由弹性电子散射数据确定电荷密度的贝叶斯方法
A Bayesian Approach for the Determination of the Charge Density from Elastic Electron Scattering Data
摘要：
由有限的电荷形状因子信息确定电荷密度的问题是一个不适定的反问题。一个贝叶斯概率的方法来解决这个问题，允许考虑到错误和先验信息的解决方案。我们将表明，许多经典的方法可以被认为是所提出的方法的特殊情况。我们还解决了离散化和解决方案的不确定性的基础函数的选择问题。一个分析模型的数值结果显示所提出的方法的性能。
英文摘要：
The problem of the determination of the charge density from limited information about the charge form factor is an ill-posed inverse problem. A Bayesian probabilistic approach to this problem which permits to take into account both errors and prior information about the solution is presented. We will show that many classical methods can be considered as special cases of the proposed approach. We address also the problem of the basis function choice for the discretization and the uncertainty of the solution. Some numerical results for an analytical model are presented to show the performance of the proposed method.
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