Detecting low-amplitude biomarker activations via decomposition of complex-valued fMRI data with collaborative phase and magnitude sparsity

Sparse decomposition of complex-valued functional magnetic resonance imaging (fMRI) data is promising in finding qualified biomarkers for brain disorders such as schizophrenia, by simultaneously using intrinsic spatial sparsity and full functional information of the brain. However, previous methods may miss disease-related low-amplitude activations, since it is challenging to determine if a low-amplitude voxel is signal or noise during the iterative update process based solely on magnitude or phase sparsity. To this end, we propose a novel sparse decomposition model with collaborative phase and magnitude sparsity constraints at the voxel level. Specifically, we impose a sparsity constraint on the product of the magnitude and phase of a voxel above a pre-defined phase threshold. The low-amplitude activations with larger phase changes can survive the update process, despite temporarily violating the small-phase-change characteristic of signal voxels. Moreover, we eliminate phase ambiguity during iterations by proving no additional phase change is introduced by the update rules and by initializing the dictionary matrix atoms using the observed time series with fixed phase angles. We evaluate the proposed method using complex-valued simulated data and experimental resting-state fMRI data from schizophrenia patients and healthy controls. Compared with three state-of-the-art algorithms, the proposed method retains more low-amplitude activations in biomarker regions such as the anterior cingulate cortex and yields sensitive phase maps to disease-related spatial changes. This provides a new tool to estimate an informative fMRI biomarker of mental disorders.