Nonlinear image reconstruction for electrical capacitance tomography using experimental data
Nonlinear image reconstruction for electrical capacitance tomography using experimental data
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DOI：
10.1088/0957-0233/16/10/014
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发表时间：
2005-10-01
影响因子：
2.4
通讯作者：
Lionheart, WRB
中科院分区：
文献类型：
--
作者：
Soleimani, M;Lionheart, WRB
电容断层扫描 (ECT) 试图通过测量放置在物体周围的电极组之间的电容来对物体的介电常数分布进行成像。 ECT 中的图像重建是一个非线性且不适定的反问题。尽管基于线性近似的重建技术速度很快，但它们并不能满足所有情况。在本文中，我们研究了ECT逆介电常数问题的非线性。正则化高斯-牛顿方案已被实现用于非线性图像重建。使用有限元方法在每次迭代中求解前向问题，并使用有效的伴随域方法重新计算雅可比矩阵。需要正则化技术来克服不适定性：在平滑变化的情况下使用平滑广义吉洪诺夫正则化，在介电常数急剧转变时使用全变分（TV）正则化。实验ECT数据的重建结果证明了TV正则化对于跳跃变化的优势，并表明使用非线性重建方法可以提高图像质量。
Electrical capacitance tomography (ECT) attempts to image the permittivity distribution of an object by measuring the electrical capacitances between sets of electrodes placed around its periphery. Image reconstruction in ECT is a nonlinear and ill-posed inverse problem. Although reconstruction techniques based on a linear approximation are fast, they are not adequate for all cases. In this paper, we study the nonlinearity of the inverse permittivity problem of ECT. A regularized Gauss-Newton scheme has been implemented for nonlinear image reconstruction. The forward problem has been solved at each iteration using the finite element method and the Jacobian matrix is recalculated using an efficient adjoint field method. Regularization techniques are required to overcome the ill-posedness: smooth generalized Tikhonov regularization for the smoothly varying case, and total variation (TV) regularization when there is a sharp transition of the permittivity have been used. The reconstruction results for experimental ECT data demonstrate the advantage of TV regularization for jump changes, and show improvement of the image quality by using nonlinear reconstruction methods.