磁共振成像中不相干采样模式对点扩散函数的影响研究

The research of influence between different incoherent sampling patterns and point spread functions in MRI

压缩感知作为从源头上减少采样数据的新理论,被视为最具前景的快速磁共振成像方法。如何准确评价压缩感知磁共振成像的不相干性是设计磁共振不相干采样轨迹的关键。现有不相干评价指标仍然沿用压缩感知的不相干评价指标,忽略了磁共振设备的物理实际,导致压缩感知在磁共振成像应用中出现理论预期与实际性能差距较大的问题,犹如一道"屏障"横亘在压缩感知与磁共振成像之间,制约了压缩感知的性能。本文通过将传输变换点扩散函数(transform point spread function,TPSF)转换为点扩散函数(point spread function,PSF),从而建立PSF与采样轨迹直接相关的数学表达式,并给出了采样点的位置对PSF形状影响的关系式,最后分别给出了不同采样模式下的PSF仿真实验。实验结果表明,除了PSF的主瓣宽度、旁瓣高度外,旁瓣的分布特征对PSF的影响非常大。

Compressed sensing （CS）, which is a new theory that emphasizes reducing sampling data at the source, is regarded as the most promising technique in fast magnetic resonance imaging （MRI）. How to evaluate the incoherence of compressed sensing-magnetic resonance imaging （CS-MRI） accurately is a key point to design the incoherent sampling track in MRI. The existing incoherence evaluation indices still follow those used in CS. They ignore the practical influence of the magnetic resonance devices so the practical performance of these incoherence evaluation indices is much different from that in theory when CS is applied to MRI. The problem is like a ＂barrier＂ between CS and MRI and restricts the performance in CS-MRI. The paper proposes to convert the transform point spread function （TPSF） to point spread function （PSF）. Therefore, the mathematical relationships between the PSFs and sampling trajectory are formulated. Further, the relationships between the positions of sampling points and the shapes of PSFs are also given. At last, simulation experiments are taken to test PSFs in different sampling modes. Simulation results show that except the width of main lobes and the height of side lobe, the distribution characteristics of side lobes have a major effect on the shapes of the PSF.