Comparison of parameter choice methods for the analytical inversion of ARXPS data

Highlights: • Nine methods for choosing the regularization parameter were evaluated. • With 0th order regularization and an accurate noise estimate, the Discrepancy Principle did best. • Generalized Maximum Likelihood was the best method not requiring additional information. - Abstract: Using 0th order Tikhonov regularization, we recovered concentration-depth profiles from simulated noisy ARXPS data using nine candidate methods for the selection of the regularization parameter α. Calculations were performed on 1000 noisy data sets at 10 levels of noise ranging from 0.1% to 9%. By comparison with the input profile, the parameter choice methods were rated in terms of the accuracy and reproducibility of the extracted profiles. We discuss the results obtained in the context of the inputs and constraints required by each method