Search Results - numerical solution to inverse problems in abstracts spaces~

Robustness and exploration of variational and machine learning approaches to inverse problems: An overview: Robustness and exploration of variational and machine learning approaches to inverse problems: an overview

Authors: Alexander Auras Kanchana Vaishnavi Gandikota Hannah Droege et al.

Source: GAMM-Mitteilungen. 47

Subject Terms: FOS: Computer and information sciences, Computer Science - Machine Learning, inverse problems, Computer Vision and Pattern Recognition (cs.CV), Image and Video Processing (eess.IV), Learning and adaptive systems in artificial intelligence, Computer Science - Computer Vision and Pattern Recognition, Numerical solution to inverse problems in abstract spaces, robustness, Numerical Analysis (math.NA), 02 engineering and technology, Electrical Engineering and Systems Science - Image and Video Processing, explorability, 01 natural sciences, Machine Learning (cs.LG), machine learning, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Mathematics - Numerical Analysis, Image processing (compression, reconstruction, etc.) in information and communication theory, 0101 mathematics

File Description: application/xml

Access URL: http://arxiv.org/abs/2402.12072
https://zbmath.org/7968740
https://doi.org/10.1002/gamm.202470003

Approximation of inverse problems for fractional differential equations in abstract spaces

Authors: Santosh Ruhil Muslim Malik Kottakkaran Sooppy Nisar et al.

Source: Alexandria Engineering Journal, Vol 121, Iss , Pp 529-538 (2025)

Subject Terms: Inverse problems, Fractional differential equations, α-resolvent family, Optimal control, Approximation theory, Engineering (General). Civil engineering (General), TA1-2040

File Description: electronic resource

Relation: http://www.sciencedirect.com/science/article/pii/S1110016825002571; https://doaj.org/toc/1110-0168

Access URL: https://doaj.org/article/55d8a9aa6e80455595b7595918032d9b

Optimization methods in inverse problems and applications to science and engineering

Authors: D. La Torre M. Ruiz Galán Herb Kunze

Source: Optimization and Engineering. 22:2151-2158

Subject Terms: Fractals, Inverse problems involving ordinary differential equations, 0211 other engineering and technologies, 0202 electrical engineering, electronic engineering, information engineering, Numerical solution to inverse problems in abstract spaces, 02 engineering and technology, Variational inequalities, Numerical solution of inverse problems involving ordinary differential equations, Numerical analysis

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Access URL: https://link.springer.com/content/pdf/10.1007/s11081-021-09688-y.pdf
https://link.springer.com/content/pdf/10.1007/s11081-021-09688-y.pdf
https://link.springer.com/article/10.1007/s11081-021-09688-y

A rotation total variation regularization for full waveform inversion

Authors: Faxuan Wu Qinglong He Jiangyan Zou et al.

Source: Journal of Inverse and Ill-posed Problems.

Subject Terms: full waveform inversion, inverse problems, rotation TV regularization, Numerical solution to inverse problems in abstract spaces, CGOPT algorithm, acoustic wave equation

File Description: application/xml

Access URL: https://zbmath.org/8025007
https://doi.org/10.1515/jiip-2022-0067

Numerical Solution of Inverse Scattering Problems with Multi-experimental Limited Aperture Data: Numerical solution of inverse scattering problems with multi-experimental limited aperture data

Authors: Gang Bao Jun Liu

Source: SIAM Journal on Scientific Computing. 25:1102-1117

Subject Terms: Hilbert spaces, smooth nonlinear operator, Numerical solutions to equations with nonlinear operators, Nonlinear ill-posed problems, Numerical solution to inverse problems in abstract spaces, global minimum, multiple data, 01 natural sciences, global convergence, inverse medium problems, Inverse problems (including inverse scattering) in optics and electromagnetic theory, homotopy continuation, limited aperture, 0101 mathematics, recursive linearization

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Access URL: https://zbmath.org/2030260
https://doi.org/10.1137/s1064827502409705

Convergence of non-linear diagonal frame filtering for regularizing inverse problems

Authors: Andrea Ebner Markus Haltmeier

Source: Inverse Problems. 40:055009

Subject Terms: Signal theory (characterization, reconstruction, filtering, etc.), Linear operators and ill-posed problems, regularization, Numerical solutions of ill-posed problems in abstract spaces, regularization, Tikhonov regularization, Hilbert space, singular value decomposition, linear inverse problem, Numerical solution to inverse problems in abstract spaces, General harmonic expansions, frames, Numerical Analysis (math.NA), 01 natural sciences, Bregman distance, diagonal frame decomposition, FOS: Mathematics, plug-and-play regularization, Mathematics - Numerical Analysis, 0101 mathematics, non-linear frame-based filtering

