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08/31/2023
Solving Poisson Problems in Polygonal Domains with Singularity Enriched Physics Informed Neural Networks
Physics informed neural networks (PINNs) represent a very powerful class...
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08/28/2023
Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Imaging Inverse Problems
Denoising diffusion models have emerged as the go-to framework for solvi...
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08/27/2023
Score-Based Generative Models for PET Image Reconstruction
Score-based generative models have demonstrated highly promising results...
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08/23/2023
Solving Elliptic Optimal Control Problems using Physics Informed Neural Networks
In this work, we present and analyze a numerical solver for optimal cont...
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08/18/2023
On the Approximation of Bi-Lipschitz Maps by Invertible Neural Networks
Invertible neural networks (INNs) represent an important class of deep n...
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08/13/2023
An Adaptive Phase-Field Method for Structural Topology Optimization
In this work, we develop an adaptive algorithm for the efficient numeric...
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07/06/2023
Recovery of Multiple Parameters in Subdiffusion from One Lateral Boundary Measurement
This work is concerned with numerically recovering multiple parameters s...
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04/18/2023
Electrical Impedance Tomography with Deep Calderón Method
Electrical impedance tomography (EIT) is a noninvasive medical imaging m...
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03/29/2023
Conductivity Imaging from Internal Measurements with Mixed Least-Squares Deep Neural Networks
In this work we develop a novel approach using deep neural networks to r...
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03/28/2023
SVD-DIP: Overcoming the Overfitting Problem in DIP-based CT Reconstruction
The deep image prior (DIP) is a well-established unsupervised deep learn...
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02/21/2023
Hybrid Neural-Network FEM Approximation of Diffusion Coefficient in Elliptic and Parabolic Problems
In this work we investigate the numerical identification of the diffusio...
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02/20/2023
Fast and Painless Image Reconstruction in Deep Image Prior Subspaces
The deep image prior (DIP) is a state-of-the-art unsupervised approach f...
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10/14/2022
Inverse Problems for Subdiffusion from Observation at an Unknown Terminal Time
Inverse problems of recovering space-dependent parameters, e.g., initial...
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09/07/2022
Solving Elliptic Problems with Singular Sources using Singularity Splitting Deep Ritz Method
In this work, we develop an efficient solver based on deep neural networ...
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07/26/2022
Recovery of a Distributed Order Fractional Derivative in an Unknown Medium
In this work, we study an inverse problem of recovering information abou...
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07/11/2022
Bayesian Experimental Design for Computed Tomography with the Linearised Deep Image Prior
We investigate adaptive design based on a single sparse pilot scan for g...
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04/05/2022
Imaging Conductivity from Current Density Magnitude using Neural Networks
Conductivity imaging represents one of the most important tasks in medic...
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03/09/2022
Convergence Rate Analysis of Galerkin Approximation of Inverse Potential Problem
In this work we analyze the inverse problem of recovering the space-depe...
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02/28/2022
A Probabilistic Deep Image Prior for Computational Tomography
Existing deep-learning based tomographic image reconstruction methods do...
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10/22/2021
Conditional Variational Autoencoder for Learned Image Reconstruction
Learned image reconstruction techniques using deep neural networks have ...
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09/14/2021
Recovery of a Space-Time Dependent Diffusion Coefficient in Subdiffusion: Stability, Approximation and Error Analysis
In this work, we study an inverse problem of recovering a space-time dep...
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08/10/2021
An Analysis of Stochastic Variance Reduced Gradient for Linear Inverse Problems
Stochastic variance reduced gradient (SVRG) is a popular variance reduct...
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07/06/2021
Unsupervised Knowledge-Transfer for Learned Image Reconstruction
Deep learning-based image reconstruction approaches have demonstrated im...
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06/06/2021
Stochastic EM methods with Variance Reduction for Penalised PET Reconstructions
Expectation-maximization (EM) is a popular and well-established method f...
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06/04/2021
Recovering Multiple Fractional Orders in Time-Fractional Diffusion in an Unknown Medium
In this work, we investigate an inverse problem of recovering multiple o...
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05/31/2021
Recovering the Potential in One-Dimensional Time-Fractional Diffusion with Unknown Initial Condition and Source
This paper is concerned with an inverse problem of recovering a potentia...
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02/05/2021
Reconstruction of a Space-Time Dependent Source in Subdiffusion Models via a Perturbation Approach
In this article we study inverse problems of recovering a space-time dep...
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01/18/2021
Recovery of the Order of Derivation for Fractional Diffusion Equations in an Unknown Medium
In this work, we investigate the recovery of a parameter in a diffusion ...
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11/17/2020
Quantifying Sources of Uncertainty in Deep Learning-Based Image Reconstruction
Image reconstruction methods based on deep neural networks have shown ou...
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10/21/2020
On the Saturation Phenomenon of Stochastic Gradient Descent for Linear Inverse Problems
Stochastic gradient descent (SGD) is a promising method for solving larg...
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10/06/2020
Error Analysis of Finite Element Approximations of Diffusion Coefficient Identification for Elliptic and Parabolic Problems
In this work, we present a novel error analysis for recovering a spatial...
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09/08/2020
An Inverse Potential Problem for Subdiffusion: Stability and Reconstruction
In this work, we study the inverse problem of recovering a potential coe...
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07/20/2020
Quantifying Model Uncertainty in Inverse Problems via Bayesian Deep Gradient Descent
Recent advances in reconstruction methods for inverse problems leverage ...
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04/30/2020
On the Discrepancy Principle for Stochastic Gradient Descent
Stochastic gradient descent (SGD) is a promising numerical method for so...
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04/23/2020
Subdiffusion with Time-Dependent Coefficients: Improved Regularity and Second-Order Time Stepping
This article concerns second-order time discretization of subdiffusion e...
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01/16/2020
L1 data fitting for robust reconstruction in magnetic particle imaging: quantitative evaluation on Open MPI dataset
Magnetic particle imaging is an emerging quantitative imaging modality, ...
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12/30/2019
A Parameter Choice Rule for Tikhonov Regularization Based on Predictive Risk
In this work, we propose a new criterion for choosing the regularization...
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09/04/2019
Regularized Linear Inversion with Randomized Singular Value Decomposition
In this work, we develop efficient solvers for linear inverse problems b...
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09/01/2019
Numerical Estimation of a Diffusion Coefficient in Subdiffusion
In this work, we consider the numerical recovery of a spatially dependen...
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08/24/2019
Wasserstein Gradient Flow Formulation of the Time-Fractional Fokker-Planck Equation
In this work, we investigate a variational formulation for a time-fracti...
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08/01/2019
Probabilistic Residual Learning for Aleatoric Uncertainty in Image Restoration
Aleatoric uncertainty is an intrinsic property of ill-posed inverse and ...
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07/06/2019
On the Convergence of Stochastic Gradient Descent for Nonlinear Ill-Posed Problems
In this work, we analyze the regularizing property of the stochastic gra...
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06/15/2019
Incomplete Iterative Solution of the Subdiffusion Problem
In this work, we develop an efficient incomplete iterative scheme for th...
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10/18/2018
Expectation Propagation for Poisson Data
The Poisson distribution arises naturally when dealing with data involvi...
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09/18/2017
Variational Gaussian Approximation for Poisson Data
The Poisson model is frequently employed to describe count data, but in ...
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03/03/2014
A Primal Dual Active Set with Continuation Algorithm for the ℓ^0-Regularized Optimization Problem
We develop a primal dual active set with continuation algorithm for solv...
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10/04/2013