I am a postdoctoral fellow at University of North Carolina at Charlotte, where I work in Prof. Taufiquar Khan’s research group. I did my Ph.D. at Tufts University under the supervision of Prof. Todd Quinto and was co-advised by Prof. Venky Krishnan at Tata Institute of Fundamental Research, India. My research interests are in Inverse Problems, Partial Differential Equations and Microlocal Analysis. More recently, I have been working on coefficient inverse problems in a stochastic setting proving results on convergence and optimality of data driven estimators built from noisy data. Please find my C.V. here.
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 . (Inverse Problems , June 2020.) (Joint work with Marc Bonnet and Shari Moskow.)
- Minimax optimal estimator in the stochastic inverse problem for exponential Radon transform. (Sankhya A, The Indian Journal of Statistics, May 2022)
- An optimal Bayesian estimator for absorption coefficient in Diffuse Optical Tomography. (SIAM J. of Imaging Sciences, June 2022) (Joint work with Thilo Strauss and Taufiquar Khan)
- Adaptive Estimation of a Function from its Exponential Radon Transform in Presence of Noise. (Sankhya A, The Indian Journal of Statistics, November 2022) (Joint work with Sakshi Arya)
- The Carleman-Newton method to globally reconstruct a source term for nonlinear parabolic equation. (Submitted) (Joint work with Thuy Le, Loc Nguyen and Taufiquar Khan)
- A Bayesian inversion method for simultaneous reconstruction of diffusion and absorption parameters in Diffuse Optical Tomography. (Preparing for Submission) (Joint work with Thilo Strauss and Taufiquar Khan)