Time‐domain principal component reconstruction (tPCR): A more efficient and stable iterative reconstruction framework for non‐Cartesian functional MRI

PURPOSE: To improve the reconstruction efficiency (i.e., computational load) and stability of iterative reconstruction for non-Cartesian fMRI when using high undersampling rates and/or in the presence of strong off-resonance effects. THEORY AND METHODS: The magnetic resonance encephalography (MREG) sequence with 3D non-Cartesian trajectory and 0.1s repetition time (TR) was applied to acquire fMRI datasets. Different from a conventional time-point-by-time-point sequential reconstruction (SR), the proposed time-domain principal component reconstruction (tPCR) performs three steps: (1) decomposing the k-t-space fMRI datasets into time-domain principal component space using singular value decomposition, (2) reconstructing each principal component with redistributed computation power according to their weights, and (3) combining the reconstructed principal components back to image-t-space. The comparison of reconstruction accuracy was performed by simulation experiments and then verified in real fMRI data. RESULTS: The simulation experiments showed that the proposed tPCR was able to significantly reduce reconstruction errors, and subsequent functional activation errors, relative to SR at identical computational cost. Alternatively, at fixed reconstruction accuracy, computation time was greatly reduced. The improved performance was particularly obvious for L1-norm nonlinear reconstructions relative to L2-norm linear reconstructions and robust to different regularization strength, undersampling rates, and off-resonance effects intensity. By examining activation maps, tPCR was also found to give similar improvements in real fMRI experiments. CONCLUSION: The proposed proof-of-concept tPCR framework could improve (1) the reconstruction efficiency of iterative reconstruction, and (2) the reconstruction stability especially for nonlinear reconstructions. As a practical consideration, the improved reconstruction speed promotes the application of highly undersampled non-Cartesian fast fMRI.