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Related papers: DRIP: Deep Regularizers for Inverse Problems

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Inverse problems correspond to a certain type of optimization problems formulated over appropriate input distributions. Recently, there has been a growing interest in understanding the computational hardness of these optimization problems,…

Machine Learning · Statistics 2018-09-03 Alex Nowak , Soledad Villar , Afonso S. Bandeira , Joan Bruna

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

Recently the field of inverse problems has seen a growing usage of mathematically only partially understood learned and non-learned priors. Based on first principles, we develop a projectional approach to inverse problems that addresses the…

Machine Learning · Computer Science 2019-08-07 Sören Dittmer , Peter Maass

A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…

Optimization and Control · Mathematics 2019-04-22 S. Bellavia , G. Gurioli , B. Morini , Ph. L. Toint

Advanced machine learning methods, and more prominently neural networks, have become standard to solve inverse problems over the last years. However, the theoretical recovery guarantees of such methods are still scarce and difficult to…

Machine Learning · Computer Science 2024-03-11 Nathan Buskulic , Jalal Fadili , Yvain Quéau

When adopting a model-based formulation, solving inverse problems encountered in multiband imaging requires to define spatial and spectral regularizations. In most of the works of the literature, spectral information is extracted from the…

Image and Video Processing · Electrical Eng. & Systems 2023-07-03 Min Zhao , Nicolas Dobigeon , Jie Chen

A broad class of problems at the core of computational imaging, sensing, and low-level computer vision reduces to the inverse problem of extracting latent images that follow a prior distribution, from measurements taken under a known…

Computer Vision and Pattern Recognition · Computer Science 2018-12-20 Steven Diamond , Vincent Sitzmann , Felix Heide , Gordon Wetzstein

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

Numerical Analysis · Mathematics 2021-01-15 Barbara Kaltenbacher , Kha Van Huynh

Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…

Optimization and Control · Mathematics 2016-11-15 Manya V. Afonso , Jose M. Bioucas-Dias , Mario A. T. Figueiredo

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 propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…

Image and Video Processing · Electrical Eng. & Systems 2024-07-10 Mehrsa Pourya , Sebastian Neumayer , Michael Unser

The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…

Numerical Analysis · Mathematics 2020-04-15 Abinash Nayak

This paper addresses the problem of inverse rendering from photometric images. Existing approaches for this problem suffer from the effects of self-shadows, inter-reflections, and lack of constraints on the surface reflectance, leading to…

Computer Vision and Pattern Recognition · Computer Science 2025-04-09 Jingzhi Bao , Guanying Chen , Shuguang Cui

In this work, we introduce a novel approach to regularization in multivariable regression problems. Our regularizer, called DLoss, penalises differences between the model's derivatives and derivatives of the data generating function as…

Machine Learning · Computer Science 2024-05-02 Enrico Lopedoto , Maksim Shekhunov , Vitaly Aksenov , Kizito Salako , Tillman Weyde

This paper introduces an optimal control framework to address the inverse problem using a learned regularizer, with applications in image reconstruction. We build upon the concept of Learnable Optimization Algorithms (LOA), which combine…

Optimization and Control · Mathematics 2024-09-04 Wanyu Bian

Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…

Optimization and Control · Mathematics 2025-08-08 Jie Gao , Cesare Molinari , Silvia Villa , Jingwei Liang

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

Optimization and Control · Mathematics 2014-12-09 Samuel Vaiter , Gabriel Peyré , Jalal M. Fadili

Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse…

Machine Learning · Computer Science 2024-08-16 Philipp Holl , Nils Thuerey

Recently, data-driven techniques have demonstrated remarkable effectiveness in addressing challenges related to MR imaging inverse problems. However, these methods still exhibit certain limitations in terms of interpretability and…

Computer Vision and Pattern Recognition · Computer Science 2023-09-19 Huayu Wang , Chen Luo , Taofeng Xie , Qiyu Jin , Guoqing Chen , Zhuo-Xu Cui , Dong Liang

The linear inverse problem is fundamental to the development of various scientific areas. Innumerable attempts have been carried out to solve different variants of the linear inverse problem in different applications. Nowadays, the rapid…

Signal Processing · Electrical Eng. & Systems 2020-10-30 Yanna Bai , Wei Chen , Jie Chen , Weisi Guo