Abstract Magnetic resonance electrical impedance tomography （MREIT, for short） is a new medical imaging technique developed recently to visualize the cross-section conduc- tivity of biologic tissues. A new MREIT ima...Abstract Magnetic resonance electrical impedance tomography （MREIT, for short） is a new medical imaging technique developed recently to visualize the cross-section conduc- tivity 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 6 and the regularizing scheme for determining ABz 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.展开更多
基金supported by the National Natural Science Foundation of China(No.91330109)the Research Found for the Doctoral Program of Higher Education of China(No.20110092110018)
文摘Abstract Magnetic resonance electrical impedance tomography （MREIT, for short） is a new medical imaging technique developed recently to visualize the cross-section conduc- tivity 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 6 and the regularizing scheme for determining ABz 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.
