The role of nonlinearity in inverse problems
The role of nonlinearity in inverse problems
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DOI：
10.1088/0266-5611/14/3/003
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发表时间：
1998-06
期刊：
影响因子：
2.1
通讯作者：
R. Snieder
中科院分区：
文献类型：
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作者：
R. Snieder
在许多实际的反问题中，人们的目标是从有限数量的数据中检索具有无限多个自由度的模型。从一个简单的变量计数可以得出结论，这不能以唯一的方式完成。因此，反演不仅仅需要估计模型：如果没有对与数据一致的模型类别的描述，任何反演都是不完整的；这称为评估问题。非线性使得评估问题变得特别困难。第一个原因是非线性误差传播是一个困难的问题。第二个原因是，对于一些非线性问题，模型参数会影响数据查询模型的方式。文中给出了两个例子，并说明了非线性如何使问题更不适定。最后，对基于解析法、数值法和常识法的非线性反问题进行了三种模型评价。
In many practical inverse problems, one aims to retrieve a model that has infinitely many degrees of freedom from a finite amount of data. It follows from a simple variable count that this cannot be done in a unique way. Therefore, inversion entails more than estimating a model: any inversion is not complete without a description of the class of models that is consistent with the data; this is called the appraisal problem. Nonlinearity makes the appraisal problem particularly difficult. The first reason for this is that nonlinear error propagation is a difficult problem. The second reason is that for some nonlinear problems the model parameters affect the way in which the model is being interrogated by the data. Two examples are given of this, and it is shown how the nonlinearity may make the problem more ill-posed. Finally, three attempts are shown to carry out the model appraisal for nonlinear inverse problems that are based on an analytical approach, a numerical approach and a common sense approach.