scholarly journals Towards adaptivity via a new discrepancy principle for Poisson inverse problems

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Grzegorz Mika ◽  
Zbigniew Szkutnik
Keyword(s):  
Inverse Problems ◽  
Discrepancy Principle

Compact discrepancy and chi-squared principles for over-determined inverse problems

2017 ◽  
Vol 25 (3) ◽  
Author(s):  
Maxim Pisarenco ◽  
Irwan D. Setija
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Regularization Parameter ◽  
Discrepancy Principle ◽  
Chi Squared

AbstractWe discuss and analyze the classical discrepancy principle and the recently proposed and closely related chi-squared principle for selecting the regularization parameter of an inverse problem. Some properties that deteriorate the performance of these methods for over-determined inverse problems are highlighted. We propose a so-called

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 [

scholarly journals Reconstruction of basal properties in ice sheets using iterative inverse methods

2012 ◽  
Vol 58 (210) ◽  
pp. 795-808 ◽  
Author(s):  
Marijke Habermann ◽  
David Maxwell ◽  
Martin Truffer
Keyword(s):  
Inverse Problems ◽  
Input Data ◽  
Large Scale ◽  
Gradient Methods ◽  
Inverse Methods ◽  
Model Parameters ◽  
Discrepancy Principle ◽  
Regularization Techniques ◽  
Ill Posed ◽  
Nonlinear Conjugate Gradient Methods

AbstractInverse problems are used to estimate model parameters from observations. Many inverse problems are ill-posed because they lack stability, meaning it is not possible to find solutions that are stable with respect to small changes in input data. Regularization techniques are necessary to stabilize the problem. For nonlinear inverse problems, iterative inverse methods can be used as a regularization method. These methods start with an initial estimate of the model parameters, update the parameters to match observation in an iterative process that adjusts large-scale spatial features first, and use a stopping criterion to prevent the overfitting of data. This criterion determines the smoothness of the solution and thus the degree of regularization. Here, iterative inverse methods are implemented for the specific problem of reconstructing basal stickiness of an ice sheet by using the shallow-shelf approximation as a forward model and synthetically derived surface velocities as input data. The incomplete Gauss-Newton (IGN) method is introduced and compared to the commonly used steepest descent and nonlinear conjugate gradient methods. Two different stopping criteria, the discrepancy principle and a recent- improvement threshold, are compared. The IGN method is favored because it is rapidly converging, and it incorporates the discrepancy principle, which leads to optimally resolved solutions.

Heuristic discrepancy principle for variational regularization of inverse problems

2020 ◽  
Vol 36 (7) ◽  
pp. 075013
Author(s):  
Huan Liu ◽  
Rommel Real ◽  
Xiliang Lu ◽  
Xianzheng Jia ◽  
Qinian Jin
Keyword(s):  
Inverse Problems ◽  
Discrepancy Principle ◽  
Variational Regularization
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