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

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          Abstract

          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).

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          Most cited references24

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          Dielectric Relaxation in Glycerol, Propylene Glycol, andn‐Propanol

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            Influence of the Discretization Methods on the Distribution of Relaxation Times Deconvolution: Implementing Radial Basis Functions with DRTtools

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              A reliable and fast method for the solution of Fredhol integral equations of the first kind based on Tikhonov regularization

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                Author and article information

                Contributors
                mzic@irb.hr
                sergiy.pereverzyev@i-med.ac.at
                Journal
                GEM
                GEM
                Gem
                Springer Berlin Heidelberg (Berlin/Heidelberg )
                1869-2672
                1869-2680
                30 November 2019
                30 November 2019
                2020
                : 11
                : 1
                : 2
                Affiliations
                [1 ]ISNI 0000 0004 0635 7705, GRID grid.4905.8, Ruđer Bošković Institute, ; P.O. Box 180, 10000 Zagreb, Croatia
                [2 ]ISNI 0000 0000 8853 2677, GRID grid.5361.1, Department of Neuroradiology, , Medical University of Innsbruck, ; Anichstrasse 35, 6020 Innsbruck, Austria
                [3 ]ISNI 0000 0000 8853 2677, GRID grid.5361.1, Neuroimaging Research Core Facility, , Medical University of Innsbruck, ; Anichstrasse 35, 6020 Innsbruck, Austria
                [4 ]ISNI 0000 0001 2294 748X, GRID grid.410413.3, Institute of Thermal Engineering, , Graz University of Technology, ; Inffeldgasse 25b, 8010 Graz, Austria
                [5 ]ISNI 0000 0001 2110 0463, GRID grid.475782.b, Johann Radon Institute for Computational and Applied Mathematics, ; Altenbergerstrasse 69, 4040 Linz, Austria
                Author information
                http://orcid.org/0000-0003-1174-6281
                Article
                138
                10.1007/s13137-019-0138-2
                6885029
                98098c62-09a0-4f9f-9ee6-7ec7df85309b
                © The Author(s) 2019

                Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

                History
                : 25 September 2019
                : 8 November 2019
                Funding
                Funded by: FundRef http://dx.doi.org/10.13039/501100001822, Österreichischen Akademie der Wissenschaften;
                Award ID: JESH
                Award Recipient :
                Funded by: FundRef http://dx.doi.org/10.13039/501100002428, Austrian Science Fund;
                Award ID: P 29514-N32
                Award Recipient :
                Categories
                Original Paper
                Custom metadata
                © Springer-Verlag GmbH Germany, part of Springer Nature 2020

                eis,dfrt,ill-posed problem,regularization,45f05,65r30
                eis, dfrt, ill-posed problem, regularization, 45f05, 65r30

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