Magnetic resonance parameter mapping using model‐guided self‐supervised deep learning

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Magnetic resonance parameter mapping using model‐guided self‐supervised deep learning

Fang Liu, Richard Kijowski, Georges El Fakhri, Li Feng



To develop a model‐guided self‐supervised deep learning MRI reconstruction framework called reference‐free latent map extraction (RELAX) for rapid quantitative MR parameter mapping.


Two physical models are incorporated for network training in RELAX, including the inherent MR imaging model and a quantitative model that is used to fit parameters in quantitative MRI. By enforcing these physical model constraints, RELAX eliminates the need for full sampled reference data sets that are required in standard supervised learning. Meanwhile, RELAX also enables direct reconstruction of corresponding MR parameter maps from undersampled k‐space. Generic sparsity constraints used in conventional iterative reconstruction, such as the total variation constraint, can be additionally included in the RELAX framework to improve reconstruction quality. The performance of RELAX was tested for accelerated T1 and T2 mapping in both simulated and actually acquired MRI data sets and was compared with supervised learning and conventional constrained reconstruction for suppressing noise and/or undersampling‐induced artifacts.


In the simulated data sets, RELAX generated good T1/T2 maps in the presence of noise and/or undersampling artifacts, comparable to artifact/noise‐free ground truth. The inclusion of a spatial total variation constraint helps improve image quality. For the in vivo T1/T2 mapping data sets, RELAX achieved superior reconstruction quality compared with conventional iterative reconstruction, and similar reconstruction performance to supervised deep learning reconstruction.


This work has demonstrated the initial feasibility of rapid quantitative MR parameter mapping based on self‐supervised deep learning. The RELAX framework may also be further extended to other quantitative MRI applications by incorporating corresponding quantitative imaging models.

Very nice work! In your opinion, might incorporating a different type of loss function further optimize your reconstruction method? For instance, this abstract from the 2021 ISMRM meeting suggests a “perpendicular loss function” for undersampled brain images:

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