Numerical methods for experimental design of large-scale linear ill-posed inverse problems
Numerical methods for experimental design of large-scale linear ill-posed inverse problems
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DOI：
10.1088/0266-5611/24/5/055012
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发表时间：
2008-10-01
期刊：
影响因子：
2.1
通讯作者：
Tenorio, L.
中科院分区：
文献类型：
--
作者：
Haber, E.;Horesh, L.;Tenorio, L.
虽然适定逆线性问题的实验设计已经得到了很好的研究，涵盖了广泛的既定设计标准和优化算法，但其不适定对应问题是一个相当新的主题。该问题的不适定性质需要结合正则化技术。在选择实验设计标准时，需要考虑正则化带来的随之而来的非随机误差。我们讨论定义最佳设计的不同方法，该设计既控制正则化估计的平均总误差，又控制设计总成本的度量。我们还引入了一个数值框架，可以有效地实现此类设计，并本身就可以解决大规模问题。为了说明该方法的可能应用，我们考虑钻孔断层扫描示例和二维函数恢复问题。
While an experimental design for well-posed inverse linear problems has been well studied, covering a vast range of well-established design criteria and optimization algorithms, its ill-posed counterpart is a rather new topic. The ill-posed nature of the problem entails the incorporation of regularization techniques. The consequent non-stochastic error introduced by regularization needs to be taken into account when choosing an experimental design criterion. We discuss different ways to define an optimal design that controls both an average total error of regularized estimates and a measure of the total cost of the design. We also introduce a numerical framework that efficiently implements such designs and natively allows for the solution of large-scale problems. To illustrate the possible applications of the methodology, we consider a borehole tomography example and a two-dimensional function recovery problem.