Beyond Ridge Regression: Enhancing Distribution of Relaxation Times Deconvolution

The distribution of relaxation times (DRT) has emerged as a promising method for analyzing electrochemical impedance spectroscopy (EIS) data. The standard approach for reconstructing the DRT from measured impedances consists of regularized regression, which usually leverages the Euclidean norm. In this work, we show for the first time that the 1-norm is often more accurate than ridge regression and the infinity-norm. We also demonstrate that the 1-norm is more robust against discontinuities in the DRT and outliers in the impedance data. Overall, this work is expected to enhance regularized regression of non-parametric methods when analyzing EIS spectra.