Publications:
Support Theorems and an Injectivity Result for Integral Moments of a Symmetric m-Tensor Field. (Joint work with Rohit Kumar Mishra) Journal of Fourier Analysis and Applications, 2019
Support theorems for the transverse ray transform of tensor fields of rank m. Journal of Mathematical Analysis and Applications, April 2020.
Modified forward and inverse Born series for the Calderon and diffuse-wave problems . (with M.Bonnett and S. Moskow) Inverse Problems , June 2020.
Minimax optimal estimator in the stochastic inverse problem for exponential Radon transform. Sankhya A Vol 85(1)
Adaptive Estimation of a Function from its Exponential Radon Transform in Presence of Noise. (with S. Arya) Sankhya A Vol 85 (2)
An Optimal Bayesian Estimator for Absorption Coefficient in Diffuse Optical Tomography, (with T. Strauss and T.Khan) SIAM J. of Imaging Sciences (2022)
Improved Training of Physics-Informed Neural Networks Using Energy-Based Priors: a Study on Electrical Impedance Tomography (with A. Pokkunuru, P. Rooshenas, T. Strauss and T.Khan) ICLR, 2023
The Carleman-Newton method to globally reconstruct a source term for nonlinear parabolic equation, (with T. Le, L. Nguyen and T. Khan), Journal of Computational and Applied Mathematics, 2024
Local reconstruction analysis of inverting the Radon transform in the plane from noisy discrete data. (SIIMS, April 2025) (with A. Katsevich and J.W. Webber)
Simultaneous estimation of piecewise constant coefficients in elliptic PDEs via Bayesian level-set methods (Communications on Analysis and Computation, 2025) (with T. Strauss and T. Khan)
Solving the Electrical Impedance Tomography Problem with a DeepONet Type Neural Network: Theory and Application. (submitted) (with T. Strauss)
MCMC-Net: Accelerating Markov Chain Monte Carlo with Neural Networks for Inverse Problems (submitted) (with S. Majee, T. Strauss, T.Khan)