6 papers
An Efficient Bayesian Framework for Uncertainty Quantification in Nonlinear Imaging Inverse Problems
Anuj Abhishek, Sakshi Arya, Madhu Gupta
Bayesian methods provide a natural framework for estimating a parameter in non-linear inverse problems and quantifying uncertainty in the estimation. However, when the forward mode…
A DeepONet for inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An approximation theoretic perspective and numerical results
Anuj Abhishek, Thilo Strauss
In this work, we consider the non-invasive medical imaging modality of Electrical Impedance Tomography (EIT), where the goal is to recover the conductivity in a medium from boundar…
MCMC-Net: Accelerating Markov Chain Monte Carlo with Neural Networks for Inverse Problems
Sudeb Majee, Anuj Abhishek, Thilo Strauss +1
In many computational problems, using the Markov Chain Monte Carlo (MCMC) can be prohibitively time-consuming. We propose MCMC-Net, a simple yet efficient way to accelerate MCMC vi…
Statistical microlocal analysis in two-dimensional X-ray CT
Anuj Abhishek, Alexander Katsevich, James W. Webber
In many imaging applications it is important to assess how well the edges of the original object, , are resolved in an image, , reconstructed from the measured dat…
Simultaneous Estimation of Piecewise Constant Coefficients in Elliptic PDEs via Bayesian Level-Set Methods
Anuj Abhishek, Thilo Strauss, Taufiquar Khan
In this article, we propose a non-parametric Bayesian level-set method for simultaneous reconstruction of two different piecewise constant coefficients in an elliptic partial diffe…
Inversion of generalized Radon transform over symmetric -tensor fields in
Anuj Abhishek, Rohit Kumar Mishra, Chandni Thakkar
In this work, we study a set of generalized Radon transforms over symmetric -tensor fields in . The longitudinal/transversal Radon transform and corresponding weig…