Liu H
Center for MR-guided Therapy and Center for Magnetic Resonance Research, Department of Radiology, University of Minnesota, Box 292 Mayo Building, University of Minnesota, 420 Delaware Street, SE 55455, Minneapolis, MN 55455, USA.
MAGMA. 2000 Jun;10(2):75-9. doi: 10.1007/BF02601841.
Since the spatial field non-linearity of gradient coils translates into image geometric distortion in MRI, in many applications, such as cardiac function analysis and interventional MR-based device tracking/guidance, where the precise geometric information is needed, the presence of geometric image distortion can not be simply ignored. To address the concern for geometric image distortion, we have developed and validated a general and efficient numerical technique for parameterizing the global image distortion for a bi-planar gradient coil as well as accomplishing image restoration as a post-imaging processing. This image correction methodology is based on a global distortion coordinate mapping function which can be systematically defined directly from the gradient field non-linearity in 3-dimension (3D) of a given gradient coil. The image correction was carried out in two steps: (1) map each pixel of the corrected image representation onto its distorted image according to the distortion mapping; (2) interpolate the pixel intensity in the distorted image using its neighboring points via a bi-linear interpolation procedure. The results showed clearly that the distortion correction method was robust in term of the capability of reducing image geometric distortion dramatically. Also it is shown that the magnetic field non-linearity or the image distortion of a typical bi-planar gradient coil can be adequately parameterized using a finite Taylor series expansion based on its design parameters. Furthermore, this image distortion correction method is very efficient in practice for performing 3D correction for any image orientation since a compact parameterized field expression contains non-zero terms.
由于梯度线圈的空间场非线性会在磁共振成像（MRI）中转化为图像几何失真，在许多需要精确几何信息的应用中，如心脏功能分析和基于介入式磁共振的设备跟踪/引导，图像几何失真的存在不能被简单地忽视。为了解决对图像几何失真的担忧，我们开发并验证了一种通用且高效的数值技术，用于对双平面梯度线圈的全局图像失真进行参数化，并作为成像后处理完成图像恢复。这种图像校正方法基于一个全局失真坐标映射函数，该函数可以直接从给定梯度线圈的三维（3D）梯度场非线性系统地定义。图像校正分两步进行：（1）根据失真映射将校正后图像表示中的每个像素映射到其失真图像上；（2）通过双线性插值过程使用其相邻点对失真图像中的像素强度进行插值。结果清楚地表明，失真校正方法在显著降低图像几何失真的能力方面是稳健的。还表明，基于典型双平面梯度线圈的设计参数，使用有限泰勒级数展开可以充分地对其磁场非线性或图像失真进行参数化。此外，这种图像失真校正方法在实践中对于对任何图像方向进行三维校正非常有效，因为一个紧凑的参数化场表达式包含非零项。
