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Iterative Reconstruction Methods for Hybrid Inverse Problems in Impedance Tomography

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Abstract

For a general formulation of hybrid inverse problems in impedance tomography the Picard and Newton iterative schemes are adapted and four iterative reconstruction algorithms are developed. The general problem formulation includes several existing hybrid imaging modalities such as current density impedance imaging, magnetic resonance electrical impedance tomography, and ultrasound modulated electrical impedance tomography, and the unified approach to the reconstruction problem encompasses several algorithms suggested in the literature. The four proposed algorithms are implemented numerically in two dimensions and the properties of the algorithms and the implementations are investigated, both theoretically and on simulated data obtained from a numerical phantom. The numerical results show similarities and differences between the proposed algorithms, and they justify that the choice of algorithm should be based on a theoretical analysis of the underlying inverse problem.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Matematiktorvet 303B, 2800 Kgs. Lyngby, Denmark

    Kristoffer Hoffmann & Kim Knudsen

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  1. Kristoffer Hoffmann
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  2. Kim Knudsen
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Correspondence to Kristoffer Hoffmann.

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This article is part of the Topical Collection on Hybrid Imaging and Image Fusion.

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Hoffmann, K., Knudsen, K. Iterative Reconstruction Methods for Hybrid Inverse Problems in Impedance Tomography. Sens Imaging 15, 96 (2014). https://doi.org/10.1007/s11220-014-0096-6

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  • DOI: https://doi.org/10.1007/s11220-014-0096-6

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