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Analysis of linearized inverse problems in ultrasound transmission imaging

Wang, H.; Gemmeke, H.; Dongen, K. W. A. van; Hopp, T. ORCID iD icon; Hesser, J.

Abstract (englisch):

The purpose of this paper is to analyze the linearized inverse problem during the iterativesolution process of the ill-posed nonlinear inverse problem of image reconstruction for ultra-sound transmission imaging. We show that the conjugate gradient applied to normal equation(CGNE) method gives more reliable solutions for linearized systems than Tikhonov regular-ization methods. The linearized systems are more sensitive when treated by CGNE than byTikhonov regularization methods. The Tikhonov regularization is less effective at the be-ginning of the outer-loop iteration, where the nonlinearity is dominating while the conjugategradient for the linearized system stops earlier. Only when the linear approximation is goodenough to describe the whole system, Tikhonov regularization can fully play its role and giveslightly better reconstruction results as compared to CGNE in a very noisy case.

Verlagsausgabe §
DOI: 10.5445/IR/1000135826
Veröffentlicht am 02.08.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Prozessdatenverarbeitung und Elektronik (IPE)
Publikationstyp Proceedingsbeitrag
Publikationsjahr 2021
Sprache Englisch
Identifikator ISBN: 978-3-7315-1054-3
ISSN: 1000124805
KITopen-ID: 1000135826
HGF-Programm 54.12.03 (POF IV, LK 01) Science Systems
Weitere HGF-Programme 54.02.02 (POF III, LK 01) Ultraschnelle Datenauswertung
Erschienen in Proceedings of the International Workshop on Medical Ultrasound Tomography: 14.-15. Oct. 2019, Wayne State University, Detroit, Michigan, USA. Ed.: C. Böhm; T. Hopp; N. Ruiter; N. Duric
Veranstaltung 2nd International Workshop on Medical Ultrasound Tomography (MUST 2019), Detroit, MI, USA, 14.10.2019 – 15.10.2019
Verlag KIT Scientific Publishing
Seiten 155-163
Schlagwörter Gauss-Newton method, Inverse problem, Sensitivity analysis, Tikhonov regular-ization, USCT
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