  Sub-sampling is applied to simulated $T_1$-$D$ NMR signals and its influence
on inversion performance is evaluated. For this different levels of
sub-sampling were employed ranging from the fully sampled signal down to only
less than two percent of the original data points. This was combined with
multiple sample schemes including fully random sampling, truncation and a
combination of both. To compare the performance of different inversion
algorithms, the so-generated sub-sampled signals were inverted using Tikhonov
regularization, modified total generalized variation (MTGV) regularization,
deep learning and a combination of deep learning and Tikhonov regularization.
Further, the influence of the chosen cost function on the relative inversion
performance was investigated. Overall, it could be shown that for a vast
majority of instances, deep learning clearly outperforms regularization based
inversion methods, if the signal is fully or close to fully sampled. However,
in the case of significantly sub-sampled signals regularization yields better
inversion performance than its deep learning counterpart with MTGV clearly
prevailing over Tikhonov. Additionally, fully random sampling could be
identified as the best overall sampling scheme independent of the inversion
method. Finally, it could also be shown that the choice of cost function does
vastly influence the relative rankings of the tested inversion algorithms
highlighting the importance of choosing the cost function accordingly to
experimental intentions.
