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We propose a new method that uses deep learning techniques to solve the inverse problems. The inverse problem is cast in the form of learning an end-to-end mapping from observed data to the ground-truth. Inspired by the splitting strategy…

Computer Vision and Pattern Recognition · Computer Science 2017-12-04 Kai Fan , Qi Wei , Wenlin Wang , Amit Chakraborty , Katherine Heller

Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have…

Optimization and Control · Mathematics 2022-11-28 Zhuo-Xu Cui , Qingyong Zhu , Jing Cheng , Dong Liang

Variational regularization methods are commonly used to approximate solutions of inverse problems. In recent years, model-based variational regularization methods have often been replaced with data-driven ones such as the fields-of-expert…

Optimization and Control · Mathematics 2024-01-17 Danilo Riccio , Matthias J. Ehrhardt , Martin Benning

Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…

Machine Learning · Computer Science 2024-02-08 Moshe Eliasof , Eldad Haber , Eran Treister

This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…

Machine Learning · Computer Science 2021-12-10 Martin Burger

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

Recently, a large number of efficient deep learning methods for solving inverse problems have been developed and show outstanding numerical performance. For these deep learning methods, however, a solid theoretical foundation in the form of…

Numerical Analysis · Mathematics 2020-02-04 Daniel Obmann , Johannes Schwab , Markus Haltmeier

In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven…

Machine Learning · Statistics 2023-01-31 Jonathan Scarlett , Reinhard Heckel , Miguel R. D. Rodrigues , Paul Hand , Yonina C. Eldar

The solution of inverse problems is crucial in various fields such as medicine, biology, and engineering, where one seeks to find a solution from noisy observations. These problems often exhibit non-uniqueness and ill-posedness, resulting…

Numerical Analysis · Mathematics 2024-10-21 Markus Haltmeier , Richard Kowar , Markus Tiefenthaler

Deep learning and (deep) neural networks are emerging tools to address inverse problems and image reconstruction tasks. Despite outstanding performance, the mathematical analysis for solving inverse problems by neural networks is mostly…

Numerical Analysis · Mathematics 2019-10-01 Johannes Schwab , Stephan Antholzer , Markus Haltmeier

While deep learning methods have achieved state-of-the-art performance in many challenging inverse problems like image inpainting and super-resolution, they invariably involve problem-specific training of the networks. Under this approach,…

Computer Vision and Pattern Recognition · Computer Science 2017-03-30 J. H. Rick Chang , Chun-Liang Li , Barnabas Poczos , B. V. K. Vijaya Kumar , Aswin C. Sankaranarayanan

In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…

Machine Learning · Computer Science 2025-03-12 Moshe Eliasof , Md Shahriar Rahim Siddiqui , Carola-Bibiane Schönlieb , Eldad Haber

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

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…

Computational Physics · Physics 2021-10-22 Feng Wang , Alberto Eljarrat , Johannes Müller , Trond Henninen , Erni Rolf , Christoph Koch

We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…

This paper proposes a new way of regularizing an inverse problem in imaging (e.g., deblurring or inpainting) by means of a deep generative neural network. Compared to end-to-end models, such approaches seem particularly interesting since…

Computer Vision and Pattern Recognition · Computer Science 2021-01-22 Thomas Oberlin , Mathieu Verm

Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…

Numerical Analysis · Mathematics 2026-05-26 Sandra R. Babyale , Jodi Mead

In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…

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

The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images.…

Image and Video Processing · Electrical Eng. & Systems 2021-06-01 Marija Vella , João F. C. Mota

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…

Image and Video Processing · Electrical Eng. & Systems 2020-06-29 Chang Min Hyun , Seong Hyeon Baek , Mingyu Lee , Sung Min Lee , Jin Keun Seo