A common approach in DRT analysis begins with selecting the prior function P(x) = x ⊤ L ⊤ Lx, where the choice of matrix L fundamentally shapes the probability distribution properties. Three key cases arise. First, when L = I (zeroth-order derivative), the term L ⊤ L = I ⊤ I = I is positive definite, yielding a proper probability distribution function. Second and third, when L represents first-order (L 1 ) or second-order (L 2 ) differentiation matrices, L ⊤ L becomes positive semi-definite. All three formulations allow a solution of (2) , which is obtained by maximizing the posterior probability p(x|Zexp) with respect to x.