In magnetic resonance electrical impedance tomography (MREIT), we try to visualize cross-sectional conductivity (or resistivity) images of a subject. We inject electrical currents into the subject through surface electrodes and measure the z component Bz of the induced internal magnetic flux density using an MRI scanner. Here, z is the direction of the main magnetic field of the MRI scanner. We formulate the conductivity image reconstruction problem in MREIT from a careful analysis of the relationship between the injection current and the induced magnetic flux density Bz. Based on the novel mathematical formulation, we propose the gradient Bz decomposition algorithm to reconstruct conductivity images. This new algorithm needs to differentiate Bz only once in contrast to the previously developed harmonic Bz algorithm where the numerical computation of ∇2Bz is required. The new algorithm, therefore, has the important advantage of much improved noise tolerance. Numerical simulations with added random noise of realistic amounts show the feasibility of the algorithm in practical applications and also its robustness against measurement noise.
Bibliographical noteFunding Information:
Manuscript received June 14, 2003; revised November 17, 2003. This work was supported by the Korea Science and Engineering Foundation under Grant R11-2002-103. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was J. Newell. Asterisk indicates corresponding author.
All Science Journal Classification (ASJC) codes
- Radiological and Ultrasound Technology
- Computer Science Applications
- Electrical and Electronic Engineering