Truncated Total Least Squares: A New Regularization Method for the Solution of ECG Inverse Problems

2008 ◽  
Vol 55 (4) ◽  
pp. 1327-1335 ◽  
Author(s):  
Guofa Shou ◽  
Ling Xia ◽  
Mingfeng Jiang ◽  
Qing Wei ◽  
Feng Liu ◽  
...  
Keyword(s):  
Inverse Problems ◽  
Least Squares ◽  
Regularization Method ◽  
Total Least Squares ◽  
Truncated Total Least Squares

scholarly journals Reply to “Comments on ‘Erroneous Model Field Representations in Multiple Pseudoproxy Studies: Corrections and Implications’”*

2013 ◽  
Vol 26 (10) ◽  
pp. 3485-3486 ◽  
Author(s):  
Jason E. Smerdon ◽  
Alexey Kaplan ◽  
Daniel E. Amrhein
Keyword(s):  
Least Squares ◽  
Northern Hemisphere ◽  
Expectation Maximization ◽  
Strong Influence ◽  
Total Least Squares ◽  
Model Field ◽  
Spatial Skill ◽  
Spatial Performance ◽  
Quantitative Results ◽  
Truncated Total Least Squares

Abstract The commenters confirm the errors identified and discussed in Smerdon et al., which either invalidated or required the reinterpretation of quantitative results from pseudoproxy experiments presented or used in several earlier papers. These errors have a strong influence on the spatial skill assessments of climate field reconstructions (CFRs), despite their small impacts on skill statistics averaged over the Northern Hemisphere. On the basis of spatial performance and contrary to the claim by the commenters, the Regularized Expectation Maximization method using truncated total least squares (RegEM-TTLS) cannot be considered a preferred CFR technique. Moreover, distinctions between CFR methods in the context of the discussion in the original paper are immaterial. Continued investigations using accurately described and faithfully executed pseudoproxy experiments are critical for further evaluation and improvement of CFR methods.

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.

scholarly journals Truncated Total Least Squares Method with a Practical Truncation Parameter Choice Scheme for Bioluminescence Tomography Inverse Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaowei He ◽  
Jimin Liang ◽  
Xiaochao Qu ◽  
Heyu Huang ◽  
Yanbin Hou ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Least Squares Method ◽  
Total Least Squares ◽  
Measurement Noise ◽  
Source Distribution ◽  
Parameter Choice ◽  
Bioluminescence Tomography ◽  
System Errors ◽  
Truncated Total Least Squares

In bioluminescence tomography (BLT), reconstruction of internal bioluminescent source distribution from the surface optical signals is an ill-posed inverse problem. In real BLT experiment, apart from the measurement noise, the system errors caused by geometry mismatch, numerical discretization, and optical modeling approximations are also inevitable, which may lead to large errors in the reconstruction results. Most regularization techniques such as Tikhonov method only consider measurement noise, whereas the influences of system errors have not been investigated. In this paper, the truncated total least squares method (TTLS) is introduced into BLT reconstruction, in which both system errors and measurement noise are taken into account. Based on the modified generalized cross validation (MGCV) criterion and residual error minimization, a practical parameter-choice scheme referred to as improved GCV (IGCV) is proposed for TTLS. Numerical simulations with different noise levels and physical experiments demonstrate the effectiveness and potential of TTLS combined with IGCV for solving the BLT inverse problem.

Sign in / Sign up

Export Citation Format

Share Document