改进正则化半阈值算法的 ECT 图像重建

针对电容层析成像技术应用于工业多相流管道检测时，图像重建中存在的不适定性、病态性问题，提出一种改进正则化半阈值算法。以L1/2范数为惩戒函数，改进求解L1/2范数所用的半阈值迭代算法中的阈值算子，并以加入加速项的Landweber算法解向量为修正向量，引入改进半阈值正则化模型，优化加速Landweber算法。实验的结果表明，改进正则化半阈值算法在重建图像中相关系数平均达0.91,图像误差平均降至0.21,成像速度保持0.04 s。复杂流型辨识中，改进算法比Landweber迭代算法相关系数提高21.67%,相对误差降低37.01%;比Tikhonov正则化算法相关系数提高22.61%,相对误差降低37.08%;比半阈值算法相关系数和误差分别提高14.85%和降低28.26%。结果表明改进正则化半阈值算法对ECT研究有较好应用前景。

ECT image reconstruction based on improved regularized half threshold algorithm

Aiming at the ill posed and ill conditioned problems in image reconstruction when electrical capacitance tomography technology is applied to the detection of industrial industrial multiphase flow pipeline, an improved regularized half threshold algorithm is proposed. Taking L1 / 2 norm as the penalty function, the threshold operator in the semi threshold iterative algorithm used to solve L1 / 2 norm is improved. Taking the solution vector of Landweber algorithm with acceleration term as the correction vector, the improved semi threshold regularization model is introduced to optimize the accelerated Landweber algorithm. The experimental results show that the average correlation coefficient of the improved regularized half threshold algorithm in the reconstructed image is as high as 0. 91, the average image error is reduced to 0. 21, and the imaging speed is maintained at 0. 04 s. For complex flow pattern identification, the correlation coefficient of the improved algorithm is increased by 21. 67% and the relative error is reduced by 37. 01% compared with the traditional Landweber iterative algorithm; Compared with Tikhonov regularization algorithm, the correlation coefficient is increased by 22. 61% and the relative error is reduced by 37. 08% ; Compared with the half threshold algorithm, the correlation coefficient and relative error are increased by 14. 85% and reduced by 28. 26% respectively. The results show that the improved regularized half threshold algorithm has a good application prospect for ECT research.