基于L曲线法的电容层析成像正则化参数优化

Regularization Parameter Optimum of Electrical Capacitance Tomography Based on L-Curve Method

电容层析成像(ECT)系统的不适定性问题严重影响重建图像质量,为此必须减小灵敏度矩阵的条件数．以Tikhonov正则化和后验策略为基础,从灵敏度矩阵广义逆的角度阐述了L曲线法并设置滤波函数,建立极小化泛函及L曲线图,最终确定正则参数．仿真实验表明,L曲线法具有较强的抗噪声性能和较快的收敛速度,明显改善了ECT系统的重构图像质量．

The reconstructed image quality of electrical capacitance tomography （ECT） system is heavily affected by the ill-posedness problem, so the condition number of the sensitivity matrix must be decreased. Based on Tikhonov regularization and the posterior strategy, the L-curve method is proposed in terms of the generalized inverse of the sensitivity matrix. The theoretical basis of the method is expounded and the filter function is established; a minimizing functional and L-curve are obtained. Finally, the regularization parameter is determined. Simulation experiments show that L-curve method has better noise immunity and fast convergence rate, and the reconstructed image quality of ECT system is improved markedly.