Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems
Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems
复制标题
大规模非线性离散不适定反问题设计的数值方法
DOI：
10.1088/0266-5611/26/2/025002
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发表时间：
2010
期刊：
影响因子：
2.1
通讯作者：
L. Horesh
中科院分区：
文献类型：
--
作者：
E. Haber;L. Horesh
离散不适定问题的实验设计是一个相对较新的研究领域。虽然已经有一些有限的工作，关于线性的情况下，很少有人做了研究不适定的非线性问题的设计准则和数值方法。我们提出了一个算法框架，非线性实验设计与有效的数值实现。数据被建模为通过一组合理的实验收集的模型的间接的、有噪声的观察。基于这些数据的反演估计通过加权Tikhonov正则化获得，其权重控制不同实验对数据失配项的贡献。这些权重通过最小化贝叶斯风险的经验估计来选择，贝叶斯风险被惩罚以促进稀疏性。这个公式需要一个双层优化问题，使用一个简单的下降法来解决。我们证明了我们的设计的可行性，在电磁成像的基础上直流电阻率和大地电磁数据的问题。
Design of experiments for discrete ill-posed problems is a relatively new area of research. While there has been some limited work concerning the linear case, little has been done to study design criteria and numerical methods for ill-posed nonlinear problems. We present an algorithmic framework for nonlinear experimental design with an efficient numerical implementation. The data are modeled as indirect, noisy observations of the model collected via a set of plausible experiments. An inversion estimate based on these data is obtained by a weighted Tikhonov regularization whose weights control the contribution of the different experiments to the data misfit term. These weights are selected by minimization of an empirical estimate of the Bayes risk that is penalized to promote sparsity. This formulation entails a bilevel optimization problem that is solved using a simple descent method. We demonstrate the viability of our design with a problem in electromagnetic imaging based on direct current resistivity and magnetotelluric data.
DOI：
10.1002/9780470685853
发表时间：
1994
期刊：
--
影响因子：
--
作者：
L. Biegler;G. Biros;O. Ghattas;M. Heinkenschloss;D. Keyes;B. Mallick;Y. Marzouk;L. Tenorio;B. V. B. Waanders-B.-V.-B.-Waanders-1863062;K. Willcox
通讯作者：
L. Biegler;G. Biros;O. Ghattas;M. Heinkenschloss;D. Keyes;B. Mallick;Y. Marzouk;L. Tenorio;B. V. B. Waanders-B.-V.-B.-Waanders-1863062;K. Willcox