Sparse representation of complex-valued fMRI data based on spatiotemporal concatenation of real and imaginary parts

Background Spatial sparsity has been found to be in line with the intrinsic characteristic of brain activation. However, identifying a sparse representation of complex-valued fMRI data is challenging due to high noise within the phase data. New methods We propose to reduce the noise by combining real and imaginary parts of complex-valued fMRI data along spatial and temporal dimensions to form a real-valued spatiotemporal concatenation model. This model not only enables flexible usage of existing real-valued sparse representation algorithms but also allows for the reconstruction of complex-valued spatial and temporal components from their real and imaginary estimates. We propose to select components from both real and imaginary estimates to reconstruct the complex-valued component, using phase denoising to recover weak brain activity from high-amplitude noise. Results The K-SVD algorithm was used to obtain a sparse representation within the spatiotemporal concatenation model. The results from simulated and experimental complex-valued fMRI datasets validated the efficacy of our method. Comparison with existing methods Compared to a magnitude-only approach, the proposed method detected additional voxels manifest within several specific regions expected to be involved but likely missing from the magnitude-only data, e.g., in the anterior cingulate cortex region. Simulation results showed that the additional voxels were accurate and unique information from the phase data. Compared to a complex-valued dictionary learning algorithm, our method exhibited lower noise for both magnitude and phase maps. Conclusions The proposed method is robust to noise and effective for identifying a sparse representation of the natively complex-valued fMRI data.