基于l_1范数的电容层析成像图像重建算法  

l1-norm-based Image Reconstruction Algorithm for Electrical Capacitance Tomography

作　　者：王丕涛[1] 王化祥[1] 孙犇渊[1] 

机构地区：[1]天津大学电气工程与自动化学院,天津市南开区300072

出　　处：《中国电机工程学报》2015年第18期4709-4714,共6页Proceedings of the CSEE

基　　金：国家自然科学基金项目(60820106002;61201350;60672076)~~

摘　　要：传统电容层析成像(electrical capacitance tomography,ECT)系统图像重建算法一般基于l2范数优化方法,其解具有一定的平滑性。文中引入l1范数同时作为数据项和正则化项,将问题转化为凸优化问题,采用原始–对偶内插点法(primal-dual interior-point method,PDIPM)进行数值计算,并对数据项和正则化项分别取l2范数或l1范数的不同模型,通过重建图像质量、迭代次数、求解时间和图像相对误差等评价指标进行比较。算法采用仿真数据和实际气固两相流实验数据进行评估。实验结果表明,该模型可以避免图像的过度平滑,能够对物场中不同介质有效区分,重建质量较好。Typically, image reconstruction for electrical capacitance tomography （ECT） system is formulated as optimization problem ofl2-norm which is feasible for signal recovery with smooth changes. An image reconstruction model withl1-norm both on the data fidelity term and regularization term was introduced, then the image reconstruction was transformed into a convex optimization problem which was solved by using the primal-dual interior-point method. The four models with different combinations ofl2-norm andl1-norm for data term and regularization term were compared with the quality of reconstruction image, the iterative numbers, the time consuming and the image relative error. The performance of the proposed algorithm was evaluated based on simulation data and experimental data of gas/solid two-phase flow. Results show that the proposed model with PDIPM algorithm for ECT image reconstruction can obtain high quality reconstruction images while avoiding over-smooth.

关 键 词：电容层析成像 原始-对偶内插点法 图像重建 正则化 L1范数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]