【作者】 严佩敏；

【导师】 王朔中； 莫玉龙；

【作者基本信息】 上海大学 ， 通信与信息系统， 2005， 博士

【摘要】 医学电阻抗断层成像技术能充分利用人体阻抗所携带的丰富生理和病理信息实现功能成像,因对人体检测无创无害而成为医学成像研究热点。EIT图像重建是具有严重病态的非线性逆问题,这是EIT技术的关键和难点。本论文以提高图像空间分辨率和成像精度为目标,着重研究EIT图像重建算法。首先提出了基于网格单元阻抗梯度变化的自适应网格细分法,将细分网格与一般均匀网格的成像性能进行比较。接着从不同角度提出了几种EIT逆问题求解改进算法,并进行性能分析。理论分析和实验结果表明所提出方法的有效性和优越性。论文最后对复阻抗成像及独立变量分析在阻抗成像中的应用进行了初步探讨。 本论文的主要创新性成果如下: 1.用FEM进行EIT正问题分析时,网格数既不能太少又不能太多。针对这一情况提出了一种自适应网格细分的EIT图像重建方法。先以粗分网格用有限元法进行阻抗图像重建,初步确定阻抗异变区域,再对此区域逐级进行细分,直至达到可接受的精度。这样既提高了局部成像的精度,又节省了存储空间。 2.在基于Tikhonov正则化的修正Newson-Raphson(MNR)传统重建算法中,由于未充分考虑阻抗图像本身的特性而任意选取正则化因子,往往使EIT重建质量不够满意。本文基于指数加权矩阵提出一种使目标函数最小化的重建算法,通过减小Hessian矩阵的条件数来减小EIT成像的病态性,加快算法的收敛速度。因为考虑了阻抗分布的自身信息,此方法与仅取单位矩阵为正则化项的Tikhonov正则化相比,图像重建效率得到提高。这一结论得到实验结果的验证。 3.在基于目标函数梯度不断迭代的正则化MNR重建算法中,由于有限元方法中二阶导数的计算和重复迭代正则化计算量巨大,算法实现和处理相当困难,而且稳定性较差甚至发散。本文基于Newton迭代思想提出一种修正的非线性共轭梯度迭代法(non-liner conjugate gradients iteration,NLCG),通过梯度搜索完成步长迭代而无需计算二阶微分即Hessian矩阵,因此只需较低的存储空间,大大提高了计算效率并改善了图像重建的稳定性。该方法对大数据量运算效果明显。更多还原

【Abstract】 Electrical impedance tomography (EIT) is a functional imaging technique, which can reveal physiological and pathological information from human body’s impedance properties. The advantages such as the non-invasive modality make EIT a hot topic in the research of medical imaging. Image reconstruction in EIT is a difficult problem because of the ill-posedness and non-linearity. This dissertation mainly studies EIT image reconstruction algorithms with the aim of increasing precision and spatial resolution of EIT. An adaptive mesh refinement method based on resistivity gradients in EIT reconstruction is proposed, and its advantage over the uniformly refined mesh analyzed. From various points of view, several reconstruction methods are proposed. Their performances are checked through theoretical analysis, computer simulation and experiments. Finally preliminary studies on imaging complex conductivity distribution and reconstruction of electrical impedance tomography based on independent component analysis are carried out.Major accomplishments of the dissertation include:1. In order to improve the solution to the forward problem in EIT based on FEM, an adaptive mesh refinement technique is introduced. Once a region of impedance change in a coarse mesh is located based on the calculated gradient, the local mesh is refined so as to achieve higher precision. This method has a major impact on obtaining an efficient solution to the forward problem, leading to the improvement in resolution quality and saving of memory space.2. As the regularization operator in the generalized Tikhonov approach lacks characteristics of both the object and the EIT reconstructed image, performance of the modified Newton-Raphson (MNR) algorithm is unsatisfactory in practice. In this dissertation, a reconstruction algorithm is proposed based on minimization of the augmented cost functional including the soft constraint. The algorithm is formulated under the exponentially weighted least square criteria. By reducing the condition number of a Hessian matrix, the ill-posedness is reduced. Experimental results indicate that the method given here is better than the traditional method in terms of EIT precision.3. The Newton-Raphson reconstruction algorithm requires second derivative since a fine mesh needs to be calculated and regularized by iteration. The algorithm tends to be lengthy, therefore unstable even divergent. An image reconstruction method for EIT based on the non-linear conjugate gradients iteration algorithm (NLCG) improved by adding a modified factor is proposed. The algorithm is computationally efficient. Stability of the EIT solution is improved because NLCG更多还原