关键词: 电容层析成像, 过度光滑, 正定矩阵, 广义正则化算法, 图像重建

Abstract: 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 l₂-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. Resultsshow 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.

Key words: electrical capacitance tomography, over-smooth, positive definite matrix, generalized regularization algorithm, image reconstruction