In fMRI, capturing brain activation during a task is dependent on how quickly k-space arrays are obtained. Acquiring full k-space arrays, which are reconstructed into images using the inverse Fourier transform (IFT), that make up volume images can take a considerable amount of scan time. Under-sampling k-space reduces the acquisition time, but results in aliased, or "folded," images. GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA) is a parallel imaging technique that yields full images from subsampled arrays of k-space. GRAPPA uses localized interpolation weights, which are estimated per-scan and fixed over time, to fill in the missing spatial frequencies of the subsampled k-space. Hence, we propose a Bayesian approach to GRAPPA (BGRAPPA) where space measurement uncertainty are assessed from the a priori calibration k-space arrays. The prior information is utilized to estimate the missing spatial frequency values from the posterior distribution and reconstruct into full field-of-view images. Our BGRAPPA technique successfully reconstructed both a simulated and experimental single slice image with less artifacts, reduced noise leading to an increased signal-to-noise ratio (SNR), and stronger power of task detection.

翻译：在功能磁共振成像中，捕获任务期间的大脑激活取决于k空间阵列的获取速度。获取构成体素图像所需的全k空间阵列（通过逆傅里叶变换重建为图像）需要相当长的扫描时间。对k空间进行欠采样可缩短采集时间，但会导致图像出现混叠或“折叠”伪影。广义自动校准部分并行采集是一种并行成像技术，可从欠采样的k空间阵列重建完整图像。该方法使用基于每次扫描估计并随时间固定的局部插值权重来填补欠采样k空间缺失的空间频率。为此，我们提出一种贝叶斯GRAPPA方法，其中空间测量不确定性通过先验校准k空间阵列进行评估。该方法利用先验信息从后验分布估计缺失的空间频率值，并重建为全视野图像。我们的BGRAPPA技术成功重建了模拟和实验单切片图像，在减少伪影、降低噪声（从而提高信噪比）以及增强任务检测效能方面均表现出显著优势。