基于模型细化改进牛顿-拉夫逊图像重建算法  

Improved Newton-Raphson image reconstruction algorithm based on model refining

作　　者：肖理庆[1,2] 王化祥[2] 邵晓根[1] 

机构地区：[1]徐州工程学院虚拟现实与多维信息处理实验室,徐州221111 [2]天津大学电气与自动化工程学院,天津300072

出　　处：《仪器仪表学报》2014年第7期1546-1554,共9页Chinese Journal of Scientific Instrument

基　　金：国家自然科学基金(61201350;61302122);江苏省高校自然科学研究面上项目(13KJD510007);中央高校基本科研业务费中国民航大学专项(3122013C007)资助项目

摘　　要：为了提高电阻层析成像重建图像分辨率,针对灵敏度分布的不均匀性,提出一种基于模型细化的改进牛顿-拉夫逊图像重建算法。通过采用在每个三角形有限元形心位置增加节点的方法,细化可有效提高正问题计算精度的有限元模型,并在算法重建过程中,遵循"计算正问题时采用细化前有限元模型,修正电阻率分布时采用细化后有限元模型及其对应的灵敏度矩阵"的原则。实验结果表明:新算法不仅提高了灵敏度分布的均匀性,同时改善了Hessian矩阵的病态性,有效提高了图像重建质量。In order to improve the space resolution of the reconstructed image in electrical resistance tomography （ERT）, an improved Newton-Raphson image reconstruction algorithm is proposed based on model refining to cope with the inhomogeneity of the sensitivity distribution. Through adding new nodes in the geometric center points of the triangular finite elements, the finite element （FE） model that could effectively improve the solution accuracy of the forward problem is refined, and in the reconstruction process, the initial FE model before refining is adopted in the forward problem, and the refined FE model and corresponding sensitivity matrix are adopted in correcting the resistivity distribution. Experiment results demonstrate that the proposed method not only enhances the homogeneity of the sensitivity distribution, but also improves the ill-posedness of the Hessian matrix, and thus improves the imaging reconstruction quality effectively.

关 键 词：电阻层析成像 模型细化 正问题 灵敏度矩阵 病态性 

分 类 号：TH701[机械工程—仪器科学与技术]