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Anuj Abhishek
Anuj Abhishek
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Email: anuj.abhishek@uncc.edu

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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:

  1. 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
  2. Support theorems for the transverse ray transform of tensor fields of rank m. Journal of Mathematical Analysis and Applications, April 2020.
  3. 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.)
  4. Minimax optimal estimator in the stochastic inverse problem for exponential Radon transform. (Sankhya A, The Indian Journal of Statistics, May 2022)
  5. 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)
  6. 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)
  7. 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)
  8. 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)

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