scholarly journals Convergence Rates of General Regularization Methods for Statistical Inverse Problems and Applications

2007 ◽  
Vol 45 (6) ◽  
pp. 2610-2636 ◽  
Author(s):  
N. Bissantz ◽  
T. Hohage ◽  
A. Munk ◽  
F. Ruymgaart
Keyword(s):  
Inverse Problems ◽  
Convergence Rates ◽  
Regularization Methods ◽  
Statistical Inverse Problems

scholarly journals Modern regularization methods for inverse problems

Acta Numerica ◽  
2018 ◽  
Vol 27 ◽  
pp. 1-111 ◽  
Author(s):  
Martin Benning ◽  
Martin Burger
Keyword(s):  
Inverse Problems ◽  
Future Research ◽  
Regularization Methods ◽  
Comprehensive Overview ◽  
Linear Inverse Problems ◽  
Recent Interest ◽  
Methods And Techniques ◽  
Ill Posed ◽  
Nonlinear Regularization ◽  
Statistical Inverse Problems

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses. In the last two decades interest has shifted from linear to nonlinear regularization methods, even for linear inverse problems. The aim of this paper is to provide a reasonably comprehensive overview of this shift towards modern nonlinear regularization methods, including their analysis, applications and issues for future research.In particular we will discuss variational methods and techniques derived from them, since they have attracted much recent interest and link to other fields, such as image processing and compressed sensing. We further point to developments related to statistical inverse problems, multiscale decompositions and learning theory.

Regularization methods for inverse problems in x-ray tomography

2010 ◽  
Author(s):  
Valeriy Titarenko ◽  
Robert Bradley ◽  
Christopher Martin ◽  
Philip J. Withers ◽  
Sofya Titarenko
Keyword(s):  
Inverse Problems ◽  
Regularization Methods ◽  
X Ray

On convergence rates for asymptotic discrepancy principle

2016 ◽  
Vol 24 (4) ◽  
Author(s):  
Anatoly Bakushinsky ◽  
Alexandra Smirnova
Keyword(s):  
Parameter Estimation ◽  
Inverse Problems ◽  
Numerical Experiments ◽  
Convergence Rates ◽  
Discrepancy Principle

AbstractA series of recent numerical experiments for parameter estimation inverse problems in epidemiology [

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