Complex-valued shift-invariant canonical polyadic decomposition (CPD) under a spatial phase sparsity constraint (pcsCPD) showed satisfying separation performance of decomposing three-way multi-subject fMRI data into shared spatial maps (SMs), shared time courses (TCs), time delays and subject-specific intensities. However, pcsCPD exploits alternating least squares (ALS) updating rule, which converges slowly and requires data strictly conforming to the shift-invariant CPD model. As the lower rank approximation can relax the CPD model, we propose...