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Journal of Applied Mathematics
Volume 2012, Article ID 973781, 15 pages
Research Article

Newton Method to Recover the Phase Accumulated during MRI Data Acquisition

Department of Mathematics, Konkuk University, Seoul 143-701, Republic of Korea

Received 29 October 2012; Accepted 28 November 2012

Academic Editor: Changbum Chun

Copyright © 2012 Oh-In Kwon and Chunjae Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For an internal conductivity image, magnetic resonance electrical impedance tomography (MREIT) injects an electric current into an object and measures the induced magnetic flux density, which appears in the phase part of the acquired MR image data. To maximize signal intensity, the injected current nonlinear encoding (ICNE) method extends the duration of the current injection until the end of the MR data reading. It disturbs the usual linear encoding of the MR k-space data used in the inverse Fourier transform. In this study, we estimate the magnetic flux density, which is recoverable from nonlinearly encoded MR k-space data by applying a Newton method.