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We study the problem of reconstructing solutions of inverse problems when only noisy measurements are available. We assume that the problem can be modeled with an infinite-dimensional forward operator that is not continuously invertible.…

Numerical Analysis · Mathematics 2023-10-23 Andrés Felipe Lerma Pineda , Philipp Christian Petersen

Implicit Neural Representations (INRs) provide a powerful continuous framework for modeling complex visual and geometric signals, but spectral bias remains a fundamental challenge, limiting their ability to capture high-frequency details.…

Machine Learning · Computer Science 2025-12-01 Yesom Park , Kelvin Kan , Thomas Flynn , Yi Huang , Shinjae Yoo , Stanley Osher , Xihaier Luo

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

High-resolution (HR) videos play a crucial role in many computer vision applications. Although existing video restoration (VR) methods can significantly enhance video quality by exploiting temporal information across video frames, they are…

Computer Vision and Pattern Recognition · Computer Science 2025-06-09 Mary Aiyetigbo , Wanqi Yuan , Feng Luo , Nianyi Li

Identification of a groundwater contaminant source simultaneously with the hydraulic conductivity in highly-heterogeneous media often results in a high-dimensional inverse problem. In this study, a deep autoregressive neural network-based…

Machine Learning · Statistics 2019-03-19 Shaoxing Mo , Nicholas Zabaras , Xiaoqing Shi , Jichun Wu

Implicit Neural Representations (INRs) have emerged as a paradigm in knowledge representation, offering exceptional flexibility and performance across a diverse range of applications. INRs leverage multilayer perceptrons (MLPs) to model…

Computer Vision and Pattern Recognition · Computer Science 2025-02-19 Amer Essakine , Yanqi Cheng , Chun-Wun Cheng , Lipei Zhang , Zhongying Deng , Lei Zhu , Carola-Bibiane Schönlieb , Angelica I Aviles-Rivero

We present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and…

Optimization and Control · Mathematics 2026-02-06 Macarena Navarro , Willem-Jan van Hoeve , Karan Singh

The use of Implicit Neural Representation (INR) through a hash-table has demonstrated impressive effectiveness and efficiency in characterizing intricate signals. However, current state-of-the-art methods exhibit insufficient…

Computer Vision and Pattern Recognition · Computer Science 2023-09-25 Hao Zhu , Fengyi Liu , Qi Zhang , Xun Cao , Zhan Ma

Increasingly in medical imaging has emerged an issue surrounding the reconstruction of noisy images from raw measurement data. Where the forward problem is the generation of raw measurement data from a ground truth image, the inverse…

Image and Video Processing · Electrical Eng. & Systems 2020-03-24 Adam Peace

Prior probability models are a fundamental component of many image processing problems, but density estimation is notoriously difficult for high-dimensional signals such as photographic images. Deep neural networks have provided…

Computer Vision and Pattern Recognition · Computer Science 2024-11-05 Zahra Kadkhodaie , Eero P. Simoncelli

Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…

Fluid Dynamics · Physics 2024-07-12 Shengfeng Xu , Chang Yan , Zhenxu Sun , Renfang Huang , Dilong Guo , Guowei Yang

Diffusion models have been used as priors for solving inverse problems. However, existing approaches typically overlook side information that could significantly improve reconstruction quality, especially in severely ill-posed settings. In…

Computer Vision and Pattern Recognition · Computer Science 2026-05-27 Mahdi Farahbakhsh , Vishnu Teja Kunde , Dileep Kalathil , Krishna Narayanan , Jean-Francois Chamberland

Accelerating Magnetic Resonance Imaging (MRI) reduces scan time but often degrades image quality. While Implicit Neural Representations (INRs) show promise for MRI reconstruction, they struggle at high acceleration factors due to weak prior…

Computer Vision and Pattern Recognition · Computer Science 2025-08-12 Ziad Al-Haj Hemidi , Eytan Kats , Mattias P. Heinrich

Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these…

Machine Learning · Computer Science 2023-12-19 Alban Gossard , Pierre Weiss

Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…

Machine Learning · Computer Science 2023-01-31 Tianci Liu , Tong Yang , Quan Zhang , Qi Lei

Implicit Neural Representations (INRs) have revolutionized signal representation by leveraging neural networks to provide continuous and smooth representations of complex data. However, existing INRs face limitations in capturing…

Computer Vision and Pattern Recognition · Computer Science 2023-10-31 Amirhossein Kazerouni , Reza Azad , Alireza Hosseini , Dorit Merhof , Ulas Bagci

Recent advances in inverse problem solving have increasingly adopted flow priors over diffusion models due to their ability to construct straight probability paths from noise to data, thereby enhancing efficiency in both training and…

Computer Vision and Pattern Recognition · Computer Science 2025-11-11 Hossein Askari , Yadan Luo , Hongfu Sun , Fred Roosta

Dealing with missing values and incomplete time series is a labor-intensive, tedious, inevitable task when handling data coming from real-world applications. Effective spatio-temporal representations would allow imputation methods to…

Machine Learning · Computer Science 2022-02-11 Andrea Cini , Ivan Marisca , Cesare Alippi

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Computational imaging, especially non-line-of-sight (NLOS) imaging, the…

Computer Vision and Pattern Recognition · Computer Science 2026-04-01 Lianfang Wang , Kuilin Qin , Xueying Liu , Huibin Chang , Yong Wang , Yuping Duan

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian…

Machine Learning · Statistics 2025-12-03 Ali Mohammad-Djafari , Ning Chu , Li Wang
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