基于广义正则化的ECT图像重建算法

ECT Image Reconstruction Algorithm Based on Generalized Regularization

针对电容层析成像(Electrical Capacitance Tomography,ECT)系统图像重建过程中Tiknonov正则化引起的解的过度光滑和奇异值分解算法引起的数值不稳定,提出了一种更为广义的正则化算法。利用正定矩阵对正则化目标函数的惩罚相修正,使其可以对包含非光滑性信息的图像进行更准确重构,在目标函数求解过程中引入对角权值矩阵,对基于l2范数的数据项改进,通过重建图像质量、图像相对误差、图像相对系数等指标对3种算法进行评估。实验结果表明,广义正则化算法相比Tiknonov正则化算法和奇异值分解算法,可以对物场中不同介质有效区分,避免图像的过度平滑,分辨率较高,重建质量较好。

Aiming at the numerical instability caused by the singular value decomposition algorithm and the over-smooth caused by the Tiknonov regularization in the image reconstruction of electrical capacitance tomography （ECT） system, a more generalized regularization algorithm was proposed. The penalty phase of the regularized objective function was modified by the positive definite matrix so that it could reconstruct the image with non smooth information, In the process of solving the objective function, the diagonal weight matrix was introduced, and the data items based on 12-norm were improved. By comparing the image quality, the relative error of the image and the relative coefficient of the image, the three algorithms were evaluated. Results show that the generalized regularization algorithm compared to Tiknonov regularization algorithm and singular value decomposition algorithm, can distinguish the substance field in different medium effectively and obtain high quality reconstruction images while avoiding over-smooth.