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Access URL: http://arxiv.org/abs/2308.15666

Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems

Authors: Freitag, Melina A Hofmann, B

Source: Freitag, M A & Hofmann, B 2005, 'Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems', Journal of Inverse and Ill-posed Problems, vol. 13, no. 2, pp. 123-148. https://doi.org/10.1515/1569394053978524

Subject Terms: Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, Tikhonov regularization, name=Applied Mathematics, Numerical solution to inverse problems in abstract spaces, compact operator, ill-posed problem, multiplication operators, 01 natural sciences, Nemytskij operator, linear operator equations, Numerical solutions to equations with linear operators, 0101 mathematics

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Access URL: https://purehost.bath.ac.uk/ws/files/141101243/endversion.pdf
https://zbmath.org/2204565
https://doi.org/10.1515/1569394053978524
https://purehost.bath.ac.uk/ws/files/141101243/endversion.pdf
https://researchportal.bath.ac.uk/en/publications/analytical-and-numerical-studies-on-the-influence-of-multiplicati
https://core.ac.uk/display/2810776

On an inverse problem: Recovery of non-smooth solutions to backward heat equation: On an inverse problem: recovery of non-smooth solutions to backward heat equation

Authors: Oscar Orellana Prabir Daripa Fabien Ternat

Source: Applied Mathematical Modelling. 36:4003-4019

Subject Terms: non-smooth solutions, heat equation, quasi-reversibility techniques, inverse problem, Numerical solution to inverse problems in abstract spaces, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, illposed problem, 0101 mathematics, finite difference methods, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/6114239
https://doi.org/10.1016/j.apm.2011.11.020
http://math.tamu.edu/~prabir.daripa/pubs/reprints/amm-2012.pdf
https://www.sciencedirect.com/science/article/pii/S0307904X11007086

Solving the acousto-electric tomography by the adaptive Nesterov method of Kaczmarz type

Authors: Kai Zhu Min Zhong

Source: Inverse Problems. 41:035007

Subject Terms: Biomedical imaging and signal processing, Numerical aspects of computer graphics, image analysis, and computational geometry, non-smooth penalty, iterative regularization, Numerical solution to inverse problems in abstract spaces, acousto-electric tomography

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Access URL: https://zbmath.org/7988277
https://doi.org/10.1088/1361-6420/adb3c4

Adaptive Wavelet Galerkin Methods for Linear Inverse Problems: Adaptive wavelet Galerkin methods for linear inverse problems

Authors: Cohen, Albert Hoffmann, Marc Reiß, Markus

Source: SIAM Journal on Numerical Analysis. 42:1479-1501

Subject Terms: nonlinear methods, ddc:330, 330 Wirtschaft, Numerical solution to inverse problems in abstract spaces, Numerical methods for integral equations, wavelets, 01 natural sciences, Galerkin methods, numerical example, Numerical solutions to equations with linear operators, Besov spaces, Numerical methods for wavelets, statistical inverse problems, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), 0101 mathematics, minimax estimation, singular integral equation, Equations and inequalities involving linear operators, with vector unknowns

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Access URL: https://edoc.hu-berlin.de/bitstream/18452/4148/1/50.pdf
https://zbmath.org/2139932
https://doi.org/10.1137/s0036142902411793
http://hdl.handle.net/10419/65296
https://www.econstor.eu/bitstream/10419/65296/1/726723541.pdf

A note on quasi-maximum likelihood solutions to an inverse problem for Poisson processes: A note on quasi-maximum likelihood solutions to an inverse problem for Poisson processes.

Authors: Zbigniew Szkutnik

Source: Statistics & Probability Letters. 60:253-263

Subject Terms: 0502 economics and business, 05 social sciences, Quasi-maximum likelihood, Numerical solution to inverse problems in abstract spaces, Point processes (e.g., Poisson, Cox, Hawkes processes), Poisson process, Intensity function, Unfolding, 0101 mathematics, Non-Markovian processes: estimation, 01 natural sciences, Discretization

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Access URL: https://zbmath.org/1907001
https://doi.org/10.1016/s0167-7152(02)00269-9
https://www.sciencedirect.com/science/article/abs/pii/S0167715202002699
https://econpapers.repec.org/RePEc:eee:stapro:v:60:y:2002:i:3:p:253-263
https://econpapers.repec.org/article/eeestapro/v_3a60_3ay_3a2002_3ai_3a3_3ap_3a253-263.htm
https://ideas.repec.org/a/eee/stapro/v60y2002i3p253-263.html

