Yong Jung Kim et al 2003 Inverse Problems 19 1213 doi:10.1088/0266-5611/19/5/312
Yong Jung Kim1, Ohin Kwon2, Jin Keun Seo3 and Eung Je Woo4
Show affiliationsMagnetic resonance electrical impedance tomography (MREIT) is a new medical imaging modality providing high resolution conductivity images based on the current injection MRI technique. In contrast to electrical impedance tomography (EIT), the MREIT system utilizes the internal information of current density distribution which plays an important role in eliminating the ill-posedness of the inverse problem in EIT. It has been shown that the J-substitution algorithm in MREIT reconstructs conductivity images with higher spatial resolution. However, fundamental mathematical questions, including the uniqueness of the MREIT problem itself and the convergence of the algorithm, have not yet been answered. This paper provides a rigorous proof of the uniqueness of the MREIT problem and analyses the convergence behaviour of the J-substitution algorithm.
87.63.Pn Electrical impedance tomography (EIT)
02.60.Gf Algorithms for functional approximation
02.60.Lj Ordinary and partial differential equations; boundary value problems
92C55 Biomedical imaging and signal processing (See also 44A12, 65R10)
35A05 General existence and uniqueness theorems
35R30 Inverse problems (undetermined coefficients, etc.) for PDE
Issue 5 (October 2003)
Received 2 April 2003, in final form 7 July 2003
Published 18 September 2003
Yong Jung Kim et al 2003 Inverse Problems 19 1213
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