Electrical Impedance Tomography Image Reconstruction Using Iterative Lavrentiev and L-Curve-Based Regularization Algorithm

Wen-Qin Wang ,Jingye Cai,Lian Xiang Yang

doi:10.4236/jemaa.2010.21007

Wen-Qin Wang , Jingye Cai + Show 1 more

Open Access

https://doi.org/10.4236/jemaa.2010.21007

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Abstract

Electrical impedance tomography (EIT) is a technique for determining the electrical conductivity and permittivity distribution inside a medium from measurements made on its surface. The impedance distribution reconstruction in EIT is a nonlinear inverse problem that requires the use of a regularization method. The generalized Tikhonov regularization methods are often used in solving inverse problems. However, for EIT image reconstruction, the generalized Tikhonov regularization methods may lose the boundary information due to its smoothing operation. In this paper, we propose an iterative Lavrentiev regularization and L-curve-based algorithm to reconstruct EIT images. The regularization parameter should be carefully chosen, but it is often heuristically selected in the conventional regularization-based reconstruction algorithms. So, an L-curve-based optimization algorithm is used for selecting the Lavrentiev regularization parameter. Numerical analysis and simulation results are performed to illustrate EIT image reconstruction. It is shown that choosing the appropriate regularization parameter plays an important role in reconstructing EIT images.

Highlights

Electrical impedance tomography (EIT) is an imaging technique which determines the electrical conductivity and permittivity distribution within a medium using electrical measurement from a series of electrodes on its surface [1,2,3]
Electrical impedance tomography (EIT) is a technique for determining the electrical conductivity and permittivity distribution inside a medium from measurements made on its surface
We propose an iterative Lavrentiev regularization and L-curve-based algorithm to reconstruct EIT images

Summary

Introduction

Electrical impedance tomography (EIT) is an imaging technique which determines the electrical conductivity and permittivity distribution within a medium using electrical measurement from a series of electrodes on its surface [1,2,3]. 46 Electrical Impedance Tomography Image Reconstruction Using Iterative Lavrentiev and L-Curve-Based Regularization Algorithm construction algorithm is the equipotential back-projection [15]. We propose an iterative Lavrentiev regularization-based algorithm to reconstruct EIT images using knowledge of the noise variance of the measurements and the covariance of the conductivity distribution. Electrical Impedance Tomography Image Reconstruction Using Iterative Lavrentiev and L-Curve-Based Regularization 47 Algorithm small measurement perturbations L ≈ L + ε may produce large variations in X such that the 3-norm residual error. The matrix AT A is 2 poor conditioned because EIT makes current injection and measurement on the medium surface including higher current densities near the surface where conductivity contrasts will result in more signal than for contrasts in the center This problem can be resolved by regularization [22]. An optimum regularization parameter α can be optimization determined

Simulation Examples

Conclusions