Fig. 8
Efficiency of standard magnitude-based DNN inverse signal model learning versus epochs, corroborated by representative relaxation time maps of single-epoch in vivo whole-brain inference. The CoD during SVNN (a) and PINN (b) training is calculated for each epoch with respect to the final-epoch model and plotted versus epochs for in vivo \(T_1\) (red) and \(T_2\) (blue) predictions in whole-brain WM, GM, and WM+GM tissue masks of an unseen test subject. Additionally, the validation loss for both DNN frameworks is shown in black on a logarithmic scale. The employed DNNs were trained on the in silico uniform noise-free data distribution. Note that the final validation loss of the SVNN framework is on the order of one magnitude lower than the one of the PINN framework due to the different definitions of the loss functions and embedding of physical constraints for the PINN. Corresponding representative axial, coronal, and sagittal slices of in vivo whole-brain \(T_1\) and \(T_2\) single-echo versus final-epoch predictions of an unseen test subject are shown for SVNN (c) and PINN (d). See Supplementary Figure S8 for the corresponding results with complex-based DNNs.
