27 citations · 34 across the 12 of their papers we have counts for
13 papers
Uncertainty Quantification for Landweber Iteration with Randomized Normal-Operator Approximation
Anuj Abhishek, Sean Holman
Iterative methods are extremely popular for solving linear ill-posed inverse problems. While deterministic convergence, or more precisely, semi-convergence of such methods is widel…
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…
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…
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…
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…
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…
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…
Local reconstruction analysis of inverting the Radon transform in the plane from noisy discrete data
Anuj Abhishek, Alexander Katsevich, James W. Webber
In this paper, we investigate the reconstruction error, $N_\e^{\text{rec}}(x)$, when a linear, filtered back-projection (FBP) algorithm is applied to noisy, discrete Radon transfor…
The Carleman-Newton method to globally reconstruct a source term for nonlinear parabolic equation
Anuj Abhishek, Thuy Le, Loc Nguyen +1
We propose to combine the Carleman estimate and the Newton method to solve an inverse source problem for nonlinear parabolic equations from lateral boundary data. The stability of…
Adaptive estimation of a function from its Exponential Radon Transform in presence of noise
Anuj Abhishek, Sakshi Arya
In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of funct…
Minimax optimal estimator in the stochastic inverse problem for exponential Radon transform
Anuj Abhishek
In this article, we consider the problem of inverting the exponential Radon transform of a function in the presence of noise. We propose a kernel estimator to estimate the true fun…
Support theorem for the transverse ray transform of tensor fields of rank 2
Anuj Abhishek
Let (M, g) be a simple, real analytic, Riemannian manifold with boundary and of dimension n>=3. In this work, we prove a support theorem for the transverse ray transform of tensor…
Support Theorems and an Injectivity Result for Integral Moments of a Symmetric m-Tensor Field
Anuj Abhishek, Rohit Kumar Mishra
In this work, we show an injectivity result and support theorems for integral moments of a m-tensor field on a simple, real analytic, Riemannian manifold. Integral moments of m-ten…