with generalized series for accelerated dynamic imaging [A]. In: Proceedings of the 2005 IEEE 27th EMBC [C]. Shanghai,2005.
[18]. Weiger M, Pruessmann KP, Boesiger P.2D SENSE for faster 3D MRI [J]. MAGMA.2002,14 (1):10-19.
[19]. Martin Blaimer, Felix Breuer, Matthias Mueller, Robin M. Heidemann, Mark A. Griswold, and Peter M. JakobSMASH, SENSE, PILS, GRAPPA How to Choose the Optimal Method [J]. Top Magn Reson Imaging,2004,15(4).
[20]. vaardingerbroek MT, Boer JA. Magnetic resonance imaging:theory and practice [M].1999,55-91.
[21]. Haacke EM, Brown RW, ThomPson MR, et al. Magnetic resonance imaging: physical principles and sequence design [M].2002,51-62.
[22]. 赵喜平.磁共振成像系统的原理及其应用[M].2002,20-139.
[23]. 高元桂,磁共振成像诊断学[M].北京：人民军医出版社,2004
[24]. 李月卿,李萌.医学影像成像原理[M].2002,151-181.
[25]. 何斌,马天予,王运坚等.Visual C++数字图像处理[M].2001,213-215
[26]. 俎栋林.核磁共振成像学[M].2004,507-529
[27]. Pruessmann KP, Weiger. M. SENSE:Sensitivity Encoding for fast MRI [J]. Magnetic Resonance in Medicine,1999,42(5):952-962.
[28]. Liu B, King K. Regularized sensitivity encoding (SENSE) reconstruction using bregman iterations [J]. Magnetic Resonance in Medicine,2009,61(1): 145-152.
[29]. 陈武凡.并行磁共振成像的回顾、现状与发展前景[J].中国生物医学工程学报,2005,24(6)：649-654.
[30]. Vijayakumar S, Duensing R, Huang F. G-factor and gradient weighted denoising with edge restoration (g-denoiser) for SENSE reconstruction MR images [C]//Christophe J, Marin O, eds.2008 5th IEEE International Symposium on Biomedical Imaging: from Nano to Macro. Paris: IEEE,2008: 472-475.
[31]. Perona P, Malik J. Scale space and edge detection using anisotropic diffusion [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(7): 629-639.
[32]. Lustig M, Donoho D, Pauly JM. Sparse MRI:the application of compressed sensing for rapid MR imaging [J]. Magnetic Resonance in Medicine,2007,58(6): 1182-1195.
[33]. Pruessmann KP, Weiger M. Advances in sensitivity encoding with arbitrary k-space trajectories [J]. Magnetic Resonance in Medicine,2001,46(4):638-651.
[34]. Rasche V, Proksa R, Sinkus R, et al. Resampling of data between arbitrary grids using convolution interpolation [J]. IEEE Trans Med Imaging,1999,18(5): 385-392.
[35]. Jackson JI, Meyer CH, Nishimura DG. Selection of a convolution function for fourier inversion using gridding [J]. IEEE Trans Med Imaging,1991,10(3): 473-478.
[36]. Osulllivan J. A fast sine function gridding algorithm for fourier inversion in computed tomography [J]. IEEE Trans Med Imaging,1985,4(4):200-207.
[37]. Cukur T, Santos JM, Nishimura DG, et al. Varying kernel-extent gridding reconstruction for undersampled variable-density spirals [J]. Magnetic Resonance in Medicine,2008,59(1):196-201.
[38]. Hoge RD, Kwan RKS, Pike GB. Density compensation functions for spiral MRI [J]. MRM,1997,38(1):117-128.
[39]. Beatty PJ, Nishimura DG. Rapid gridding reconstruction with a minimal oversampling ratio [J]. IEEE Trans Med Imaging,2005,24(6):799-808.
[40]. Osher S, Burger M, Goldfarb D. An iterative regularization method for total variation-based image restoration [J]. Multiscale Model Simul,2005,4(2): 460-489.
[41]. Huang F, Chen YM, Duensing GR. Application of partial differential equation-based inpainting on sensitivity maps [J]. Magnetic Resonance in Medicine,2005,53(2):388-397.
