Scholand Nick, Schaten Philip, Graf Christina, Mackner Daniel, Holme H Christian M, Blumenthal Moritz, Mao Andrew, Assländer Jakob, Uecker Martin
ArXiv. 2024 Jul 12:arXiv:2401.02892v4.
To develop a generic radial sampling scheme that combines the advantages of golden ratio sampling with simplicity of equidistant angular patterns. The irrational angle between consecutive spokes in golden ratio based sampling schemes enables a flexible retrospective choice of temporal resolution, while preserving good coverage of k-space for each individual bin. Nevertheless, irrational increments prohibit precomputation of the point-spread function (PSF), can lead to numerical problems, and require more complex processing steps. To avoid these problems, a new sampling scheme based on a rational approximation of golden angles (RAGA) is developed.
The theoretical properties of RAGA sampling are mathematically derived. Sidelobe-to-peak ratios (SPR) are numerically computed and compared to the corresponding golden ratio sampling schemes. The sampling scheme is implemented in the BART toolbox and in a radial gradient-echo sequence. Feasibility is shown for quantitative imaging in a phantom and a cardiac scan of a healthy volunteer.
RAGA sampling can accurately approximate golden ratio sampling and has almost identical PSF and SPR. In contrast to golden ratio sampling, each frame can be reconstructed with the same equidistant trajectory using different sampling masks, and the angle of each acquired spoke can be encoded as a small index, which simplifies processing of the acquired data.
RAGA sampling provides the advantages of golden ratio sampling while simplifying data processing, rendering it a valuable tool for dynamic and quantitative MRI.
开发一种通用的径向采样方案，该方案结合了黄金比例采样的优点和等距角模式的简单性。基于黄金比例的采样方案中相邻辐条之间的无理角度允许灵活地回顾性选择时间分辨率，同时为每个单独的 bins 保持对 k 空间的良好覆盖。然而，无理增量禁止预计算点扩散函数（PSF），可能导致数值问题，并需要更复杂的处理步骤。为避免这些问题，开发了一种基于黄金角度有理近似（RAGA）的新采样方案。
从数学上推导了 RAGA 采样的理论特性。通过数值计算旁瓣与峰值比（SPR），并与相应的黄金比例采样方案进行比较。该采样方案在 BART 工具箱和径向梯度回波序列中实现。在体模和健康志愿者的心脏扫描中展示了定量成像的可行性。
RAGA 采样可以准确地近似黄金比例采样，并且具有几乎相同的 PSF 和 SPR。与黄金比例采样不同，每个帧可以使用不同的采样掩码以相同的等距轨迹进行重建，并且每个采集的辐条角度可以编码为一个小索引，这简化了采集数据的处理。
RAGA 采样在简化数据处理的同时提供了黄金比例采样的优点，使其成为动态和定量 MRI 的有价值工具。
