Computational methods for large-scale inverse problems: a survey on hybrid projection methods
This paper surveys an important class of methods that combine iterative projection methods
and variational regularization methods for large-scale inverse problems. Iterative methods …
and variational regularization methods for large-scale inverse problems. Iterative methods …
A variable projection method for large-scale inverse problems with ℓ1 regularization
Inference by means of mathematical modeling from a collection of observations remains a
crucial tool for scientific discovery and is ubiquitous in application areas such as signal …
crucial tool for scientific discovery and is ubiquitous in application areas such as signal …
On optimal regularization parameters via bilevel learning
MJ Ehrhardt, S Gazzola, SJ Scott - arXiv preprint arXiv:2305.18394, 2023 - arxiv.org
Variational regularization is commonly used to solve linear inverse problems, and involves
augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori …
augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori …
Goal-oriented Uncertainty Quantification for Inverse Problems via Variational Encoder-Decoder Networks
In this work, we describe a new approach that uses variational encoder-decoder (VED)
networks for efficient goal-oriented uncertainty quantification for inverse problems. Contrary …
networks for efficient goal-oriented uncertainty quantification for inverse problems. Contrary …
Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks
In this work, we describe a new approach that uses variational encoder-decoder (VED)
networks for efficient uncertainty quantification for goal-oriented inverse problems. Contrary …
networks for efficient uncertainty quantification for goal-oriented inverse problems. Contrary …
Robust estimation of structural orientation parameters and 2D/3D local anisotropic Tikhonov regularization
Understanding the orientation of geologic structures is crucial for analyzing the complexity of
the earths' subsurface. For instance, information about geologic structure orientation can be …
the earths' subsurface. For instance, information about geologic structure orientation can be …
The variable projected augmented Lagrangian method
Inference by means of mathematical modeling from a collection of observations remains a
crucial tool for scientific discovery and is ubiquitous in application areas such as signal …
crucial tool for scientific discovery and is ubiquitous in application areas such as signal …
Automatic nonstationary anisotropic Tikhonov regularization through bilevel optimization
Regularization techniques are necessary to compute meaningful solutions to discrete ill-
posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped …
posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped …
Recycling MMGKS for large-scale dynamic and streaming data
Reconstructing high-quality images with sharp edges requires the use of edge-preserving
constraints in the regularized form of the inverse problem. The use of the $\ell_q $-norm on …
constraints in the regularized form of the inverse problem. The use of the $\ell_q $-norm on …
The image deblurring problem: Matrices, wavelets, and multilevel methods
D Austin, MI Español, M Pasha - Notices of the American Mathematical …, 2022 - ams.org
After the launch of the Hubble Space Telescope in 1990, astronomers were gravely
disappointed by the quality of the images as they began to arrive. Due to miscalibrated …
disappointed by the quality of the images as they began to arrive. Due to miscalibrated …