Regularized total least squares approach for nonconvolutional linear inverse problems

1999 ◽  
Vol 8 (11) ◽  
pp. 1657-1661 ◽  
Author(s):  
Wenwu Zhu ◽  
Yao Wang ◽  
N.P. Galatsanos ◽  
Jun Zhang
Keyword(s):  
Inverse Problems ◽  
Least Squares ◽  
Total Least Squares ◽  
Linear Inverse Problems ◽  
Regularized Total Least Squares ◽  
Least Squares Approach

A model function method in regularized total least squares

2010 ◽  
Vol 89 (11) ◽  
pp. 1693-1703 ◽  
Author(s):  
Shuai Lu ◽  
Sergei V. Pereverzev ◽  
Ulrich Tautenhahn
Keyword(s):  
Least Squares ◽  
Function Method ◽  
Total Least Squares ◽  
Model Function ◽  
Regularized Total Least Squares

Total least squares approach for the solution of the perturbation equation

1995 ◽  
Author(s):  
Wenwu Zhu ◽  
Yao Wang ◽  
Jenghwa Chang ◽  
Harry L. Graber ◽  
Randall L. Barbour
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Perturbation Equation ◽  
Least Squares Approach

Regularized total least squares based on the nonlinear Arnoldi method

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 1020407-1020408 ◽  
Author(s):  
Jörg Lampe ◽  
Heinrich Voss
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Arnoldi Method ◽  
Regularized Total Least Squares

Inverse Problems With Errors in the Independent Variables Errors-in-Variables, Total Least Squares, and Bayesian Inference

2008 ◽  
Author(s):  
A. F. Emery
Keyword(s):  
Bayesian Inference ◽  
Maximum Likelihood ◽  
Inverse Problems ◽  
Least Squares ◽  
Total Least Squares ◽  
Errors In Variables ◽  
Independent Variables ◽  
Error In Variables ◽  
Best Estimates ◽  
Normally Distributed

Most practioners of inverse problems use least squares or maximum likelihood (MLE) to estimate parameters with the assumption that the errors are normally distributed. When there are errors both in the measured responses and in the independent variables, or in the model itself, more information is needed and these approaches may not lead to the best estimates. A review of the error-in-variables (EIV) models shows that other approaches are necessary and in some cases Bayesian inference is to be preferred.

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