Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems

Abhishake Rastogi;

doi:10.3934/cpaa.2020183

Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2020183 ◽

2020 ◽

Vol 19 (8) ◽

pp. 4111-4126

Author(s):

Abhishake Rastogi ◽

Keyword(s):

Inverse Problems ◽

Tikhonov Regularization ◽

Statistical Inverse Problems

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Convergence analysis of Tikhonov regularization for non-linear statistical inverse problems

Electronic Journal of Statistics ◽

10.1214/20-ejs1735 ◽

2020 ◽

Vol 14 (2) ◽

pp. 2798-2841

Author(s):

Abhishake Rastogi ◽

Gilles Blanchard ◽

Peter Mathé

Keyword(s):

Inverse Problems ◽

Convergence Analysis ◽

Tikhonov Regularization ◽

Non Linear ◽

Statistical Inverse Problems

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Nonlinear Tikhonov regularization in Hilbert scales with balancing principle tuning parameter in statistical inverse problems

Inverse Problems in Science and Engineering ◽

10.1080/17415977.2018.1454918 ◽

2018 ◽

Vol 27 (2) ◽

pp. 205-236 ◽

Cited By ~ 2

Author(s):

M. Pricop-Jeckstadt

Keyword(s):

Inverse Problems ◽

Tikhonov Regularization ◽

Tuning Parameter ◽

Statistical Inverse Problems ◽

Balancing Principle

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Statistical inverse problems: Discretization, model reduction and inverse crimes

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2005.09.027 ◽

2007 ◽

Vol 198 (2) ◽

pp. 493-504 ◽

Cited By ~ 281

Author(s):

Jari Kaipio ◽

Erkki Somersalo

Keyword(s):

Inverse Problems ◽

Model Reduction ◽

Statistical Inverse Problems

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Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems

SIAM Journal on Scientific Computing ◽

10.1137/090775622 ◽

2010 ◽

Vol 32 (5) ◽

pp. 2523-2542 ◽

Cited By ~ 123

Author(s):

Chad Lieberman ◽

Karen Willcox ◽

Omar Ghattas

Keyword(s):

Inverse Problems ◽

Model Reduction ◽

Large Scale ◽

State Model ◽

Statistical Inverse Problems

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Statistical Inverse Problems on Manifolds

Journal of Fourier Analysis and Applications ◽

10.1007/s00041-005-3041-1 ◽

2005 ◽

Vol 11 (6) ◽

pp. 639-653 ◽

Cited By ~ 6

Author(s):

Peter T. Kim ◽

Ja-Yong Koo

Keyword(s):

Inverse Problems ◽

Statistical Inverse Problems

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Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: A (Numerical) Survey

Trends in Mathematics - New Trends in Parameter Identification for Mathematical Models ◽

10.1007/978-3-319-70824-9_15 ◽

2018 ◽

pp. 291-316

Author(s):

Frank Werner

Keyword(s):

Inverse Problems ◽

Oracle Inequalities ◽

Statistical Inverse Problems

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Surrogate and Reduced-Order Modeling: A Comparison of Approaches for Large-Scale Statistical Inverse Problems

Large-Scale Inverse Problems and Quantification of Uncertainty ◽

10.1002/9780470685853.ch7 ◽

2010 ◽

pp. 123-149 ◽

Cited By ~ 22

Author(s):

M. Frangos ◽

Y. Marzouk ◽

K. Willcox ◽

B. van Bloemen Waanders

Keyword(s):

Inverse Problems ◽

Large Scale ◽

Reduced Order Modeling ◽

Reduced Order ◽

Statistical Inverse Problems

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The taut string approach to statistical inverse problems: Theory and applications

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.113098 ◽

2021 ◽

Vol 382 ◽

pp. 113098 ◽

Cited By ~ 1

Author(s):

Sangjin Kim ◽

Michael Pokojovy ◽

Xiang Wan

Keyword(s):

Inverse Problems ◽

Taut String ◽

Statistical Inverse Problems

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Modeling of uncertainties in statistical inverse problems

Journal of Physics Conference Series ◽

10.1088/1742-6596/135/1/012107 ◽

2008 ◽

Vol 135 ◽

pp. 012107 ◽

Cited By ~ 1

Author(s):

Jari Kaipio

Keyword(s):

Inverse Problems ◽

Statistical Inverse Problems

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Adaptive discretization for signal detection in statistical inverse problems

Applicable Analysis ◽

10.1080/00036811.2014.900662 ◽

2014 ◽

Vol 94 (3) ◽

pp. 494-505

Author(s):

Peter Mathé

Keyword(s):

Inverse Problems ◽

Signal Detection ◽

Adaptive Discretization ◽

Statistical Inverse Problems

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