We commenced our analysis by examining synthetic data generated using the single ZARC model with a noise level of σ exp n = 0.5 Ω (circuit parameter values are detailed in Table ). Figure (a) presents the normalized DRT residuals, ε γ , for each regularization method across a range of regularization parameter, λ, from 10 -6 to 10 2 . Notably, the entropy method yielded the lowest ε γ value, achieving an error magnitude at least one order of magnitude smaller than those observed with regularization using each differentiation matrix. This superior performance stems from the entropy method's ability to accurately recover the DRT without introducing spurious ridges at the main peak's edges, as visually confirmed in Figure (c) and (e), as well as Figure (a) and (c). In terms of impedance recovery, all regularization methods performed comparably well, as indicated by the normalized impedance residuals in Figure (a). To further substantiate these initial findings, we extended our analysis to 100 synthetic spectra. The additional results corroborated the initial observations, demonstrating that the entropy method consistently produced the lowest DRT residuals, as shown in the violin plots in Figure (a) and the mean values summarized in Table , which were 50% smaller than the values obtained with the other regularization methods.