Summary
Unlike deterministic inversion methods, statistical approaches are capable of taking into account inherent measurement and model uncertainties into the inverse problem solution in a very simple and natural way. Statistical inversion theory reformulates inverse problems as problems of Bayesian statistical inference. In this framework, the solution to an inverse problem is the probability distribution of the quantity of interest, i.e. the unknown parameters. This paper discusses the robust solution of inverse problems from the perspective of statistical inversion theory and reviews two different approaches for stationary and non-stationary electrical capacitance tomography.
Zusammenfassung
Im Gegensatz zu deterministischen Verfahren erlauben statistische Ansätze die Berücksichtigung von Messunsicherheiten und Systemvariabilitäten in einfacher und sinnvoller Weise. Im Zuge der statistischen Inversion werden inverse Probleme als Bayes'sche Inferenzprobleme formuliert. Die Lösung des inversen Problems entspricht einer Wahrscheinlichkeitsverteilung der zu ermittelnden Systemgrössen, d. h. der unbekannten Parameter. In diesem Beitrag wird die robuste Lösung von inversen Problemen aus dem Blickwinkel der statistischen Inversion diskutiert. Darüber hinaus werden zwei verschiedene Ansätze für statische und dynamische Kapazitätstomografle untersucht.
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Watzenig, D. Bayesian inference for inverse problems – statistical inversion. Elektrotech. Inftech. 124, 240–247 (2007). https://doi.org/10.1007/s00502-007-0449-0
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DOI: https://doi.org/10.1007/s00502-007-0449-0