x is the estimate of x, Z exp is the experimental impedance data vector, and P(x) is the penalty function weighted by the scalar λ. The penalty term is essential for enforcing smoothness and mitigating the formation of spurious peaks, which can hinder the identification of genuine electrochemical features , as seen for instance in the case of lithium-sulfur batteries . Common penalty functions include L2-norm (ridge regression, RR), L1-norm (lasso regression), and elastic net regularization .