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Related papers: Inverse Problems with Learned Forward Operators

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In this work we deal with parametric inverse problems, which consist in recovering a finite number of parameters describing the structure of an unknown object, from indirect measurements. State-of-the-art methods for approximating a…

Numerical Analysis · Mathematics 2021-12-22 Paolo Massa , Sara Garbarino , Federico Benvenuto

Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as…

Computer Vision and Pattern Recognition · Computer Science 2024-03-29 Zhenghan Fang , Sam Buchanan , Jeremias Sulam

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…

Numerical Analysis · Mathematics 2015-06-19 Julianne Chung , Matthias Chung

We consider solving ill-posed imaging inverse problems without access to an explicit image prior or ground-truth examples. An overarching challenge in inverse problems is that there are many undesired images that fit to the observed…

Image and Video Processing · Electrical Eng. & Systems 2023-03-23 Angela F. Gao , Oscar Leong , He Sun , Katherine L. Bouman

In the past few years, deep learning-based methods have demonstrated enormous success for solving inverse problems in medical imaging. In this work, we address the following question:\textit{Given a set of measurements obtained from real…

Image and Video Processing · Electrical Eng. & Systems 2019-05-24 Ortal Senouf , Sanketh Vedula , Tomer Weiss , Alex Bronstein , Oleg Michailovich , Michael Zibulevsky

Inverse problems describe the task of recovering an underlying signal of interest given observables. Typically, the observables are related via some non-linear forward model applied to the underlying unknown signal. Inverting the non-linear…

Signal Processing · Electrical Eng. & Systems 2023-05-19 Jihui Jin , Etienne Ollivier , Richard Touret , Matthew McKinley , Karim G. Sabra , Justin K. Romberg

Learning-based methods have demonstrated remarkable performance in solving inverse problems, particularly in image reconstruction tasks. Despite their success, these approaches often lack theoretical guarantees, which are crucial in…

Numerical Analysis · Mathematics 2025-10-21 Clemens Arndt , Judith Nickel

Deep learning-based methods have revolutionized the field of imaging inverse problems, yielding state-of-the-art performance across various imaging domains. The best performing networks incorporate the imaging operator within the network…

Computer Vision and Pattern Recognition · Computer Science 2026-01-06 Romain Vo , Julián Tachella

Inverse problems challenge existing neural operator architectures because ill-posed inverse maps violate continuity, uniqueness, and stability assumptions. We introduce B2B${}^{-1}$, an inverse basis-to-basis neural operator framework that…

Machine Learning · Computer Science 2025-12-23 Adam J. Thorpe , Stepan Tretiakov , Dibakar Roy Sarkar , Krishna Kumar , Ufuk Topcu

In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of…

Numerical Analysis · Mathematics 2021-01-26 S. Kindermann , A. Leitao

The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the…

Numerical Analysis · Mathematics 2019-01-30 Martin Burger , Yury Korolev , Julian Rasch

Inverse problems are important mathematical problems that seek to recover model parameters from noisy data. Since inverse problems are often ill-posed, they require regularization or incorporation of prior information about the underlying…

Numerical Analysis · Mathematics 2026-02-09 Oluwatosin Akande , Gabriel P. Langlois , Akwum Onwunta

Inverse problems, where in broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific…

Methodology · Statistics 2017-07-24 Debashis Chatterjee , Sourabh Bhattacharya

Learned optimizers are algorithms that can themselves be trained to solve optimization problems. In contrast to baseline optimizers (such as momentum or Adam) that use simple update rules derived from theoretical principles, learned…

Machine Learning · Computer Science 2021-12-09 Niru Maheswaranathan , David Sussillo , Luke Metz , Ruoxi Sun , Jascha Sohl-Dickstein

Solving an ill-posed linear inverse problem requires knowledge about the underlying signal model. In many applications, this model is a priori unknown and has to be learned from data. However, it is impossible to learn the model using…

Machine Learning · Statistics 2024-10-22 Julián Tachella , Dongdong Chen , Mike Davies

Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…

Optimization and Control · Mathematics 2024-10-10 Houra Mahmoudzadeh , Kimia Ghobadi

Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying…

Computer Vision and Pattern Recognition · Computer Science 2019-01-14 Sebastian Lunz , Ozan Öktem , Carola-Bibiane Schönlieb

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…

Numerical Analysis · Mathematics 2018-01-31 Martin Benning , Martin Burger

Machine Learning (ML) methods and tools have gained great success in many data, signal, image and video processing tasks, such as classification, clustering, object detection, semantic segmentation, language processing, Human-Machine…

Machine Learning · Computer Science 2023-09-06 Ali Mohammad-Djafari , Ning Chu , Li Wang , Liang Yu

We present a framework which enables the analysis of dynamic inverse problems for wave phenomena that are modeled through second-order hyperbolic PDEs. This includes well-posedness and regularity results for the forward operator in an…

Analysis of PDEs · Mathematics 2020-02-19 Thies Gerken