一种基于时空变换和压缩感知的磁共振螺旋采样的图像重建算法

摘要

Spiral magnetic resonance imaging (MRI) plays an important role in functional imaging, parallel imaging and dynamic imaging. Most of the traditional image reconstruction algorithms for spiral imaging are based on kernel functions which interpolate thek-space data acquired with spiral trajectories onto a uniform grid in Cartesian space. Non-uniform fast Fourier transform (NUFFT) and least square method could then be applied after gridding to reconstruct the images. With these algorithms, the results are dependent on the choice of kernel function, and reconstruction errors are unavoidable during the gridding process. In this study, a spatio-temporal transform (STT) matrix, representing the relation between the image and sampledk-space data, is introduced inl1 norm to optimize the problem based on spatio-temporal transform and compressed sensing (CS). Thek-space data, rather than the after-gridding data, are used as the fidelity term, such that the gridding errors can be avoided. In addition, parallel computing on GPU can be applied to reduce the computation time for the STT matrix, making the algorithm more efficient.%螺旋采样磁共振快速成像在功能性成像、并行成像和动态成像等领域发挥着越来越重要的作用。螺旋采样图像重建的传统算法是用核函数将螺旋状分布的k空间数据插值到均匀网格中，再利用傅里叶变换和最小二乘法进行重建。但是基于网格化的算法对核函数过于依赖，在网格化过程中产生难以避免的误差。该文提出了基于时空变换和压缩感知的l1范数的最优化模型和重建算法。时空变换矩阵描述了空间上的磁共振图像与采集到的时域信号间的关系，使得算法直接使用采集到的数据作为保真约束项，避免了网格化过程产生的误差。此外，基于图像处理单元的并行计算被用来提高时空变换矩阵的运算速度，使得算法具有较强的应用价值。