First, we will consider the regularization functional Φ reg = α 2 x T x (Eq. 18) in the same sense as the maximal likelihood estimator (see Eqs. 14 and 15). In this case, α is related to uncertainty of individual component of vector x for deviation from zero (δ ) as α = δ -2 . This uncertainty will consist of two components: 1) systematic deviation of each component x k from zero (δ sys ) and 2) experimental measurement uncertainty for each x k value (δ exp ). The optimal, in this sense, regularization parameter α opt will be given with equation