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Related papers: Augmented NETT Regularization of Inverse Problems

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An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how…

Machine Learning · Computer Science 2023-11-06 Zakhar Shumaylov , Jeremy Budd , Subhadip Mukherjee , Carola-Bibiane Schönlieb

Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…

Numerical Analysis · Mathematics 2020-06-09 Markus Haltmeier , Linh V. Nguyen

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in reconstruction quality. Unfortunately, these new methods often lack reliability and explainability, and there is a…

Image and Video Processing · Electrical Eng. & Systems 2023-08-28 Alexis Goujon , Sebastian Neumayer , Pakshal Bohra , Stanislas Ducotterd , Michael Unser

Regularization techniques are necessary to compute meaningful solutions to discrete ill-posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped with a discretization of the gradient operator as regularization…

Numerical Analysis · Mathematics 2024-06-05 Silvia Gazzola , Ali Gholami

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…

Numerical Analysis · Mathematics 2021-04-15 Babak Maboudi Afkham , Julianne Chung , Matthias Chung

Solving ill-posed inverse problems necessitates effective regularization strategies to stabilize the inversion process against measurement noise. While classical methods like Tikhonov regularization require heuristic parameter tuning, and…

Machine Learning · Statistics 2026-03-24 Hang-Cheng Dong , Pengcheng Cheng , Shuhuan Li

The standard approach for dealing with the ill-posedness of the training problem in machine learning and/or the reconstruction of a signal from a limited number of measurements is regularization. The method is applicable whenever the…

Optimization and Control · Mathematics 2020-07-13 Michael Unser

These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…

Numerical Analysis · Mathematics 2025-08-26 Danielle Bednarski , Tim Roith

Recently, caption generation with an encoder-decoder framework has been extensively studied and applied in different domains, such as image captioning, code captioning, and so on. In this paper, we propose a novel architecture, namely…

Computer Vision and Pattern Recognition · Computer Science 2018-04-10 Xinpeng Chen , Lin Ma , Wenhao Jiang , Jian Yao , Wei Liu

The Deep neural networks (DNNs) have achieved great success on a variety of computer vision tasks, however, they are highly vulnerable to adversarial attacks. To address this problem, we propose to improve the local smoothness of the…

Computer Vision and Pattern Recognition · Computer Science 2019-09-23 Yaoyao Zhong , Weihong Deng

These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…

Functional Analysis · Mathematics 2021-02-09 Christian Clason

In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy…

Statistics Theory · Mathematics 2024-04-09 Abhishake Rastogi

Incorporating prior knowledge or specifications of input-output relationships into machine learning models has attracted significant attention, as it enhances generalization from limited data and yields conforming outputs. However, most…

Machine Learning · Computer Science 2025-10-21 Youngjae Min , Navid Azizan

We construct custom regularization functions for use in supervised training of deep neural networks. Our technique is applicable when the ground-truth labels themselves exhibit internal structure; we derive a regularizer by learning an…

Computer Vision and Pattern Recognition · Computer Science 2018-04-09 Mohammadreza Mostajabi , Michael Maire , Gregory Shakhnarovich

Predicting distant future trajectories of agents in a dynamic scene is not an easy problem because the future trajectory of an agent is affected by not only his/her past trajectory but also the scene contexts. To tackle this problem, we…

Computer Vision and Pattern Recognition · Computer Science 2020-03-11 Dooseop Choi , Kyoungwook Min , Jeongdan Choi

State-of-the-art image reconstruction often relies on complex, highly parameterized deep architectures. We propose an alternative: a data-driven reconstruction method inspired by the classic Tikhonov regularization. Our approach iteratively…

Image and Video Processing · Electrical Eng. & Systems 2025-02-07 Mehrsa Pourya , Erich Kobler , Michael Unser , Sebastian Neumayer

The present paper deals with the data-driven design of regularizers in the form of artificial neural networks, for solving certain inverse problems formulated as optimal control problems. These regularizers aim at improving accuracy,…

Optimization and Control · Mathematics 2023-03-06 Sebastien Court

Learning meaningful representations using deep neural networks involves designing efficient training schemes and well-structured networks. Currently, the method of stochastic gradient descent that has a momentum with dropout is one of the…

Machine Learning · Computer Science 2016-01-15 Taehoon Lee , Minsuk Choi , Sungroh Yoon

We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various…

Machine Learning · Statistics 2019-05-15 Alberto Bietti , Grégoire Mialon , Dexiong Chen , Julien Mairal

As a new neural machine translation approach, Non-Autoregressive machine Translation (NAT) has attracted attention recently due to its high efficiency in inference. However, the high efficiency has come at the cost of not capturing the…

Computation and Language · Computer Science 2019-02-28 Yiren Wang , Fei Tian , Di He , Tao Qin , ChengXiang Zhai , Tie-Yan Liu