Material Characterization via Microwave Spectroscopy: Singular Spectrum Analysis

Determining the characteristic of materials is of paramount importance in different branches of science since it provides information about the structure, chemical composition, and molecular processes in the matter. The problem consists in exploiting the dielectric spectrum to gain information about the dipolar strengths, the dielectric losses, and the correlation times of the relaxation processes present in the system. Looking for the DRT avoids drawbacks related to non-linear inversion, since the problem is linearly formulated, and does not require information about the model order. However, it entails to invert a Fredholm integral equation of first kind, a notoriously ill-posed problem. In this paper, by exploiting the dilationally-invariance nature of the operator, an appropriate transformation is used to obtain a convolutional-type operator. Analytical upper and lower bound of the SVD of the transformed operator are then established. This allows for an analytical prediction of how many singular values to maintain in the TSVD regularization, given a certain threshold.