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用于解决反问题的有效性，例如从头皮电位分布或正电子发射断层扫描（PET）数据估计神经活动。动态正则化是在运行网络反演时，根据迭代的进度改变正则化参数的一种技术。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对三个偶极子的同时估计，从而将皮质活动的轨迹表示为位于顶点上的三个偶极子的三角形轨迹。为了可视化FDG在大脑中的分布，我们在FDG转移模型中引入了一个隐马尔可夫模型，以利用FDG浓度在每个隔室的时间连续性的先验知识。在获得电导率剖面的情况下，我们还利用了动态正则化技术，以稳定电阻抗层析成像结果。除此之外，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表面的逆问题。在这个问题中，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和光滑曲面的生成。通过上述实例，我们证明了逆问题求解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.