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 reconstr...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.展开更多
文摘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.
文摘针对LSQR(least square QR-factorization)算法在求解电阻抗层析成像(electrical impedance tomography,EIT)逆问题时,由于矩阵维数高、计算量大而导致重建速度较慢的问题,提出基于小波多分辨分析的LSQR算法(wavelet multi-resolution based least square QR-factorization,WALSQR)。该方法将EIT的图像重建过程投影到低维的尺度空间进行,通过提取有效信息减少数据计算量,明显提高了图像重建速度。同时由于去除了噪声和冗余信息,保证了成像质量。本文将SALSQR方法分别应用于二维、三维EIT成像实验,证明其有效性,并为三维动态EIT图像重建算法的研究奠定了基础。
