On the Error Estimate of the Harmonic Bz Algorithm inMREIT from Noisy Magnetic Flux Field?

Citation:

Qun CHEN,Jijun LIU.On the Error Estimate of the Harmonic Bz Algorithm inMREIT from Noisy Magnetic Flux Field?[J].Chinese Annals of Mathematics B,2014,35(3):319~336
Page view: 2498        Net amount: 2216

Authors:

Qun CHEN; Jijun LIU;

Foundation:

National Natural Science Foundation of China (No. 91330109) and theResearch Found for the Doctoral Program of Higher Education of China (No. 20110092110018).
Abstract: Magnetic resonance electrical impedance tomography (MREIT, for short) is a new medical imaging technique developed recently to visualize the cross-section conductivity of biologic tissues. A new MREIT image reconstruction method called harmonic Bz algorithm was proposed in 2002 with the measurement of Bz that is a single component of an induced magnetic flux density subject to an injection current. The key idea is to solve a nonlinear integral equation by some iteration process. This paper deals with the convergence analysis as well as the error estimate for noisy input data Bz, which is the practical situation for MREIT. By analyzing the iteration process containing the Laplacian operation on the input magnetic field rigorously, the authors give the error estimate for the iterative solution in terms of the noisy level δ and the regularizing scheme for determining ΔBz approximately from the noisy input data. The regularizing scheme for computing the Laplacian from noisy input data is proposed with error analysis. Our results provide both the theoretical basis and the implementable scheme for evaluating the reconstruction accuracy using harmonic Bz algorithm with practical measurement data containing noise.

Keywords:

MREIT, Image reconstruction, Iteration, Error estimate

Classification:

35R30, 35J05, 65N12
Download PDF Full-Text

Organizer:The Ministry of Education of China Sponsor:Fudan University Address:220 Handan Road, Fudan University, Shanghai, China E-mail:edcam@fudan.edu.cn
Designed by Beijing E-Tiller Co.,Ltd.