{"id":5,"date":"2012-10-25T22:04:15","date_gmt":"2012-10-25T22:04:15","guid":{"rendered":"http:\/\/pages.charlotte.edu\/template-faculty01\/?page_id=5"},"modified":"2022-11-09T08:23:42","modified_gmt":"2022-11-09T13:23:42","slug":"home","status":"publish","type":"page","link":"https:\/\/pages.charlotte.edu\/anuj-abhishek\/","title":{"rendered":"Home"},"content":{"rendered":"

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I am a postdoctoral fellow at University of North Carolina at Charlotte, where I work in Prof. Taufiquar Khan’s<\/a> research group. I did my Ph.D. at Tufts University under the supervision of Prof. Todd Quinto<\/a> and was co-advised by Prof. Venky Krishnan<\/a> 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.<\/a><\/strong> here.<\/p>\n<\/div>\n<\/div>\n\n\n\n

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Publications:<\/strong><\/p>\n\n\n\n

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  1. Support Theorems and an Injectivity Result for Integral Moments of a Symmetric m-Tensor Field<\/strong>. <\/a>(Joint work with Rohit Kumar Mishra) Journal of Fourier Analysis and Applications, 2019<\/em><\/li>
  2. Support theorems for the transverse ray transform of tensor fields of rank m.<\/a> <\/strong>Journal of Mathematical Analysis and Applications, April 2020.<\/em><\/li>
  3. Modified forward and inverse Born series for the Calderon and diffuse-wave problems<\/strong> . <\/a>(Inverse Problems , June 2020.) (Joint work with Marc Bonnet and Shari Moskow.)<\/li>
  4. Minimax optimal estimator in the stochastic inverse problem for exponential Radon transform. <\/a><\/strong>(Sankhya A, The Indian Journal of Statistics, May 2022)<\/li>
  5. An optimal Bayesian estimator for absorption coefficient in Diffuse Optical Tomography.<\/a><\/strong> (SIAM J. of Imaging Sciences, June 2022) (Joint work with Thilo Strauss and Taufiquar Khan)<\/li>
  6. Adaptive Estimation of<\/strong> <\/a><\/a>a Function from<\/strong> <\/a>its Exponential Radon Transform<\/strong> <\/a>in Presence<\/strong> <\/a>of Noise<\/strong>. (Sankhya A, The Indian Journal of Statistics, November 2022) (Joint work with Sakshi Arya)<\/li>
  7. The Carleman-Newton method to globally reconstruct a source term for nonlinear parabolic equation.<\/a> <\/strong>(Submitted) (Joint work with Thuy Le, Loc Nguyen and Taufiquar Khan)<\/li>
  8. A Bayesian inversion method for simultaneous reconstruction of diffusion and absorption parameters in Diffuse Optical Tomography.<\/strong> (Preparing for Submission) (Joint work with Thilo Strauss and Taufiquar Khan)<\/li><\/ol>\n\n\n\n

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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 […]<\/p>\n","protected":false},"author":3813,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-5","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/anuj-abhishek\/wp-json\/wp\/v2\/pages\/5","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.charlotte.edu\/anuj-abhishek\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pages.charlotte.edu\/anuj-abhishek\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/anuj-abhishek\/wp-json\/wp\/v2\/users\/3813"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/anuj-abhishek\/wp-json\/wp\/v2\/comments?post=5"}],"version-history":[{"count":24,"href":"https:\/\/pages.charlotte.edu\/anuj-abhishek\/wp-json\/wp\/v2\/pages\/5\/revisions"}],"predecessor-version":[{"id":93,"href":"https:\/\/pages.charlotte.edu\/anuj-abhishek\/wp-json\/wp\/v2\/pages\/5\/revisions\/93"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/anuj-abhishek\/wp-json\/wp\/v2\/media?parent=5"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}