Generalized Cross-Validation as a Method of Hyperparameter Search for MTGV Regularization

Abstract: The concept of generalized cross-validation (GCV) is applied to modified total generalized variation (MTGV) regularization. Current implementations of the MTGV regularization rely on manual (or semi-manual) hyperparameter optimization, which is both time-consuming and subject to bias. The combination of MTGV-regularization and GCV allows for a straightforward hyperparameter search during regularization. This significantly increases the efficiency of the MTGV-method, because it limits the number of hyperparameters, which have to be tested and, improves the practicality of MTGV regularization as a standard technique for inversion of NMR signals. The combined method is applied to simulated and experimental NMR data and the resulting reconstructed distributions are presented. It is shown that for all data sets studied the proposed combination of MTGV and GCV minimizes the GCV score allowing an optimal hyperparameter choice.