Department of Radiology - Medical Physics, University Hospital Freiburg, Germany.
Magn Reson Med. 2010 Nov;64(5):1390-403. doi: 10.1002/mrm.22393. Epub 2010 Sep 16.
A basic framework for image reconstruction from spatial encoding by curvilinear, nonbijective magnetic encoding fields in combination with multiple receivers is presented. The theory was developed in the context of the recently introduced parallel imaging technique using localized gradients (PatLoc) approach. In this new imaging modality, the linear gradient fields are generalized to arbitrarily shaped, nonbijective spatial encoding magnetic fields, which lead to ambiguous encoding. Ambiguities are resolved by adaptation of concepts developed for parallel imaging. Based on theoretical considerations, a practical algorithm for Cartesian trajectories is derived in the case that the conventional gradient coils are replaced by coils for PatLoc. The reconstruction method extends Cartesian sensitivity encoding (SENSE) reconstruction with an additional voxelwise intensity-correction step. Spatially varying resolution, signal-to-noise ratio, and truncation artifacts are described and analyzed. Theoretical considerations are validated by two-dimensional simulations based on multipolar encoding fields and they are confirmed by applying the reconstruction algorithm to initial experimental data.
提出了一种基于空间编码的图像重建的基本框架，该空间编码由曲线、非一一对应的磁场编码场与多个接收器组合而成。该理论是在最近引入的使用局部梯度（PatLoc）方法的并行成像技术的背景下发展起来的。在这种新的成像模式中，线性梯度场被推广到任意形状的、非一一对应的空间编码磁场，这导致了编码的模糊性。通过适应为并行成像开发的概念来解决这些模糊性。基于理论考虑，在常规梯度线圈被用于 PatLoc 的线圈替换的情况下，为笛卡尔轨迹推导了一种实用的算法。该重建方法通过附加的体素强度校正步骤扩展了笛卡尔灵敏度编码（SENSE）重建。描述和分析了空间变化的分辨率、信噪比和截断伪影。通过基于多极编码场的二维模拟验证了理论考虑，并且通过将重建算法应用于初始实验数据来确认了这些模拟。
