Linearized solution to electrical impedance tomography based on the Schur conjugate gradient method

Zhao, Bo; Wang, Huaxiang; Chen, Xiaoyan; Shi, Xianbo; Yang, Wuqiang

doi:10.1088/0957-0233/18/11/017

Cited by 33 publications

(22 citation statements)

References 25 publications

(28 reference statements)

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“…Our approach is different from that proposed in [10], where only the projection v is solved in the Schur complement system. The level-by-level Schur complement decomposition can be schematically illustrated as in Figure 1.…”

Section: Methodsmentioning

confidence: 99%

Image reconstruction of fluorescent molecular tomography based on the tree structured Schur complement decomposition

2010

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BackgroundThe inverse problem of fluorescent molecular tomography (FMT) often involves complex large-scale matrix operations, which may lead to unacceptable computational errors and complexity. In this research, a tree structured Schur complement decomposition strategy is proposed to accelerate the reconstruction process and reduce the computational complexity. Additionally, an adaptive regularization scheme is developed to improve the ill-posedness of the inverse problem.MethodsThe global system is decomposed level by level with the Schur complement system along two paths in the tree structure. The resultant subsystems are solved in combination with the biconjugate gradient method. The mesh for the inverse problem is generated incorporating the prior information. During the reconstruction, the regularization parameters are adaptive not only to the spatial variations but also to the variations of the objective function to tackle the ill-posed nature of the inverse problem.ResultsSimulation results demonstrate that the strategy of the tree structured Schur complement decomposition obviously outperforms the previous methods, such as the conventional Conjugate-Gradient (CG) and the Schur CG methods, in both reconstruction accuracy and speed. As compared with the Tikhonov regularization method, the adaptive regularization scheme can significantly improve ill-posedness of the inverse problem.ConclusionsThe methods proposed in this paper can significantly improve the reconstructed image quality of FMT and accelerate the reconstruction process.

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Section: Methodsmentioning

confidence: 99%

Image reconstruction of fluorescent molecular tomography based on the tree structured Schur complement decomposition

2010

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“…In the reconstruction process, δU 0 (EIT measured voltage) is the input, and the output is δσ (reconstructed conductivity distribution). A fast Schur conjugate gradient (Schur CG) method is used to accelerate the computation [20]. Let δU 0 multiplied by J as initial δσ 0 .…”

Section: Image Reconstruction Based On Dictionary Learningmentioning

confidence: 99%

Recursive Least Squares Dictionary Learning Algorithm for Electrical Impedance Tomography

Li¹,

Zhang²,

Wang³

et al. 2019

PIER C

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Electrical impedance tomography (EIT) is a technique for reconstructing conductivity distribution by injecting currents at the boundary of a subject and measuring the resulting changes in voltage. Sparse reconstruction can effectively reduce the noise and artifacts of reconstructed images and maintain edge information. The effective selection of sparse dictionary is the key to accurate sparse reconstruction. The EIT image can be efficiently reconstructed with adaptive dictionary learning, which is an iterative reconstruction algorithm by alternating the process of image reconstruction and dictionary learning. However, image accuracy and convergence rate depend on the initial dictionary, which was not given full consideration in previous studies. This leads to the low accuracy of image reconstruction model. In this paper, Recursive Least Squares Dictionary Learning Algorithm (RLS-DLA) is used to learn the initial dictionary for dictionary learning of sparse EIT reconstruction. Both simulated and experimental results indicate that the improved dictionary learning method not only improves the quality of reconstruction but also accelerates the convergence.

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“…In this paper, we investigate three different multilayer electrode structures for 3D models, including the bar electrode structure of both two and three layers, and the two-layer electrode structure of spiral property. Considering the dimension of the problem becomes larger than monolayer structure, an advanced version of the conjugate gradient (CG) method [5], i.e. the Schur CG method, is used to solve the inverse problem.…”

Section: Imentioning

confidence: 99%

“…the Schur CG method, is used to solve the inverse problem for 3D EIT. As an preconditioned algorithm, Schur CG method can accelerate the convergence of iterative steps and also get more stable and accurate results [5]. …”

Section: Bmentioning

confidence: 99%

Three dimensional EIT models for human lung reconstruction based on Schur CG algorithm

Fan

Wang

Chen

et al. 2009

2009 ICME International Conference on Complex Medical Engineering

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It is urgent to define the nature and severity of persisting lung disease and to identify risk factors for developing chronic lung problems with objective, non-invasive measurements of lung oxygen requirements and lung function, suitable for use in medical treatment. At present, there is no system for continuous monitoring lung function for lung cancer sufferers to reduce the risk of syndrome after radial treatment. As electrical impedance tomography (EIT) aims to estimate the electrical properties inside the body from electrical signal measurements on the boundary, we are in the process of developing a new integrated EIT system based on portable technology to integrate three dimensional (3D) body structure from CT scan into the reconstruction algorithm. In principle, this approach, incorporated with prior information of anatomy, could provide a reduction of image artifacts in the reconstructed image associated with incorrect boundary model assumptions. In this paper, we investigate the suitable boundary model to minimize artifacts in the reconstruction for lung function. Three different 3D models with monolayer electrode are generated to represent a full range of geometric integrity and corresponding reconstructed images are compared, using conjugate gradient (CG) method. In order to improve the disadvantage of ill-posed for EIT problem, we also investigate three different multilayer electrode structures for 3D models. An advanced version of the conjugate gradient (CG) method, i.e. the Schur CG method, is used to solve the inverse problem. The result indicates that the quality of the reconstructed image depends on the structures of electrode.

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Linearized solution to electrical impedance tomography based on the Schur conjugate gradient method

Cited by 33 publications

References 25 publications

Image reconstruction of fluorescent molecular tomography based on the tree structured Schur complement decomposition

Image reconstruction of fluorescent molecular tomography based on the tree structured Schur complement decomposition

Recursive Least Squares Dictionary Learning Algorithm for Electrical Impedance Tomography

Three dimensional EIT models for human lung reconstruction based on Schur CG algorithm

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