English
Related papers

Related papers: Variational Regularization of Inverse Problems for…

200 papers

Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and…

Computer Vision and Pattern Recognition · Computer Science 2019-04-08 Wenqi Lu , Jinming Duan , David Orive-Miguel , Lionel Herve , Iain B Styles

We propose an unsupervised approach for learning end-to-end reconstruction operators for ill-posed inverse problems. The proposed method combines the classical variational framework with iterative unrolling, which essentially seeks to…

Computer Vision and Pattern Recognition · Computer Science 2021-06-08 Subhadip Mukherjee , Marcello Carioni , Ozan Öktem , Carola-Bibiane Schönlieb

We extend a recently introduced deep unrolling framework for learning spatially varying regularisation parameters in inverse imaging problems to the case of Total Generalised Variation (TGV). The framework combines a deep convolutional…

Computer Vision and Pattern Recognition · Computer Science 2025-03-07 Thanh Trung Vu , Andreas Kofler , Kostas Papafitsoros

Given a multi-input, nonlinear, time-invariant, control-affine system and a controlled invariant, closed, embedded submanifold $\mathsf{N}$, the local transverse feedback linearization (TFL) problem seeks a coordinate and feedback…

Optimization and Control · Mathematics 2022-04-29 Rollen S. D'Souza , Christopher Nielsen

Regularization is critical for solving ill-posed geophysical inverse problems. Explicit regularization is often used, but there are opportunities to explore the implicit regularization effects that are inherent in a Neural Network…

Machine Learning · Computer Science 2024-07-10 Anran Xu , Lindsey J. Heagy

We consider linear inverse problems that are formulated in the continuous domain. The object of recovery is a function that is assumed to minimize a convex objective functional. The solutions are constrained by imposing a continuous-domain…

Information Theory · Computer Science 2018-08-15 Harshit Gupta , Julien Fageot , Michael Unser

Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our…

Information Theory · Computer Science 2016-01-05 Ulugbek S. Kamilov

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

Optimization and Control · Mathematics 2021-11-10 Andreas Habring , Martin Holler

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…

Statistics Theory · Mathematics 2025-10-22 Jonathan Chirinos Rodriguez , Ernesto De Vito , Cesare Molinari , Lorenzo Rosasco , Silvia Villa

In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing…

Numerical Analysis · Mathematics 2020-04-28 Kha Van Huynh , Barbara Kaltenbacher

Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational…

Machine Learning · Computer Science 2021-08-04 Minh-Ngoc Tran , Dang H. Nguyen , Duy Nguyen

The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…

Optimization and Control · Mathematics 2025-06-24 Clemens Kirisits , Bochra Mejri , Sergei Pereverzev , Otmar Scherzer , Cong Shi

In this paper, regularized lightweight deep convolutional neural network models, capable of effectively operating in real-time on devices with restricted computational power for high-resolution video input are proposed. Furthermore, a novel…

Computer Vision and Pattern Recognition · Computer Science 2021-08-27 Maria Tzelepi , Anastasios Tefas

The concept of generalized cross-validation (GCV) is applied to modified total generalized variation (MTGV) regularization. Current implementations of the MTGV regularization rely on manual (or semi-manual) hyperparameter optimization,…

In this work, we propose Regularization-by-Equivariance (REV), a novel structure-adaptive regularization scheme for solving imaging inverse problems under incomplete measurements. This regularization scheme utilizes the equivariant…

Optimization and Control · Mathematics 2022-02-15 Junqi Tang

Modeling data using manifold values is a powerful concept with numerous advantages, particularly in addressing nonlinear phenomena. This approach captures the intrinsic geometric structure of the data, leading to more accurate descriptors…

Numerical Analysis · Mathematics 2025-07-08 Wael Mattar , Nir Sharon

Total Variation (TV) based regularization has been widely applied in restoration problems due to its simple derivative filters based formulation and robust performance. While first order TV suffers from staircase effect, second order TV…

Signal Processing · Electrical Eng. & Systems 2019-04-08 Sanjay Viswanath , Muthuvel Arigovindan

In this paper we propose and study a novel optimal transport based regularization of linear dynamic inverse problems. The considered inverse problems aim at recovering a measure valued curve and are dynamic in the sense that (i) the…

Functional Analysis · Mathematics 2023-04-26 Kristian Bredies , Silvio Fanzon

We consider a class of regularization methods for inverse problems where a coupled regularization is employed for the simultaneous reconstruction of data from multiple sources. Applications for such a setting can be found in multi-spectral…

Optimization and Control · Mathematics 2018-08-01 Martin Holler , Richard Huber , Florian Knoll

Can regularization terms in the training of invertible neural networks lead to known Bayesian point estimators in reconstruction? Invertible networks are attractive for inverse problems due to their inherent stability and interpretability.…

Machine Learning · Computer Science 2025-10-31 Nick Heilenkötter