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Effective Use of a priori Knowledge in Solving Inverse Problems

有效利用先验知识解决反问题

基本信息

批准号：
09450168
负责人：
KOSUGI Yokio
金额：
$ 7.23万
依托单位：
Tokyo Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 2000
项目状态：
已结题

项目摘要

In this research, we evaluated the effectiveness of dynamic regularization used in solving inverse problems, such as estimating the neural activities from electrical potential distribution on the scalp, or positron emission tomograpy (PET) data. The dynamic regularization is a technique to change the regularization parameter, according to the progress of iteration in operating the network inversion.In the case of estimating the equivalent current dipoles from evoked potentials, we have realized the estimation of three dipoles simultaneously by introducing the dynamic regularization, for indicating the trace of cortical activities as a locus of a triangle with three dipoles located on the vertices.In case of the visualization of FDG distribution in the brain, we introduced a hidden Markov model into the FDG transfer model for utilizing the a priori knowledge of temporal continuity of the FDG concentration in cach compartment.For the case of obtaining conductivity profile, from the electrical potential data, we also made use of the dynamic regularization technique, to stabilize the electrical impedance tomography results.In addition to the above, we expanded our dynamic regularization technique to the inverse problems of reconstructing a 3-D surface, from a set of stereo images. In this problem, we developed a new network which automatically realizes the corresponding points acquisition as well as generating the smooth surface in the iterative operation.Through the above examples, we showed the effectiveness of the dynamic regularization built in with the iterative procedure of inverse problem solvers.

在这项研究中，我们评估了动态正则化在解决逆问题中的有效性，例如从头皮上的电位分布或正电子发射断层扫描（PET）数据估计神经活动。动态正则化是一种在网络反演中根据迭代的进程来改变正则化参数的技术，在由诱发电位估计等效电流偶极子的情况下，通过引入动态正则化，实现了三个偶极子的同时估计，用于将皮层活动的轨迹指示为具有位于顶点上的三个偶极子的三角形的轨迹。在脑中FDG分布的可视化的情况下，本文在FDG传输模型中引入了隐马尔可夫模型，利用了FDG浓度在时间上连续的先验知识，对于从电位数据中获取电导率剖面的情况，我们还利用了动态正则化技术，稳定了电阻抗断层成像的结果，除此之外，我们将我们的动态正则化技术扩展到从一组立体图像重建3-D表面的逆问题。在该问题中，我们开发了一种新的网络，在迭代运算中自动实现相应点的获取以及光滑曲面的生成，通过上述算例，我们展示了反问题求解器迭代过程中内置的动态正则化的有效性。