293 citations · 1.8k across the 110 of their papers we have counts for
9 papers · 1 filter
A Parameter Choice Rule for Tikhonov Regularization Based on Predictive Risk
Federico Benvenuto, Bangti Jin
In this work, we propose a new criterion for choosing the regularization parameter in Tikhonov regularization when the noise is white Gaussian. The criterion minimizes a lower boun…
Regularized Linear Inversion with Randomized Singular Value Decomposition
Kazufumi Ito, Bangti Jin
In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical re…
Numerical Estimation of a Diffusion Coefficient in Subdiffusion
Bangti Jin, Zhi Zhou
In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involv…
Wasserstein Gradient Flow Formulation of the Time-Fractional Fokker-Planck Equation
Manh Hong Duong, Bangti Jin
In this work, we investigate a variational formulation for a time-fractional Fokker-Planck equation which arises in the study of complex physical systems involving anomalously slow…
Probabilistic Residual Learning for Aleatoric Uncertainty in Image Restoration
Chen Zhang, Bangti Jin
Aleatoric uncertainty is an intrinsic property of ill-posed inverse and imaging problems. Its quantification is vital for assessing the reliability of relevant point estimates. In…
On the Convergence of Stochastic Gradient Descent for Nonlinear Ill-Posed Problems
Bangti Jin, Zehui Zhou, Jun Zou
In this work, we analyze the regularizing property of the stochastic gradient descent for the efficient numerical solution of a class of nonlinear ill-posed inverse problems in Hil…
Incomplete Iterative Solution of the Subdiffusion Problem
Bangti Jin, Zhi Zhou
In this work, we develop an efficient incomplete iterative scheme for the numerical solution of the subdiffusion model involving a Caputo derivative of order in time. I…
Adaptive Reconstruction for Electrical Impedance Tomography with a Piecewise Constant Conductivity
Bangti Jin, Yifeng Xu
In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is…
Numerical Reconstruction in Magnetic Particle Imaging
Tobias Kluth, Bangti Jin
Magnetic particle imaging (MPI) is a medical imaging modality of recent origin, and it exploits the nonlinear magnetization phenomenon to recover the spatially dependent concentrat…