Uncertainty in regularized measurements

Calibration of measured waveforms is the correction of known epistemic errors and the quantification of aleatoric uncertainties. As an example, we study measurements with sampling oscilloscopes. Modeled as linear and time invariant systems, the epistemic error is described by a convolution. Correcting this error is an ill-posed deconvolution problem, which requires regularization. We discuss the phenomenon how the regularization parameter depends on the data, i.e. for correlated aleatoric uncertainties, by means of Tikhonov regularization and the L-curve criterion. To evaluate the reconstructions, we use simulations that provide a fully informed perspective.