18 citations · 75 across the 23 of their papers we have counts for
13 papers · 1 filter
Designing Neural Networks for Hyperbolic Conservation Laws
Zhen Chen, Anne Gelb, Yoonsang Lee
We propose a new data-driven method to learn the dynamics of an unknown hyperbolic system of conservation laws using deep neural networks. Inspired by classical methods in numerica…
Improving numerical accuracy for the viscous-plastic formulation of sea ice
Tongtong Li, Anne Gelb, Yoonsang Lee
Accurate modeling of sea ice dynamics is critical for predicting environmental variables and is important in applications such as navigating ice breaker ships. Research for both mo…
Sequential image recovery from noisy and under-sampled Fourier data
Yao Xiao, Jan Glaubitz, Anne Gelb +1
A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is m…
Generalized sparse Bayesian learning and application to image reconstruction
Jan Glaubitz, Anne Gelb, Guohui Song
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolu…
Empirical Bayesian Inference using Joint Sparsity
Jiahui Zhang, Anne Gelb, Theresa Scarnati
This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of under-sampled and noisy observable…
Stabilizing Radial Basis Function Methods for Conservation Laws Using Weakly Enforced Boundary Conditions
Jan Glaubitz, Anne Gelb
It is well understood that boundary conditions (BCs) may cause global radial basis function (RBF) methods to become unstable for hyperbolic conservation laws (CLs). Here we investi…
Accelerated Variance Based Joint Sparsity Recovery of Images from Fourier Data
Theresa Scarnati, Anne Gelb
Several problems in imaging acquire multiple measurement vectors (MMVs) of Fourier samples for the same underlying scene. Image recovery techniques from MMVs aim to exploit the joi…
High Order Edge Sensors with Regularization for Enhanced Discontinuous Galerkin Methods
Jan Glaubitz, Anne Gelb
This paper investigates the use of regularization for solving hyperbolic conservation laws based on high order discontinuous Galerkin (DG) approximations. We first use the…
Using Frame Theoretic Convolutional Gridding for Robust Synthetic Aperture Sonar Imaging
John McKay, Anne Gelb, Vishal Monga +1
Recent progress in synthetic aperture sonar (SAS) technology and processing has led to significant advances in underwater imaging, outperforming previously common approaches in bot…
Recovering Fine Details from Under-Resolved Electron Tomography Data using HOTV Regularization
Toby Sanders, Anne Gelb, Rodrigo Platte +2
Over the last decade or so, reconstruction methods using regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilit…
A Two-dimensional Inverse Frame Operator Approximation Technique
Guohui Song, Jacqueline Davis, Anne Gelb
The ability to efficiently and accurately construct an inverse frame operator is critical for establishing the utility of numerical frame approximations. Recently, the admissible f…
Approximating the Inverse Frame Operator from Localized Frames
Guohui Song, Anne Gelb
This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analy…
Detection of Edges in Spectral Data II. Nonlinear Enhancement
Anne Gelb, Eitan Tadmor
We discuss a general framework for recovering edges in piecewise smooth functions with finitely many jump discontinuities, where . Our approach is based…