[42]. Rudin LI, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms [J]. Physica,1992,60(1-4):259-268.
[43]. Block KT, Uecker M, Frahm J. Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint [J]. Magnetic Resonance in Medicine,2007,57(6):1086-1098.
[44]. Larsson EG, Erdogmus D, Yan R, et al. SNR-optimality of sum-of-squares reconstruction for phased-array magnetic resonance imaging [J]. Journal of Magnetic Resonance,2003,163(1):121-123
[45]. G.T. Herman, image reconstruction from projections, Academic, New York,1980.
[46]. Jiang H. Computed tomography: principle, design, artifacts and recent advances [M]. NewYork:International Society for Optical Engineering,2003.
[47]. F.Natter, The mathematics of computerized tomography, J. Wiley & Sons, New York,1986.
[48]. Yu L, Liu X, Leng S, et al. Radiation dose reduction in computed tomography techniques and future perspective [J]. Imaging in Medicine,2009, 1(1):65-84.
[49]. Fricke E, Fricke H, Weise R, et al. Attenuation correction of myocardial SPECT perfusion images with low-dose CT:evaluation of the method by comparison with perfusion PET [J]. J Nucl Med,2005,46(5):736-744.
[50]. Kajander S, Ukkonen H, Sipila H, et al. Low radiation dose imaging of myocardial perfusion and coronary angiography with a hybrid PET/CT scanner [J]. Clin Physiol Funct Imaging,2009,29(1):81-88.
[51]. O'Halloran R L, Wen Z, Holmes J H, et al. Iterative projection reconstruction of time-resolved images using highly-constrained back-projection (HYPR)[J]. Magn Reson Med,2008,59(1):132-139.
[52]. Jakobs T F, Becker C R, Ohnesorge B, et al. Multislice helical CT of the heart with retrospective ECG gating:reduction of radiation exposure by ECG-controlled tube current modulation [J]. Eur Radiol,2002,12(5):1081-1086.
[53]. Yu H, Zhao S, Hoffman E A, et al. Ultra-low dose lung CT perfusion regularized by a previous scan[J]. Acad Radiol,2009,16(3):363-373
[54]. Yu L, Liu X, Leng S, et al. Radiation dose reduction in computed tomography techniques and future perspective [J]. Imaging in Medicine,2009, 1(1):65-84.
[55]. Gutte H, Mortensen J, Jensen C V, et al. Detection of pulmonary embolism with combined ventilation-perfusion SPECT and low-dose CT:head-to-head comparison with multidetector CT angiography [J]. J Nucl Med,2009, 50(12):1987-1992.
[56]. Saito N, Kudo K, Sasaki T, et al. Realization of reliable cerebral-blood-flow maps from low-dose CT perfusion images by statistical noise reduction using nonlinear diffusion filtering[J]. Radiol Phys Technol,2008, 1(1):62-74.
[57]. Verhoeven D. Limited-data computed tomography algorithms for the physical sciences [J]. Appl Opt,1993,32(20):3736-3754.
[58]. Hsieh J, Wei Y, Wang G. Fractional scan algorithms for low-dose perfusion CT [J]. Med Phys,2004,31(5):1254-1257.
[59]. Nassi M, Brody W R, Medoff B P, et al. Iterative reconstruction reprojection: an algorithm for limited data cardiac-computed tomography [J]. IEEE Trans Biomed Eng,1982,29(5):333-341.
[60]. Papoulis A. A new algorithm in spectral analysis and bandlimited singal extrapolation [J]. Circ Sys,1975(32):735-742.
[61]. Emamnuel J, Candes. Compressive Sampling [Z]. Madrid Spain:2006, 1433-1452.
[62]. Candes EJ, Justin Romberg.Robust uncertainty principles Exact signal reconstruction from highly incomplete frequency information [J]. IEEE Trans on Information Theory,2006,52(2):489-509.
[63]. Lustig M, Donoho D, Pauly J M. Sparse MRI: The application of compressed sensing for rapid MR imaging [J]. Magn Reson Med,2007, 58(6):1182-1195.
[64]. D L Donoho Y T. Extensions of compressed sensing [J]. Signal Process, 2006,86(3):533-548.