On Learned Operator Correction in Inverse Problems

DOI10.1137/20M1338460zbMath1474.65182arXiv2005.07069OpenAlexW3122711257MaRDI QIDQ5860277

Sebastian Lunz, Andreas Hauptmann, Tanja Tarvainen, Carola-Bibiane Schönlieb, Simon R. Arridge

Publication date: 19 November 2021

Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.07069

zbMATH Keywords

inverse problemsvariational methodsdeep learningphotoacoustic tomographymodel correctionoperator learning

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Ill-posedness and regularization problems in numerical linear algebra (65F22) Numerical optimization and variational techniques (65K10) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Linear operators and ill-posed problems, regularization (47A52)

Related Items (10)

Operator Shifting for General Noisy Matrix Systems ⋮ On global normal linear approximations for nonlinear Bayesian inverse problems ⋮ Learning and correcting non-Gaussian model errors ⋮ Deep learning for inverse problems. Abstracts from the workshop held March 7--13, 2021 (hybrid meeting) ⋮ Divide-and-conquer DNN approach for the inverse point source problem using a few single frequency measurements ⋮ In focus -- hybrid deep learning approaches to the HDC2021 challenge ⋮ Operator shifting for noisy elliptic systems ⋮ Sequential Model Correction for Nonlinear Inverse Problems ⋮ Utilizing Variational Autoencoders in the Bayesian Inverse Problem of Photoacoustic Tomography ⋮ Proximal nested sampling for high-dimensional Bayesian model selection

Uses Software

• k-Wave
• U-Net
• DeepAdverserialRegulariser
• NETT

Cites Work

• Statistical and computational inverse problems.
• Less is often more: applied inverse problems using \(hp\)-forward models
• Statistical inverse problems: discretization, model reduction and inverse crimes
• Bayesian Calibration of Computer Models
• Approximation errors and model reduction with an application in optical diffusion tomography
• Mathematics of thermoacoustic tomography
• Model reduction methods based on Krylov subspaces
• Solving ill-posed inverse problems using iterative deep neural networks
• Deep Convolutional Neural Network for Inverse Problems in Imaging
• Convergence rates and structure of solutions of inverse problems with imperfect forward models
• Deep null space learning for inverse problems: convergence analysis and rates
• Image Reconstruction with Imperfect Forward Models and Applications in Deblurring
• Deep learning for photoacoustic tomography from sparse data
• Reduced order models for spectral domain inversion: embedding into the continuous problem and generation of internal data
• NETT: solving inverse problems with deep neural networks
• Parameter identification in a structured population model
• Solving inverse problems using data-driven models
• Identification of Chemotaxis Models with Volume-Filling
• Learning the invisible: a hybrid deep learning-shearlet framework for limited angle computed tomography

This page was built for publication: On Learned Operator Correction in Inverse Problems