中文摘要：

磁共振成像（Magnetic Resonance Imaging,简称MRI）技术已被广泛应用于现代医学的临床诊断上。MRI多采用最小二乘（Least Squares,简称LS）算法通过非笛卡尔扫描轨迹进行医学图像的重构。LS算法需计算所谓的向量FHd和矩阵Q以重构图像。对于LS算法,计算向量FHd和矩阵Q占据了算法绝大部分工作量。本文基于开放计算语言（Open Computing Language,简称Open CL）编程框架,在中央处理器和图形处理器上对LS算法计算向量FHd实现并行化,且在使用内建函数、访存和分割循环等方面进行优化,得到近300倍的加速比。本文所提出的并行加速方案通过简单修改可用于计算矩阵Q。

英文摘要：

Magnetic resonance imaging （MRI） has been widely applied to modem clinical diagnosis. MRI usually uses the least squares （LS） algorithm to reconstruct medical images through non-Cartesian scanning trajectory. The LS al- gorithm needs to calculate the so-called vector FHd and matrix Q for the purpose of image reconstruction. Regarding the LS algorithm, the calculation of FHd and Q accounts for most of the work load. Based on the open computing lan- guage （OpenCL）programming framework, this paper parallelizes the calculation of FHd, optimizes the exploitation of built-in functions, memory access and the division of loops on the system with both central and graphic processing u- nits. An acceleration of approximate 300 times has been achieved. The parallel acceleration scheme proposed in this paper can be applied to the calculation of Q with a slight modification.