Low-Rank Tucker Decomposition of Multi-Subject Complex-Valued fMRI Data

Tucker decomposition has shown advantages in simultaneously extracting group shared and individual features for studying brain function from multi-subject fMRI data. However, Tucker decomposition of complex-valued fMRI data is challenging, since the data are highly noisy, and imposing sparsity constraints on spatial maps, previously used for denoising magnitude-only fMRI data, may remove signal voxels with low amplitudes. Here we propose a new complex-valued low-rank Tucker decomposition (clrTKD) method to extract principal group and individual components from multi-subject fMRI data, and to denoise spatial components based on the small phase change property at a post-processing stage. We derive the update rules using the alternating direction method of multipliers. Simulated and experimental complex-valued fMRI data are used to evaluate the proposed clrTKD method. Results show that the proposed method can extract more contiguous and vital brain activations such as the anterior cingulate cortex region, compared to Tucker decomposition for magnitude-only fMRI data.