Taking the 4D Nature of fMRI Data Into Account Promises Significant Gains in Data Completion

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.