A nonlinear operator for radial MOLLI is constructed in BART, allowing accurate derivative calculation via automatic differentiation. The constructed nonlinear MOLLI operator is further integrated into a model-based reconstruction framework where myocardial $$$T_{1}$$$ maps are reconstructed directly from undersampled k-space data. Results on an experimental phantom and one healthy subject have demonstrated that high resolution ($$$1.0 \times 1.0 \times 6$$$ mm$$$^{3}$$$) myocardial $$$T_{1}$$$ maps can be achieved within 4 heartbeats with good accuracy and precision using the proposed method.
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