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Iterative Reconstruction Methods for Hybrid Inverse Problems in Impedance Tomography

机译：阻抗层析成像中混合反问题的迭代重建方法

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摘要

For a general formulation of hybrid inverse problems in impedancerntomography the Picard and Newton iterative schemes are adapted and four iterativernreconstruction algorithms are developed. The general problem formulation includesrnseveral existing hybrid imaging modalities such as current density impedancernimaging, magnetic resonance electrical impedance tomography, and ultrasoundrnmodulated electrical impedance tomography, and the unified approach to thernreconstruction problem encompasses several algorithms suggested in the literature.rnThe four proposed algorithms are implemented numerically in two dimensions andrnthe properties of the algorithms and the implementations are investigated, bothrntheoretically and on simulated data obtained from a numerical phantom. Thernnumerical results show similarities and differences between the proposed algorithms,rnand they justify that the choice of algorithm should be based on a theoreticalrnanalysis of the underlying inverse problem.
机译：对于阻抗层析成像中混合逆问题的一般表述，采用了Picard和Newton迭代方案，并开发了四种迭代重建算法。一般的问题表述包括几种现有的混合成像方式，例如电流密度阻抗成像，磁共振电阻抗层析成像和超声调制电阻抗层析成像，而重构问题的统一方法包含了文献中提出的几种算法。四种提出的算法是在数字方式下实现的。从理论上和从数字体模获得的模拟数据上，研究了算法和实现的二维和性质。数值结果表明了所提算法之间的异同，并证明了算法的选择应基于对底层反问题的理论分析。

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