293 citations · 1.8k across the 110 of their papers we have counts for
8 papers · 1 filter
Expectation Propagation for Nonlinear Inverse Problems -- with an Application to Electrical Impedance Tomography
Matthias Gehre, Bangti Jin
In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulat…
An Analysis of Finite Element Approximation in Electrical Impedance Tomography
Matthias Gehre, Bangti Jin, Xiliang Lu
We present a finite element analysis of electrical impedance tomography for reconstructing the conductivity distribution from electrode voltage measurements by means of Tikhonov re…
A Unified Primal Dual Active Set Algorithm for Nonconvex Sparse Recovery
Jian Huang, Yuling Jiao, Bangti Jin +3
In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for…
Error Analysis of Finite Element Methods for Space-Fractional Parabolic Equations
Bangti Jin, Raytcho Lazarov, Joseph Pasciak +1
We consider an initial/boundary value problem for one-dimensional fractional-order parabolic equations with a space fractional derivative of Riemann-Liouville type and order $α\in…
A Finite Element Method for the Fractional Sturm-Liouville Problem
Bangti Jin, Raytcho Lazarov, Joseph Pasciak +1
In this work, we propose an efficient finite element method for solving fractional Sturm-Liouville problems involving either the Caputo or Riemann-Liouville derivative of order $α\…
Variational formulation of problems involving fractional order differential operators
Bangti Jin, Raytcho Lazarov, Joseph Pasciak
In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order on the unit interval . These fractional…
Error Analysis of Semidiscrete Finite Element Methods for Inhomogeneous Time-Fractional Diffusion
Bangti Jin, Raytcho Lazarov, Joseph Pasciak +1
We consider the initial boundary value problem for the inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and a nonsmooth right hand s…
Multi-Parameter Tikhonov Regularization -- An Augmented Approach
Kazufumi Ito, Bangti Jin, Tomoya Takeuchi
We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a…