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Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major…

Machine Learning · Computer Science 2024-11-12 Conlain Kelly , Surya R. Kalidindi

Simulation-based ultrasound training can be an essential educational tool. Realistic ultrasound image appearance with typical speckle texture can be modeled as convolution of a point spread function with point scatterers representing tissue…

Computer Vision and Pattern Recognition · Computer Science 2020-06-19 Lin Zhang , Valery Vishnevskiy , Orcun Goksel

High-frequency features are critical in multiscale phenomena such as turbulent flows and phase transitions, since they encode essential physical information. The recently proposed Wavelet Neural Operator (WNO) utilizes wavelets'…

Numerical Analysis · Mathematics 2025-06-24 Wei-Min Lei , Hou-Biao Li

We present statistical convergence results for the learning of (possibly) non-linear mappings in infinite-dimensional spaces. Specifically, given a map $G_0:\mathcal X\to\mathcal Y$ between two separable Hilbert spaces, we analyze the…

Statistics Theory · Mathematics 2024-12-24 Niklas Reinhardt , Sven Wang , Jakob Zech

Harvesting data from distributed Internet of Things (IoT) devices with multiple autonomous unmanned aerial vehicles (UAVs) is a challenging problem requiring flexible path planning methods. We propose a multi-agent reinforcement learning…

Multiagent Systems · Computer Science 2021-06-04 Harald Bayerlein , Mirco Theile , Marco Caccamo , David Gesbert

This paper considers the problem of noise-robust neural operator approximation for the solution map of Calder\'on's inverse conductivity problem. In this continuum model of electrical impedance tomography (EIT), the boundary measurements…

Numerical Analysis · Mathematics 2025-11-26 Maarten V. de Hoop , Nikola B. Kovachki , Matti Lassas , Nicholas H. Nelsen

Imaging problems such as the one in nanoCT require the solution of an inverse problem, where it is often taken for granted that the forward operator, i.e., the underlying physical model, is properly known. In the present work we address the…

Medical ultrasound (US) is a widespread imaging modality owing its popularity to cost efficiency, portability, speed, and lack of harmful ionizing radiation. In this paper, we demonstrate that replacing the traditional ultrasound processing…

Computer Vision and Pattern Recognition · Computer Science 2020-04-07 Sanketh Vedula , Ortal Senouf , Grigoriy Zurakhov , Alex Bronstein , Oleg Michailovich , Michael Zibulevsky

In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning the mapping between highly oscillatory functions, with application to the nonlinear mapping between the…

Numerical Analysis · Mathematics 2024-12-31 Zhilin You , Zhenli Xu , Wei Cai

In ultrasound (US) imaging, individual channel RF measurements are back-propagated and accumulated to form an image after applying specific delays. While this time reversal is usually implemented using a hardware- or software-based…

Image and Video Processing · Electrical Eng. & Systems 2019-07-17 Shujaat Khan , Jaeyoung Huh , Jong Chul Ye

An alternative approach to ultrasound computed tomography (USCT) for medical imaging is proposed, with the intent to (i) shorten acquisition time for devices with a large number of emitters, (ii) eliminate the calibration step, and (iii)…

Medical Physics · Physics 2022-01-25 Ines Elisa Ulrich , Christian Boehm , Andrea Zunino , Cyrill Bösch , Andreas Fichtner

This work explores the feasibility of steering a drone with a (recurrent) neural network, based on input from a forward looking camera, in the context of a high-level navigation task. We set up a generic framework for training a network to…

Computer Vision and Pattern Recognition · Computer Science 2017-02-27 Klaas Kelchtermans , Tinne Tuytelaars

Tear film (TF) breakup is a key driver of understanding dry eye disease, yet estimating TF thickness and osmolarity from fluorescence (FL) imaging typically requires solving computationally expensive inverse problems. We propose an operator…

Numerical Analysis · Mathematics 2026-01-14 Qinying Chen , Arnab Roy , Tobin A. Driscoll

Flat panel computed tomography is used intraoperatively to assess the result of surgery. Due to workflow issues, the acquisition typically cannot be carried out in such a way that the axis aligned multiplanar reconstructions (MPR) of the…

Image and Video Processing · Electrical Eng. & Systems 2020-07-08 Celia Martín Vicario , Florian Kordon , Felix Denzinger , Markus Weiten , Sarina Thomas , Lisa Kausch , Jochen Franke , Holger Keil , Andreas Maier , Holger Kunze

Medical imaging datasets often contain heterogeneous biases ranging from erroneous labels to inconsistent labeling styles. Such biases can negatively impact deep segmentation networks performance. Yet, the identification and…

Computer Vision and Pattern Recognition · Computer Science 2025-06-27 Samuel Joutard , Marijn Stollenga , Marc Balle Sanchez , Mohammad Farid Azampour , Raphael Prevost

In this work, we employ neural fields, which use neural networks to map a coordinate to the corresponding physical property value at that coordinate, in a test-time learning manner. For a test-time learning method, the weights are learned…

Machine Learning · Computer Science 2025-07-25 Anran Xu , Lindsey J. Heagy

Automatic motion compensation and adjustment of an intraoperative imaging modality's field of view is a common problem during interventions. Optical coherence tomography (OCT) is an imaging modality which is used in interventions due to its…

Computer Vision and Pattern Recognition · Computer Science 2019-03-12 Nils Gessert , Martin Gromniak , Matthias Schlüter , Alexander Schlaefer

Optical coherence tomography (OCT) captures cross-sectional data and is used for the screening, monitoring, and treatment planning of retinal diseases. Technological developments to increase the speed of acquisition often results in systems…

Image and Video Processing · Electrical Eng. & Systems 2023-01-03 Timothy T. Yu , Da Ma , Jayden Cole , Myeong Jin Ju , Mirza F. Beg , Marinko V. Sarunic

Although neural operators are widely used in data-driven physical simulations, their training remains computationally expensive. Recent advances address this issue via downstream learning, where a model pretrained on simpler problems is…

Machine Learning · Computer Science 2025-11-17 Mikhail Masliaev , Dmitry Gusarov , Ilya Markov , Alexander Hvatov

The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators,…

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