基于加权SVD截断共轭梯度的ECT图像重建算法

针对电容层析成像技术中的“软场”效应和病态问题，基于灵敏度矩阵的奇异值分解理论，提出了一种加权SVD截断共轭梯度的ECT图像重建算法，给出了算法的数学模型，完成了算法的收敛性分析和证明，并将其应用在电容层析成像系统的图像重建中。仿真和实验结果表明，同LBP算法和CG算法相比，该算法有成像效果好，成像速度快，易于实现等特点。

An Image Reconstruction Algorithm Based on weighted SVD Truncation Conjugate Gradient Algorithm for Electrical Capacitance Tomography System

To solve the “soft-field” nature and the ill-posed problem in electrical capacitance tomography technology, on the basis of the singular value decomposition theory of the sensitivity matrix, a SVD truncation conjugate gradient weighted image reconstruction algorithm for electrical capacitance tomography system is presented, a mathematic model for this algorithm is established and its convergence characteristic is proved, and this method is applied to the image reconstruction for electrical capacitance tomography system. Experiment results and simulation data indicate that the precision of the reconstructed image is higher, the speed is faster and it is easier to implement compared with LBP algorithm and CG algorithm.