Adaptive multi-parameter regularization approach to construct the distribution function of relaxation times.

Autor: Žic M; 1Ruđer Bošković Institute, P.O. Box 180, 10000 Zagreb, Croatia., Pereverzyev S Jr; 2Department of Neuroradiology, Medical University of Innsbruck, Anichstrasse 35, 6020 Innsbruck, Austria.; 3Neuroimaging Research Core Facility, Medical University of Innsbruck, Anichstrasse 35, 6020 Innsbruck, Austria., Subotić V; 4Institute of Thermal Engineering, Graz University of Technology, Inffeldgasse 25b, 8010 Graz, Austria., Pereverzyev S; 5Johann Radon Institute for Computational and Applied Mathematics, Altenbergerstrasse 69, 4040 Linz, Austria.
Jazyk: angličtina
Zdroj: GEM : international journal on geomathematics [GEM] 2020; Vol. 11 (1), pp. 2. Date of Electronic Publication: 2019 Nov 30.
DOI: 10.1007/s13137-019-0138-2
Abstrakt: Determination of the distribution function of relaxation times (DFRT) is an approach that gives us more detailed insight into system processes, which are not observable by simple electrochemical impedance spectroscopy (EIS) measurements. DFRT maps EIS data into a function containing the timescale characteristics of the system under consideration. The extraction of such characteristics from noisy EIS measurements can be described by Fredholm integral equation of the first kind that is known to be ill-posed and can be treated only with regularization techniques. Moreover, since only a finite number of EIS data may actually be obtained, the above-mentioned equation appears as after application of a collocation method that needs to be combined with the regularization. In the present study, we discuss how a regularized collocation of DFRT problem can be implemented such that all appearing quantities allow symbolic computations as sums of table integrals. The proposed implementation of the regularized collocation is treated as a multi-parameter regularization. Another contribution of the present work is the adjustment of the previously proposed multiple parameter choice strategy to the context of DFRT problem. The resulting strategy is based on the aggregation of all computed regularized approximants, and can be in principle used in synergy with other methods for solving DFRT problem. We also report the results from the experiments that apply the synthetic data showing that the proposed technique successfully reproduced known exact DFRT. The data obtained by our techniques is also compared to data obtained by well-known DFRT software (DRTtools).
(© The Author(s) 2019.)
Databáze: MEDLINE
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