Belyaeva Irina, Bhinge Suchita, Long Qunfang, Adali Tülay
Department of CSEE, University of Maryland, Baltimore County, Baltimore, MD 21250, USA.
IEEE Access. 2021;9:145334-145362. doi: 10.1109/access.2021.3121417. Epub 2021 Oct 19.
Functional magnetic resonance imaging (fMRI) is a powerful, noninvasive tool that has significantly contributed to the understanding of the human brain. FMRI data provide a sequence of whole-brain volumes over time and hence are inherently four dimensional (4D). Missing data in fMRI experiments arise from image acquisition limits, susceptibility and motion artifacts or during confounding noise removal. Hence, significant brain regions may be excluded from the data, which can seriously undermine the quality of subsequent analyses due to the significant number of missing voxels. We take advantage of the four dimensional (4D) nature of fMRI data through a tensor representation and introduce an effective algorithm to estimate missing samples in fMRI data. The proposed Riemannian nonlinear spectral conjugate gradient (RSCG) optimization method uses tensor train (TT) decomposition, which enables compact representations and provides efficient linear algebra operations. Exploiting the Riemannian structure boosts algorithm performance significantly, as evidenced by the comparison of RSCG-TT with state-of-the-art stochastic gradient methods, which are developed in the Euclidean space. We thus provide an effective method for estimating missing brain voxels and, more importantly, clearly show that taking the full 4D structure of fMRI data into account provides important gains when compared with three-dimensional (3D) and the most commonly used two-dimensional (2D) representations of fMRI data.
功能磁共振成像（fMRI）是一种强大的非侵入性工具，对理解人类大脑做出了重大贡献。fMRI数据随时间提供一系列全脑体积数据，因此本质上是四维（4D）的。fMRI实验中的缺失数据源于图像采集限制、敏感性和运动伪影，或在去除混杂噪声期间产生。因此，重要的脑区可能会被排除在数据之外，由于大量体素缺失，这可能会严重影响后续分析的质量。我们通过张量表示利用fMRI数据的四维（4D）特性，并引入一种有效算法来估计fMRI数据中的缺失样本。所提出的黎曼非线性谱共轭梯度（RSCG）优化方法使用张量列车（TT）分解，这使得能够进行紧凑表示并提供高效的线性代数运算。利用黎曼结构显著提高了算法性能，RSCG-TT与在欧几里得空间中开发的最先进的随机梯度方法的比较证明了这一点。因此，我们提供了一种估计缺失脑体素的有效方法，更重要的是，清楚地表明，与fMRI数据的三维（3D）和最常用的二维（2D）表示相比，考虑fMRI数据的完整4D结构会带来重要的收获。
