基于最优控制与滤波理论的快速磁共振成像关键技术研究

Magnetic Resonance Imaging（MRI）is one of the most important and widely used imaging modalities in healthcare and biomedical research. MRI can generate cross-sectional images in any plane with high resolution and good contrast between the different soft tissues without the hazards of ionizing radiation. However, the slow scanning speed hinders the further application of MRI due to severe motion artifacts and low clinical throughtput.And how to speed up the scanning process and achieve fast MRI is the common aim in MRI society which normally can be attempted either by reducing the amount of sampling data or by increasing the field strength of MRI...The purpose of this project is to study two key problems of fast MRI, one is the compressed sensing MRI which is a core technique in MRI aiming at reducing the amount of sampling data, and another is the design of radio frequency (RF) pulses for multi-transmit parallel excitation which is an essential technique of high field MRI. The research of this project will be conducted from control theory and information theory point of view. Firstly we will improve the compressed sensing theory by considering the prior information of signals, and design the best sampling trajectory which is smooth, short with randomly spread sampling points. Also the performance of the image reconstruction will be analyzed theoretically. Moreover, the chaotic function will be applied to define the sampling trajectory for compressed sensing MRI. And optimal filtering method will be introduced to compressed sensing MRI to further sparsify signals and improve the performance of signal recovery...For high field MRI, multi-transmit technique is the latest and advanced technique where the parallel excitation RF pulses design is the key problem. In this project the RF pulses design will be formulated as an optimal control problem with constraints and a nonlinear technique will be applied to obtain an efficient algorithm for solving the optimal control problem such that the optimality of the performance and the safety of RF excitation will be guaranteed. Then the Dielectric artefact and the RF-induced heating can be strictly controlled, which are usually the main issues of high field MRI ...The results of this project will directly benefit the design and practical use of high field MRI and fast MRI, and will make the MRI faster, safter, more economical, and more applicable in healthcare and biomedical research.

磁共振成像（MRI）因分辨率高、无放射线辐射、观测角度灵活等优点，是最高端最具前景的影像学技术，但扫描速度慢是困扰其发展的瓶颈问题。因此"快速磁共振成像"成为该领域研究的一致目标，主要实现途径有1)减少采样数据; 2)提高静磁场的场强。. 本项目将针对这两个途径各自的关键核心技术"压缩感知磁共振成像"和"多源并行激励射频脉冲设计"，创新性地从控制学、信息学的视角来展开研究。通过发展基于信号先验信息的压缩感知理论，设计最优采样轨迹，并给出算法误差分析。此外创新性地引入混沌采样轨迹，并提出基于最优滤波压缩感知MRI成像算法。. 同时还将并行激励射频脉冲设计问题转化为一个带约束最优控制问题，并运用最新非线性理论方法给出有效算法，保证了最优设计性能及射频脉冲的严格安全性，根本解决了抗电阴影和因局部射频热限制扫描速度的高场MRI关键技术问题。必将有效推动高场磁共振和快速磁共振技术的发展。

本项目围绕如何实现快速磁共振扫描这一核心问题，分别从磁共振图像重建算法、磁共振扫描轨迹设计、磁共振脉冲及序列设计三方面入手展开研究。. 在磁共振图像重建算法方面，提出了快速自适应压缩感知重建算法，该方法能够改进接收线圈的敏感度估计、自适应调整优化约束项权重，并采用基于残差块熵方差的迭代终止条件，改善了现有算法需要事先设定图像重建过程参数以及迭代次数的问题。课题组基于该算法参加了14年国际医学磁共振学会年会（ISMRM）上“动态心脏成像”竞赛，在全球一百多个参赛队伍中位列前七名，并获提名奖（Finalist）。. 在磁共振扫描轨迹设计方面，先后提出了两种全新的轨迹，分别是广义花环扫描轨迹（the generalized rosette trajectory）和混沌轨迹。和目前常见的Cartesian轨迹、螺旋轨迹、放射状线轨迹相比，具有遍历速度快、高不相干性的特点，适合压缩感知磁共振成像。. 在磁共振脉冲及序列设计方面，提出了一种基于Bloch方程的射频脉冲信号的波形函数参数优化算法，并将最优控制理论用于增强两种组织对比度的激发脉冲设计问题，从而获得最优的成像效果。此外，课题组还将最优滤波方法引入量化磁共振成像问题中，和目前最热门的Finger Printing方法相比，它能够大大提高量化磁共振的扫描速度和成像速度。