  Purpose: To develop a neural network architecture for improved
calibrationless reconstruction of radial data when no ground truth is available
for training. Methods: NLINV-Net is a model-based neural network architecture
that directly estimates images and coil sensitivities from (radial) k-space
data via non-linear inversion (NLINV). Combined with a training strategy using
self-supervision via data undersampling (SSDU), it can be used for imaging
problems where no ground truth reconstructions are available. We validated the
method for (1) real-time cardiac imaging and (2) single-shot subspace-based
quantitative T1 mapping. Furthermore, region-optimized virtual (ROVir) coils
were used to suppress artifacts stemming from outside the FoV and to focus the
k-space based SSDU loss on the region of interest. NLINV-Net based
reconstructions were compared with conventional NLINV and PI-CS (parallel
imaging + compressed sensing) reconstruction and the effect of the
region-optimized virtual coils and the type of training loss was evaluated
qualitatively. Results: NLINV-Net based reconstructions contain significantly
less noise than the NLINV-based counterpart. ROVir coils effectively suppress
streakings which are not suppressed by the neural networks while the
ROVir-based focussed loss leads to visually sharper time series for the
movement of the myocardial wall in cardiac real-time imaging. For quantitative
imaging, T1-maps reconstructed using NLINV-Net show similar quality as PI-CS
reconstructions, but NLINV-Net does not require slice-specific tuning of the
regularization parameter. Conclusion: NLINV-Net is a versatile tool for
calibrationless imaging which can be used in challenging imaging scenarios
where a ground truth is not available.
