scholarly journals Parameter Selection Methods in Inverse Problem Formulation

2012 ◽  
pp. 43-73 ◽  
Author(s):  
H. T. Banks ◽  
Ariel Cintrón-Arias ◽  
Franz Kappel
Keyword(s):  
Inverse Problem ◽  
Problem Formulation ◽  
Parameter Selection ◽  
Selection Methods

Regularizing Biomechanical Maps for Partially Known Material Properties

2017 ◽  
Vol 09 (02) ◽  
pp. 1750020 ◽  
Author(s):  
Yue Mei ◽  
Mahsa Tajderi ◽  
Sevan Goenezen
Keyword(s):  
Inverse Problem ◽  
Elastic Modulus ◽  
Problem Formulation ◽  
Small Region ◽  
Parameter Distribution ◽  
Atherosclerotic Plaques ◽  
Surgical Interventions ◽  
Constrained Minimization Problem ◽  
Soft Inclusion ◽  
Unique Parameter

We present the solution of the inverse problem for partially known elastic modulus values, e.g., the elastic modulus is known in some small region on the boundary of the domain from measurements. The inverse problem is posed as a constrained minimization problem and regularized with two different regularization types. In particular, the total variation diminishing (TVD) and the total contrast diminishing (TCD) regularizations are employed. We test both regularization strategies with theoretical diseased tissues, such as a stiff tumor surrounded by healthy background tissue and an atherosclerotic plaque having a soft inclusion surrounded by a stiff cap. In the present study, it is assumed that no traction data is available and the absolute elastic modulus distribution is calibrated from partially known elastic modulus values. We observe that this calibration fails with TVD regularization, while TCD regularization yields well-recovered absolute elastic modulus reconstructions in the presence of high noise levels in the displacement data. Finally, we investigate this problem analytically and provide an explanation for these observations. This work will advance efforts in parameter identification of heterogeneous materials as it provides a methodology to incorporate partially known parameters into the inverse problem formulation that will ultimately drive the inverse solution to an absolute and unique parameter distribution. This has great importance in classifying breast tumors based on their elastic modulus values and in planning surgical interventions of atherosclerotic plaques.

Book Reviews

2013 ◽  
Vol 51 (3) ◽  
pp. 886-888
Keyword(s):  
Inverse Problem ◽  
Empirical Likelihood ◽  
Method Of Moments ◽  
Linear Models ◽  
Choice Model ◽  
Generalized Method Of Moments ◽  
Problem Formulation ◽  
Distribution Functions ◽  
Binary Response ◽  
Quadratic Loss

Provides a conceptual and empirical understanding of basic information theoretic econometric models and methods. Discusses formulation and analysis of parametric and semiparametric linear models; method of moments, generalized method of moments, and estimating equations; a stochastic-empirical likelihood inverse problem—formulation and estimation; a stochastic empirical likelihood inverse problem—estimation and inference; Kullback–Leibler information and the maximum empirical exponential likelihood; the Cressie–Read family of divergence measures and empirical maximum likelihood functions; Cressie–Read minimum power divergence (MPD) type estimators in practice—Monte Carlo evidence of estimation and inference sampling performance; family of MPD distribution functions for the binary response-choice model; estimation and inference for the binary response model based on the MPD family of distributions; and choosing the optimal divergence under quadratic loss. Judge is a professor at the University of California, Berkeley. Mittelhammer is Regents Professor of Economic Sciences and Statistics at Washington State University.

Automatic parameter selection for Tikhonov regularization in ECT Inverse problem

2016 ◽  
Vol 246 ◽  
pp. 73-80 ◽  
Author(s):  
Dario J. Pasadas ◽  
Artur L. Ribeiro ◽  
Helena G. Ramos ◽  
Tiago J. Rocha
Keyword(s):  
Inverse Problem ◽  
Tikhonov Regularization ◽  
Parameter Selection ◽  
Selection For

scholarly journals Inverse Problem Solution and Regularization Parameter Selection for Current Distribution Reconstruction in Switching Arcs by Inverting Magnetic Fields

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jinlong Dong ◽  
Guogang Zhang ◽  
Zhiqiang Zhang ◽  
Yingsan Geng ◽  
Jianhua Wang
Keyword(s):  
Inverse Problem ◽  
Density Distribution ◽  
Current Density ◽  
Cross Validation ◽  
Regularization Parameter ◽  
Current Density Distribution ◽  
Optimality Criteria ◽  
Parameter Selection ◽  
Selection Strategies ◽  
Regularization Parameter Selection

Current density distribution in electric arcs inside low voltage circuit breakers is a crucial parameter for us to understand the complex physical behavior during the arcing process. In this paper, we investigate the inverse problem of reconstructing the current density distribution in arcs by inverting the magnetic fields. A simplified 2D arc chamber is considered. The aim of this paper is the computational side of the regularization method, regularization parameter selection strategies, and the estimation of systematic error. To address the ill-posedness of the inverse problem, Tikhonov regularization is analyzed, with the regularization parameter chosen by Morozov’s discrepancy principle, the L-curve, the generalized cross-validation, and the quasi-optimality criteria. The provided range of regularization parameter selection strategies is much wider than in the previous works. Effects of several features on the performance of these criteria have been investigated, including the signal-to-noise ratio, dimension of measurement space, and the measurement distance. The numerical simulations show that the generalized cross-validation and quasi-optimality criteria provide a more satisfactory performance on the robustness and accuracy. Moreover, an optimal measurement distance can be expected when using a planner sensor array to perform magnetic measurements.

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