18 citations · 75 across the 23 of their papers we have counts for
24 papers
Leveraging joint sparsity in hierarchical Bayesian learning
Jan Glaubitz, Anne Gelb
We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian pri…
Sequential edge detection using joint hierarchical Bayesian learning
Yao Xiao, Anne Gelb, Guohui Song
This paper introduces a new sparse Bayesian learning (SBL) algorithm that jointly recovers a temporal sequence of edge maps from noisy and under-sampled Fourier data. The new metho…
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…
Sub-aperture SAR Imaging with Uncertainty Quantification
Victor Churchill, Anne Gelb
In the problem of spotlight mode airborne synthetic aperture radar (SAR) image formation, it is well-known that data collected over a wide azimuthal angle violate the isotropic sca…
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…
Estimation and uncertainty quantification for piecewise smooth signal recovery
Victor Churchill, Anne Gelb
This paper presents a sparse Bayesian learning (SBL) algorithm for linear inverse problems with a high order total variation (HOTV) sparsity prior. For the problem of sparse signal…
Synthetic Aperture Radar Image Formation with Uncertainty Quantification
Victor Churchill, Anne Gelb
Synthetic aperture radar (SAR) is a day or night any-weather imaging modality that is an important tool in remote sensing. Most existing SAR image formation methods result in a max…
Thresholded Non-Uniform Fourier Frame-Based Reconstruction for Stripmap SAR
John McKay, Anne Gelb, Suren Jayasuriya +1
Fourier domain methods are fast algorithms for SAR imaging. They typically involve an interpolation in the frequency domain to re-grid non-uniform data so inverse fast Fourier tran…
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…
Total Variation Bayesian Learning via Synthesis
Victor Churchill, Anne Gelb
This paper presents a sparse Bayesian learning algorithm for inverse problems in signal and image processing with a total variation (TV) sparsity prior. Because of the prior used,…
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…
Image reconstruction enhancement via masked regularization
Victor Churchill, Anne Gelb
Image reconstruction based on an edge-sparsity assumption has become popular in recent years. Many methods of this type are capable of reconstructing nearly perfect edge-sparse ima…
Edge-masked CT image reconstruction from limited data
Victor Churchill, Anne Gelb
This paper presents an iterative inversion algorithm for computed tomography image reconstruction that performs well in terms of accuracy and speed using limited data. The computat…
Detecting edges from non-uniform Fourier data via sparse Bayesian learning
Victor Churchill, Anne Gelb
In recent investigations, the problem of detecting edges given non-uniform Fourier data was reformulated as a sparse signal recovery problem with an l1-regularized least squares co…
Edge-adaptive l2 regularization image reconstruction from non-uniform Fourier data
Victor Churchill, Rick Archibald, Anne Gelb
Total variation regularization based on the l1 norm is ubiquitous in image reconstruction. However, the resulting reconstructions are not always as sparse in the edge domain as des…
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…