Hoge R D, Kwan R K, Pike G B
McConnell Brain Imaging Centre, Montreal Neurological Institute, McGill University, Quebec, Canada.
Magn Reson Med. 1997 Jul;38(1):117-28. doi: 10.1002/mrm.1910380117.
In interleaved spiral MRI, an object's Fourier transform is sampled along a set of curved trajectories in the spatial frequency domain (k-space). An image of the object is then reconstructed, usually by interpolating the sampled Fourier data onto a Cartesian grid and applying the fast Fourier transform (FFT) algorithm. To obtain accurate results, it is necessary to account for the nonuniform density with which k-space is sampled. An analytic density compensation function (DCF) for spiral MRI, based on the Jacobian determinant for the transformation between Cartesian coordinates and the spiral sampling parameters of time and interleaf rotation angle, is derived in this paper, and the reconstruction accuracy achieved using this function is compared with that obtained using several previously published expressions. Various nonideal conditions, including intersecting trajectories, are considered. The new DCF eliminated intensity cupping that was encountered in images reconstructed with other functions, and significantly reduced the level of artifact observed when unevenly spaced sampling trajectories, such as those achieved with trapezoidal gradient waveforms, were employed. Modified forms of this function were found to provide similar improvements when intersecting trajectories made the spiral-Cartesian transformation noninvertible, and when the shape of the spiral trajectory varied between interleaves.
在交错螺旋磁共振成像（MRI）中，物体的傅里叶变换是在空间频率域（k空间）中沿着一组弯曲轨迹进行采样的。然后通常通过将采样的傅里叶数据插值到笛卡尔网格上并应用快速傅里叶变换（FFT）算法来重建物体的图像。为了获得准确的结果，有必要考虑k空间采样的非均匀密度。本文推导了一种基于笛卡尔坐标与螺旋采样的时间和层间旋转角度参数之间变换的雅可比行列式的螺旋MRI解析密度补偿函数（DCF），并将使用该函数实现的重建精度与使用先前发表的几个表达式获得的精度进行了比较。考虑了各种非理想条件，包括相交轨迹。新的DCF消除了用其他函数重建的图像中出现的强度凹陷，并显著降低了使用不均匀间隔采样轨迹（如梯形梯度波形实现的轨迹）时观察到的伪影水平。当相交轨迹使螺旋-笛卡尔变换不可逆时，以及当螺旋轨迹的形状在层间变化时，发现该函数的修改形式也能提供类似的改进。