Replica Exchange Preconditioned Crank-Nicolson Langevin Dynamic MCMC Method with Multi-Variance Strategy for Bayesian Inverse Problems: A replica exchange preconditioned Crank-Nicolson Langevin dynamic MCMC method with multi-variance strategy for Bayesian inverse problems

Authors: Na Ou Zecheng Zhang Guang Lin

Source: Journal of Computational Physics. 510:113067

Subject Terms: Bayesian inverse problem, preconditioned Crank-Nicolson scheme, Numerical solution to inverse problems in abstract spaces, Numerical analysis or methods applied to Markov chains, Langevin diffusion, replica exchange Monte Carlo

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Access URL: https://zbmath.org/8021033
https://doi.org/10.1016/j.jcp.2024.113067

Projection based summation-by-parts methods, embeddings and the pseudoinverse

Authors: Pelle Olsson Gustav Eriksson Ken Mattsson

Source: Journal of Computational Physics. 524:113689

Subject Terms: high-order accuracy, Beräkningsmatematik, projection method, Numerical solution to inverse problems in abstract spaces, stability, High-order accuracy, Computational Mathematics, Finite difference methods, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Projection method, boundary treatment, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Stability, finite difference methods, Boundary treatment

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Access URL: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-546211

Uncertainty quantification for DeepONets with ensemble Kalman inversion: Uncertainty quantification for DeepONet with ensemble Kalman inversion

Authors: Andrew Pensoneault Xueyu Zhu

Source: Journal of Computational Physics. 523:113670

Subject Terms: FOS: Computer and information sciences, Computer Science - Machine Learning, uncertainty quantification, Computer Science - Artificial Intelligence, Numerical solution to inverse problems in abstract spaces, Machine Learning (stat.ML), Numerical Analysis (math.NA), Inference from stochastic processes and prediction, ensemble Kalman inversion, Machine Learning (cs.LG), operator learning, Artificial Intelligence (cs.AI), Statistics - Machine Learning, FOS: Mathematics, Mathematics - Numerical Analysis, Artificial neural networks and deep learning

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Access URL: http://arxiv.org/abs/2403.03444
https://zbmath.org/7986892
https://doi.org/10.1016/j.jcp.2024.113670

Tubenet: A Special Trumpetnet for Explicit Solutions to Inverse Problems: TubeNet: a special TrumpetNet for explicit solutions to inverse problems

Authors: Gui-Rong Liu Shuyong Duan Zhang Zhanming et al.

Source: International Journal of Computational Methods. 18:2050030

Subject Terms: 0211 other engineering and technologies, Numerical solution to inverse problems in abstract spaces, 02 engineering and technology, artificial intelligence, 16. Peace & justice, parametric inverse problems, 01 natural sciences, data-driven method, mechanics of composites, Trumpet neural net, deepnets, physic-law-based method, 0101 mathematics, Artificial neural networks and deep learning, TrumpetNet

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Access URL: https://zbmath.org/7342029
https://doi.org/10.1142/s0219876220500309
https://www.worldscientific.com/doi/abs/10.1142/S0219876220500309

On some inverse problems for distributed parameter systems

Authors: V. I. Agoshkov

Source: Russian Journal of Numerical Analysis and Mathematical Modelling. 18:455-465

Subject Terms: Hilbert spaces, Numerical optimization and variational techniques, convergence, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, numerical algorithms, Numerical solution to inverse problems in abstract spaces, distributed parameter systems, 01 natural sciences, Banach spaces, optimal control, Inverse problems in optimal control, Existence theories for problems in abstract spaces, 0101 mathematics

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Access URL: https://zbmath.org/2051997
https://doi.org/10.1515/156939803322681130
https://www.degruyter.com/view/j/rnam.2003.18.issue-6/156939803322681130/156939803322681130.pdf
http://www.ingentaselect.com/rpsv/cgi-bin/cgi?ini=xref&body=linker&reqdoi=10.1163/156939803322681130

Efficient algorithms for the regularization of dynamic inverse problems: I. Theory: Efficient algorithms for the regularization of dynamic inverse problems. I: Theory

Authors: Alfred K. Louis Uwe Schmitt

Source: Inverse Problems. 18:645-658

Subject Terms: Hilbert spaces, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, dynamic inverse problem, measuring process, static inverse problem, Numerical solution to inverse problems in abstract spaces, Tikhonov Phillips method, 02 engineering and technology, regularizing algorithms, 01 natural sciences, linear operator equations, Numerical solutions to equations with linear operators, projection methods, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Equations and inequalities involving linear operators, with vector unknowns

