  Objective. Imaging dynamic object with high temporal resolution is
challenging in magnetic resonance imaging (MRI). Partial separable (PS) model
was proposed to improve the imaging quality by reducing the degrees of freedom
of the inverse problem. However, PS model still suffers from long acquisition
time and even longer reconstruction time. The main objective of this study is
to accelerate the PS model, shorten the time required for acquisition and
reconstruction, and maintain good image quality simultaneously. Approach. We
proposed to fully exploit the dimension reduction property of the PS model,
which means implementing the optimization algorithm in subspace. We optimized
the data consistency term, and used a Tikhonov regularization term based on the
Frobenius norm of temporal difference. The proposed dimension-reduced
optimization technique was validated in free-running cardiac MRI. We have
performed both retrospective experiments on public dataset and prospective
experiments on in-vivo data. The proposed method was compared with four
competing algorithms based on PS model, and two non-PS model methods. Main
results. The proposed method has robust performance against shortened
acquisition time or suboptimal hyper-parameter settings, and achieves superior
image quality over all other competing algorithms. The proposed method is
20-fold faster than the widely accepted PS+Sparse method, enabling image
reconstruction to be finished in just a few seconds. Significance. Accelerated
PS model has the potential to save much time for clinical dynamic MRI
examination, and is promising for real-time MRI applications.
