Effective Use of a priori Knowledge in Solving Inverse Problems

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，例如根据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。动态正则化是一种根据网络逆运算的迭代进度来改变正则化参数的技术。在从诱发电位估计等效电流偶极子的情况下，我们通过引入动态正则化来实现同时估计三个偶极子，以将皮层活动的轨迹表示为垂直于三个偶极子的三角形的轨迹。在脑内FDG分布可视化的情况下，我们将隐马尔可夫模型引入FDG转移模型中，利用缓存区FDG浓度的时间连续性的先验知识。在从电导数据中获得电导率剖面的情况下，从电导数据中获得电导率剖面，以获得电导率分布。在FDG传输模型中，我们将隐马尔可夫模型引入到FDG转移模型中，利用缓存区FDG浓度的时间连续性的先验知识，从电导数据中获得电导率剖面，从而得到大脑中FDG分布的可视化我们还利用动态正则化技术来稳定电阻抗断层成像结果。此外，我们还将动态正则化技术扩展到从一组立体图像重建三维曲面的逆问题。在这个问题中，我们开发了一种新的网络，它在迭代运算中自动实现对应点的获取和光滑曲面的生成，通过上述例子，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。

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.