联合改进稀疏正则化ECT图像重建算法  

Jointly Improved Sparse Regularization ECT Image Reconstruction Algorithm

作　　者：马敏 孙妮 MA Min;SUN Ni(College of Electronic Information and Automation,Civil Aviation University of China,Tianjin 300300,China)

机构地区：[1]中国民航大学电子信息与自动化学院,天津300300

出　　处：《计量学报》2024年第8期1132-1138,共7页Acta Metrologica Sinica

基　　金：国家自然科学基金(61871379);天津市教委科研计划(2020KJ012)。

摘　　要：针对电容层析成像技术逆问题求解过程中的病态性和不适定问题,提出了联合改进稀疏正则化图像重建算法。首先利用自适应截断奇异值算法对灵敏度矩阵进行优化预处理,以消除矩阵中的冗余信息;其次,基于优化后的灵敏度矩阵联合改进的L1-αL2稀疏正则化,构建凸函数项,增强解的稀疏性和稳定性;最后通过快速迭代阈值收缩算法进行求解,加速迭代收敛速度。改进算法在重建图像中相关系数平均达0.8813,图像误差平均降至0.2111,成像速度保持在0.10 s以内。仿真与实验结果表明,改进算法改善了逆问题的病态性和不适定性,提高了图像重建精度,同时具有较强的鲁棒性和实时性。To improve the ill-conditioned and ill-posed problem in the inverse problem solving process of electrical capacitance tomography(ECT),a jointly improved sparse regularization image reconstruction algorithm is proposed.Firstly,the sensitivity matrix is optimally preprocessed by the adaptive truncated singular value algorithm to eliminate the redundant information in the matrix.Secondly,in order to enhance the sparsity and stability of the solution,the L1-αL2 sparse regularization is jointly improved based on the optimized sensitivity matrix to construct new convex function terms.Finally,the solution is performed by the fast iterative threshold shrinkage algorithm to accelerate the iterative convergence speed.The improved algorithm achieves an average correlation coefficient of 0.8813 in the reconstructed image,the image error is reduced to 0.2111 on average,and the imaging speed is kept within 0.10s.The simulation and experimental results show that the improved algorithm improves the ill-posed and ill-condition degree and enhances the image reconstruction accuracy while having strong robustness and real-time performance.

关 键 词：多相流测量 电容层析技术 自适应截断奇异值 稀疏正则化 图像重建 

分 类 号：TB937[一般工业技术—计量学] TB973[机械工程—测试计量技术及仪器]