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Access URL: https://zbmath.org/1787294
https://doi.org/10.1088/0266-5611/18/3/308
http://ui.adsabs.harvard.edu/abs/2002InvPr..18..645S/abstract
http://iopscience.iop.org/article/10.1088/0266-5611/18/3/308/pdf

An improved model function method for choosing regularization parameters in linear inverse problems

Authors: Jun Zou Jianli Xie

Source: Inverse Problems. 18:631-643

Subject Terms: Hilbert spaces, Linear operators and ill-posed problems, regularization, Tikhonov regularization, linear inverse problems, Numerical solution to inverse problems in abstract spaces, 01 natural sciences, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, damped discrepancy principle, model function method, a posteriori parameter choice strategies, Numerical solutions to equations with linear operators, linear ill-posed problems, 0101 mathematics, regularization method

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Access URL: https://zbmath.org/1787293
https://doi.org/10.1088/0266-5611/18/3/307
https://iopscience.iop.org/article/10.1088/0266-5611/18/3/307/pdf
http://ui.adsabs.harvard.edu/abs/2002InvPr..18..631X/abstract
https://iopscience.iop.org/article/10.1088/0266-5611/18/3/307

An iterative thresholding algorithm for linear inverse problems with a sparsity constraint

Authors: Daubechies, Ingrid Defrise, Michel De Mol, Christine et al.

Contributors: Daubechies, Ingrid Defrise, Michel De Mol, Christine et al.

Source: Communications on Pure and Applied Mathematics. 57:1413-1457

Subject Terms: Analyse fonctionnelle, Numerical solutions of ill-posed problems in abstract spaces, regularization, thresholding, Numerical solution to inverse problems in abstract spaces, Nontrigonometric harmonic analysis involving wavelets and other special systems, ill-posed problem, 02 engineering and technology, wavelets, Numerical solutions to equations with linear operators, Numerical methods for wavelets, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Mathematics - Numerical Analysis, nonquadratic constraints, Equations intégrales, iterative algorithm, convergence, Linear operators and ill-posed problems, regularization, linear inverse problems, Hilbert space, Numerical Analysis (math.NA), stability, 16. Peace & justice, Functional Analysis (math.FA), Mathematics - Functional Analysis, Analyse harmonique, Mathématiques, generalization of the Tikhonov method, sparse extension

File Description: application/xml; 1 full-text file(s): application/pdf

Access URL: http://arxiv.org/pdf/math/0307152
http://arxiv.org/abs/math/0307152
https://onlinelibrary.wiley.com/doi/10.1002/cpa.20042
https://core.ac.uk/display/8850482
https://www.arxiv-vanity.com/papers/math/0307152/
https://math.duke.edu/~ingrid/publications/Comm_Pure_Appl_Math_57.pdf
http://math.duke.edu/~ingrid/publications/Comm_Pure_Appl_Math_57.pdf
https://difusion.ulb.ac.be/vufind/Record/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/50535/Details
https://biblio.vub.ac.be/vubir/an-iterative-thresholding-algorithm-for-linear-inverse-problems-with-a-sparsity-constraint(f957882f-5b1e-4f3b-a045-0468093903f1).html

Efficient algorithms for the regularization of dynamic inverse problems: II. Applications: Efficient algorithms for the regularization of dynamic inverse problems. II: Applications

Authors: Schmitt, U. Louis, A. Wolters, C. et al.

Source: Inverse Problems

Subject Terms: Biomedical imaging and signal processing, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, electrical impedance problem, Numerical solution to inverse problems in abstract spaces, regularizing algorithms, 01 natural sciences, dynamic inverse problems, density reconstruction, ill-posed problems, computational methods, 03 medical and health sciences, 0302 clinical medicine, Numerical solutions to equations with linear operators, statistical methods, Inverse problems (including inverse scattering) in optics and electromagnetic theory, computerized tomography, 0101 mathematics, Kalman filters, Equations and inequalities involving linear operators, with vector unknowns

File Description: application/xml; application/pdf

Access URL: https://pure.mpg.de/pubman/item/item_721912_5/component/file_721911/schmitt.pdf
https://zbmath.org/1787295
https://doi.org/10.1088/0266-5611/18/3/309
https://pure.mpg.de/pubman/item/item_721912_5/component/file_721911/schmitt.pdf
https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_721912
http://pubman.mpdl.mpg.de/pubman/item/escidoc:721912
http://ui.adsabs.harvard.edu/abs/2002InvPr..18..659S/abstract
https://iopscience.iop.org/article/10.1088/0266-5611/18/3/309
https://core.ac.uk/display/45689193
http://hdl.handle.net/11858/00-001M-0000-0010-AF20-9
http://hdl.handle.net/11858/00-001M-0000-0010-AF21-7