Purpose To implement physics‐based regularization as a stopping condition in tuning an untrained deep neural network for reconstructing MR images from accelerated data. Methods The ConvDecoder (CD) neural network was trained with a physics‐based regularization term incorporating the spoiled gradient echo equation that describes variable‐flip angle data. Fully‐sampled variable‐flip angle k‐space data were retrospectively accelerated by factors of R = {8, 12, 18, 36} and reconstructed with CD, CD with the proposed regularization (CD + r), locally low‐rank (LR) reconstruction, and compressed sensing with L1‐wavelet regularization (L1). Final images from CD + r training were evaluated at the “argmin” of the regularization loss; whereas the CD, LR, and L1 reconstructions were chosen optimally based on ground truth data. The performance measures used were the normalized RMS error, the concordance correlation coefficient, and the structural similarity index. Results The CD + r reconstructions, chosen using the stopping condition, yielded structural similarity indexs that were similar to the CD (p = 0.47) and LR structural similarity indexs (p = 0.95) across R and that were significantly higher than the L1 structural similarity indexs (p = 0.04). The concordance correlation coefficient values for the CD + r T1 maps across all R and subjects were greater than those corresponding to the L1 (p = 0.15) and LR (p = 0.13) T1 maps, respectively. For R ≥ 12 (≤4.2 min scan time), L1 and LR T1 maps exhibit a loss of spatially refined details compared to CD + r. Conclusion The use of an untrained neural network together with a physics‐based regularization loss shows promise as a measure for determining the optimal stopping point in training without relying on fully‐sampled ground truth data.

Acquiring high-resolution MRI data for tissue parameter mapping for quantitative imaging requires additional scan time. As a proof-of-principle, we evaluated the ability of the ConvDecoder architecture regularized with a physical model to reconstruct accelerated variable-flip angle MRI data of the brain for T1-mapping. The performance of our method was compared to non-regularized ConvDecoder, low rank reconstruction, and compressed sensing. Our results suggest that ConvDecoder with physics-based regularization may provide a stopping condition for training that is not dependent on the ground truth data while improving parameter mapping at higher accelerations.

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