Computational methods for large-scale inverse problems: a survey on hybrid projection methods

J Chung, S Gazzola - Siam Review, 2024 - SIAM
This paper surveys an important class of methods that combine iterative projection methods
and variational regularization methods for large-scale inverse problems. Iterative methods …

A variable projection method for large-scale inverse problems with ℓ1 regularization

M Chung, RA Renaut - Applied Numerical Mathematics, 2023 - Elsevier
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 …

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 …

Goal-oriented Uncertainty Quantification for Inverse Problems via Variational Encoder-Decoder Networks

BM Afkham, J Chung, M Chung - arXiv preprint arXiv:2304.08324, 2023 - arxiv.org
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 …

Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks

B Afkham, J Chung, M Chung - Inverse Problems, 2024 - iopscience.iop.org
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 …

Robust estimation of structural orientation parameters and 2D/3D local anisotropic Tikhonov regularization

A Gholami, S Gazzola - Geophysics, 2024 - library.seg.org
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 variable projected augmented Lagrangian method

M Chung, R Renaut - arXiv preprint arXiv:2207.08216, 2022 - arxiv.org
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 …

Automatic nonstationary anisotropic Tikhonov regularization through bilevel optimization

S Gazzola, A Gholami - arXiv preprint arXiv:2406.02209, 2024 - arxiv.org
Regularization techniques are necessary to compute meaningful solutions to discrete ill-
posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped …

Recycling MMGKS for large-scale dynamic and streaming data

M Pasha, E de Sturler, ME Kilmer - arXiv preprint arXiv:2309.15759, 2023 - arxiv.org
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 …

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 …