In the image reconstruction of the electrical capacitance tomography (ECT) system, the application of the total least squares theory transforms the ill-posed problem into a nonlinear unconstrained minimization problem, which avoids calculating the matrix inversion. But in the iterative process of the coefficient matrix, the ill-posed problem is also produced. For the effect on the final image reconstruction accuracy of this problem, combined with the principle of the ECT system, the coefficient matrix is targeted and updated in the overall least squares iteration process. The new coefficient matrix is calculated, and then, the regularization matrix is corrected according to the adaptive targeting singular value, which can reduce the ill-posed effect. In this study, the total least squares iterative method is improved by introducing the mathematical model of EIV to deal with the errors in the measured capacitance data and coefficient matrix. The effect of noise interference on the measurement capacitance data is reduced, and finally, the high-quality reconstructed images are calculated iteratively.

中文翻译：

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基于总最小二乘目标校正的ECT图像重建算法

在电容断层扫描（ECT）系统的图像重建中，总最小二乘理论的应用将不适定问题转化为非线性无约束最小化问题，从而避免计算矩阵求逆。但是在系数矩阵的迭代过程中，也会产生不适定问题。针对该问题对最终图像重建精度的影响，结合ECT系统的原理，在整体最小二乘迭代过程中，有针对性地更新系数矩阵。计算新的系数矩阵，然后根据自适应目标奇异值修正正则化矩阵，可以减少不适定效应。在这项研究中，通过引入EIV的数学模型来处理测量电容数据和系数矩阵中的误差，改进了总最小二乘迭代法。降低噪声干扰对测量电容数据的影响，最终迭代计算出高质量的重建图像。