Reconstruction of highly under-sampled FMRI data using low-rank constraints can suffer from loss of fidelity at high acceleration factors, or when signals are relatively weak. We introduce a method for improving reconstruction fidelity using external constraints, i.e., informative signals that are not data-derived. We show that this improves FMRI reconstruction quality in a number of conditions, including detecting subtle latency shifts between brain regions, and improving resting state network characterization using simultaneously acquired EEG information. We further show that this approach works with noisy or approximate constraints, and the derived benefit is commensurate with the information content they provide.
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