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| On the Error Estimate of the Harmonic Bz Algorithm inMREIT from Noisy Magnetic Flux Field? |
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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 |
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Net amount： 2404 |
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). |
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| 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 |
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