11 citations · 35 across the 15 of their papers we have counts for
16 papers
Principal Component Flow Map Learning of PDEs from Incomplete, Limited, and Noisy Data
Victor Churchill
We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed part…
Unraveling Consumer Purchase Journey Using Neural Network Models
Victor Churchill, H. Alice Li, Dongbin Xiu
This study utilizes an ensemble of feedforward neural network models to analyze large-volume and high-dimensional consumer touchpoints and their impact on purchase decisions. When…
Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks
Victor Churchill, Dongbin Xiu
Flow map learning (FML), in conjunction with deep neural networks (DNNs), has shown promises for data driven modeling of unknown dynamical systems. A remarkable feature of FML is t…
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…
Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence
Victor Churchill, Dongbin Xiu
Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long term prediction of the dynamic…
Deep Learning of Chaotic Systems from Partially-Observed Data
Victor Churchill, Dongbin Xiu
Recently, a general data driven numerical framework has been developed for learning and modeling of unknown dynamical systems using fully- or partially-observed data. The method ut…
Robust Modeling of Unknown Dynamical Systems via Ensemble Averaged Learning
Victor Churchill, Steve Manns, Zhen Chen +1
Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long time prediction of the evoluti…
Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space
Zhen Chen, Victor Churchill, Kailiang Wu +1
We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recen…
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…
Use of convexity in contour detection
Victor Churchill
In this paper, we formulate a simple algorithm that detects contours around a region of interest in an image. After an initial smoothing, the method is based on viewing an image as…
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,…
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…