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We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow network within the boundary integral formulation. With randomly…

Numerical Analysis · Mathematics 2026-03-30 Ye Lin , Wentao Liu , Young Ju Lee , Jiwei Jia

The removal of multiplicative Gamma noise is a critical research area in the application of synthetic aperture radar (SAR) imaging, where neural networks serve as a potent tool. However, real-world data often diverges from theoretical…

Computer Vision and Pattern Recognition · Computer Science 2024-12-24 Yi Ran , Zhichang Guo , Jia Li , Yao Li , Martin Burger , Boying Wu

This paper is an introduction to the membrane potential equation for neurons. Its properties are described, as well as sample applications. Networks of these equations can be used for modeling neuronal systems, which also process images and…

Neurons and Cognition · Quantitative Biology 2018-01-29 Matthias S. Keil

Rendering an accurate image of an isosurface in a volumetric field typically requires large numbers of data samples. Reducing the number of required samples lies at the core of research in volume rendering. With the advent of deep learning…

Graphics · Computer Science 2022-05-31 Sebastian Weiss , Mengyu Chu , Nils Thuerey , Rüdiger Westermann

We present MR-Net, a general architecture for multiresolution neural networks, and a framework for imaging applications based on this architecture. Our coordinate-based networks are continuous both in space and in scale as they are composed…

Computer Vision and Pattern Recognition · Computer Science 2022-09-13 Hallison Paz , Tiago Novello , Vinicius Silva , Luiz Schirmer , Guilherme Schardong , Fabio Chagas , Helio Lopes , Luiz Velho

Recently, differentiable volume rendering in neural radiance fields (NeRF) has gained a lot of popularity, and its variants have attained many impressive results. However, existing methods usually assume the scene is a homogeneous volume so…

Computer Vision and Pattern Recognition · Computer Science 2022-11-29 Jen-I Pan , Jheng-Wei Su , Kai-Wen Hsiao , Ting-Yu Yen , Hung-Kuo Chu

We present neural radiance fields for rendering and temporal (4D) reconstruction of humans in motion (H-NeRF), as captured by a sparse set of cameras or even from a monocular video. Our approach combines ideas from neural scene…

Computer Vision and Pattern Recognition · Computer Science 2021-11-03 Hongyi Xu , Thiemo Alldieck , Cristian Sminchisescu

Single image super-resolution (SISR), as a traditional ill-conditioned inverse problem, has been greatly revitalized by the recent development of convolutional neural networks (CNN). These CNN-based methods generally map a low-resolution…

Image and Video Processing · Electrical Eng. & Systems 2024-10-30 Yuqing Liu , Shiqi Wang , Jian Zhang , Shanshe Wang , Siwei Ma , Wen Gao

Modern inexpensive imaging sensors suffer from inherent hardware constraints which often result in captured images of poor quality. Among the most common ways to deal with such limitations is to rely on burst photography, which nowadays…

Computer Vision and Pattern Recognition · Computer Science 2019-04-01 Filippos Kokkinos , Stamatios Lefkimmiatis

Randomized neural networks for representation learning have consistently achieved prominent results in texture recognition tasks, effectively combining the advantages of both traditional techniques and learning-based approaches. However,…

Computer Vision and Pattern Recognition · Computer Science 2025-10-06 Ricardo T. Fares , Lucas C. Ribas

Modeling the distribution of natural images is a landmark problem in unsupervised learning. This task requires an image model that is at once expressive, tractable and scalable. We present a deep neural network that sequentially predicts…

Computer Vision and Pattern Recognition · Computer Science 2016-08-22 Aaron van den Oord , Nal Kalchbrenner , Koray Kavukcuoglu

Deep learning has excelled on complex pattern recognition tasks such as image classification and object recognition. However, it struggles with tasks requiring nontrivial reasoning, such as algorithmic computation. Humans are able to solve…

Machine Learning · Computer Science 2022-07-01 Yilun Du , Shuang Li , Joshua B. Tenenbaum , Igor Mordatch

The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…

Machine Learning · Computer Science 2022-01-10 Jihun Han , Yoonsang Lee

Convolutional neural networks (CNNs) show outstanding performance in many image processing problems, such as image recognition, object detection and image segmentation. Semantic segmentation is a very challenging task that requires…

Computer Vision and Pattern Recognition · Computer Science 2019-07-12 Fan Jia , Jun Liu , Xue-cheng Tai

Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…

Classical Physics · Physics 2023-10-03 Farhang Loran , Ali Mostafazadeh

Image denoising is a typical ill-posed problem due to complex degradation. Leading methods based on normalizing flows have tried to solve this problem with an invertible transformation instead of a deterministic mapping. However, the…

Computer Vision and Pattern Recognition · Computer Science 2023-02-01 Wenchao Du , Hu Chen , Yi Zhang , H. Yang

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

Recent work on Neural Radiance Fields (NeRF) exploits multi-view 3D consistency, achieving impressive results in 3D scene modeling and high-fidelity novel-view synthesis. However, there are limitations. First, existing methods assume enough…

Computer Vision and Pattern Recognition · Computer Science 2024-01-09 Mengfei Li , Ming Lu , Xiaofang Li , Shanghang Zhang

Recent works use the Neural radiance field (NeRF) to perform multi-view 3D reconstruction, providing a significant leap in rendering photorealistic scenes. However, despite its efficacy, NeRF exhibits limited capability of learning…

Computer Vision and Pattern Recognition · Computer Science 2023-11-29 Congyue Deng , Jiawei Yang , Leonidas Guibas , Yue Wang

High resolution magnetic resonance (MR) imaging is desirable in many clinical applications due to its contribution to more accurate subsequent analyses and early clinical diagnoses. Single image super resolution (SISR) is an effective and…

Computer Vision and Pattern Recognition · Computer Science 2019-09-17 Xiaole Zhao , Yulun Zhang , Tao Zhang , Xueming Zou