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The explicit low-rank regularization, e.g., nuclear norm regularization, has been widely used in imaging sciences. However, it has been found that implicit regularization outperforms explicit ones in various image processing tasks. Another…

机器学习 · 计算机科学 2023-03-30 Zhemin Li , Tao Sun , Hongxia Wang , Bao Wang

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…

数值分析 · 数学 2024-10-21 Markus Haltmeier , Richard Kowar , Markus Tiefenthaler

While recent model-free Reinforcement Learning (RL) methods have demonstrated human-level effectiveness in gaming environments, their success in everyday tasks like visual navigation has been limited, particularly under significant…

机器学习 · 计算机科学 2024-04-04 Rudra P. K. Poudel , Harit Pandya , Stephan Liwicki , Roberto Cipolla

In this paper we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable…

统计理论 · 数学 2017-04-17 Garvesh Raskutti , Ming Yuan , Han Chen

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…

数值分析 · 数学 2021-04-15 Babak Maboudi Afkham , Julianne Chung , Matthias Chung

In this survey paper, we review recent uses of convolution neural networks (CNNs) to solve inverse problems in imaging. It has recently become feasible to train deep CNNs on large databases of images, and they have shown outstanding…

图像与视频处理 · 电气工程与系统科学 2018-09-11 Michael T. McCann , Kyong Hwan Jin , Michael Unser

Inverse Reinforcement Learning (IRL) aims to facilitate a learner's ability to imitate expert behavior by acquiring reward functions that explain the expert's decisions. Regularized IRL applies strongly convex regularizers to the learner's…

机器学习 · 计算机科学 2020-12-04 Wonseok Jeon , Chen-Yang Su , Paul Barde , Thang Doan , Derek Nowrouzezahrai , Joelle Pineau

The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based…

计算机视觉与模式识别 · 计算机科学 2019-09-04 T. A. Bubba , G. Kutyniok , M. Lassas , M. März , W. Samek , S. Siltanen , V. Srinivasan

Accelerating the data acquisition of dynamic magnetic resonance imaging (MRI) leads to a challenging ill-posed inverse problem, which has received great interest from both the signal processing and machine learning community over the last…

计算机视觉与模式识别 · 计算机科学 2018-10-16 Chen Qin , Jo Schlemper , Jose Caballero , Anthony Price , Joseph V. Hajnal , Daniel Rueckert

Nonconvex methods have emerged as a dominant approach for low-rank matrix estimation, a problem that arises widely in machine learning and AI for learning and representing high-dimensional data. Existing analyses for these methods often…

机器学习 · 统计学 2026-05-08 Chengyu Cui , Gongjun Xu

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

最优化与控制 · 数学 2022-09-28 Kristian Bredies , Marcello Carioni , Martin Holler

Virtual Adversarial Training (VAT) has shown impressive results among recently developed regularization methods called consistency regularization. VAT utilizes adversarial samples, generated by injecting perturbation in the input space, for…

机器学习 · 计算机科学 2022-12-27 Genki Osada , Budrul Ahsan , Revoti Prasad Bora , Takashi Nishide

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…

最优化与控制 · 数学 2019-04-22 S. Bellavia , G. Gurioli , B. Morini , Ph. L. Toint

Recovering a function or high-dimensional parameter vector from indirect measurements is a central task in various scientific areas. Several methods for solving such inverse problems are well developed and well understood. Recently, novel…

数值分析 · 数学 2019-12-10 Housen Li , Johannes Schwab , Stephan Antholzer , Markus Haltmeier

Learning neural networks using only few available information is an important ongoing research topic with tremendous potential for applications. In this paper, we introduce a powerful regularizer for the variational modeling of inverse…

机器学习 · 计算机科学 2023-05-17 Fabian Altekrüger , Alexander Denker , Paul Hagemann , Johannes Hertrich , Peter Maass , Gabriele Steidl

The solution of inverse problems is of fundamental interest in medical and astronomical imaging, geophysics as well as engineering and life sciences. Recent advances were made by using methods from machine learning, in particular deep…

计算机视觉与模式识别 · 计算机科学 2023-12-29 Moritz Piening , Fabian Altekrüger , Johannes Hertrich , Paul Hagemann , Andrea Walther , Gabriele Steidl

We consider the problem of recovering elements of a low-dimensional model from under-determined linear measurements. To perform recovery, we consider the minimization of a convex regularizer subject to a data fit constraint. Given a model,…

信号处理 · 电气工程与系统科学 2024-04-22 Yann Traonmilin , Rémi Gribonval , Samuel Vaiter

In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep…

计算机视觉与模式识别 · 计算机科学 2021-11-16 Shima Kamyab , Zohreh Azimifar , Rasool Sabzi , Paul Fieguth

Convolutional Neural Networks (CNNs) excel in many visual tasks but remain susceptible to adversarial attacks-imperceptible perturbations that degrade performance. Prior research reveals that brain-inspired regularizers, derived from neural…

机器学习 · 计算机科学 2026-02-16 Elie Attias , Cengiz Pehlevan , Dina Obeid

In the last years, the design of image reconstruction methods in the field of quantitative Magnetic Resonance Imaging (qMRI) has experienced a paradigm shift. Often, when dealing with (quantitative) MR image reconstruction problems, one is…

最优化与控制 · 数学 2024-03-01 Andreas Kofler , Felix Frederik Zimmermann , Kostas Papafitsoros