Evaluation of Image Restoration Techniques for Dielectric Resonator Mapping of Materials

Complex permittivity maps obtained by Split Post Dielectric Resonator (SPDR) material measurement technique yield limited resolution due to the weighted averaging over the region interacting with DR field. The motivation of this work is to improve spatial resolution for examining inhomogeneous samples and smaller homogeneous samples that do not meet the resonator’s minimum size requirements. To achieve this, attempts were made to reverse the averaging. The electric field pattern is known from finite-difference time-domain (FDTD) simulation, and on this basis, an inverse problem is formulated. Due to the presence of additive noise in the measurements, matrix regularization techniques are investigated, such as Truncated Singular Value Decomposition (TSVD) and Tikhonov regularization, alongside established image restoration methods for noise-prone deblurring, such as Richardson-Lucy deconvolution, Wiener filter and Plug-and-Play Alternating Direction method of multiplier (ADMM).