论文标题
纤维bragg光光谱倒置的正则化
Regularization for the inversion of Fibre Bragg Grating spectra
论文作者
论文摘要
纤维布拉格光栅已成为工程和其他应用领域的广泛测量设备。在除少数情况下，所有因素和效果之间的关系被简化为比例模型。但是，在数学核心上是一个非线性反问题，在文献中似乎并没有得到太多关注。在本文中，我们向数学社区提出了这个核心问题，并提供了有关正规化方法的机会和局限性的首次报告。特别是，我们表明困难源于非唯一性和对于具有多个正则化参数的非线性反问题的已建立参数选择规则。然而，本文迈出了从单个FBG测量中提取更多信息的第一步。
Fibre Bragg Gratings have become widespread measurement devices in engineering and other fields of application. In all but a few cases, the relation between cause and effect is simplified to a proportional model. However, at its mathematical core lies a nonlinear inverse problem which appears not to have received much attention in the literature. In this paper, we present this core problem to the mathematical community and provide a first report on opportunities and limitations of a regularization approach. In particular, we show that difficulties arise from non-uniqueness and the absence of established parameter selection rules for nonlinear inverse problems with multiple regularization parameters. Nevertheless, the paper takes a first step toward extracting more information from a single FBG measurement.
