# Research

# Articles

On the null space of the backprojection operator and Rubin's conjecture for the spherical mean transform, with Divyansh Agrawal, Gaik Ambartsoumian and Nisha Singhal.

Ray transform on Sobolev spaces of symmetric tensor fields, II: Range characterization, with Vladimir A. Sharafutdinov.

Normal operators for momentum ray transforms, I: The inversion formula, with Shubham Jathar, Manas Kar and Vladimir A. Sharafutdinov.

A simple range characterization for spherical mean transform in odd dimensions and its applications, with Divyansh Agrawal, Gaik Ambartsoumian and Nisha Singhal.

Determination of lower order perturbations of a polyharmonic operator in two dimensions, with Rajat Bansal and Rahul Raju Pattar.

Unique determination of anisotropic perturbations of a polyharmonic operator from partial boundary data, with Sombuddha Bhattacharyya and Suman Kumar Sahoo, SIAM J. Math. Anal. 55 (2023), no. 4, 4000–4038.

Point sources and stability for an inverse problem for a hyperbolic PDE with space and time dependent coefficients, with Rakesh and Soumen Senapati, J. Differential Equations 342 (2023), 622–665.

Unique continuation results for certain generalized ray transforms of symmetric tensor fields, with Divyansh Agrawal and Suman Kumar Sahoo, J. Geom. Anal. 32 (2022), no. 10, Paper No. 245, 27 pp.

A diffeomorphic aging model for adult human brain from cross-sectional data, with Alphin Thottupattu and Jayanthi Sivaswamy, Accepted for publication in Scientific Reports, 2022.

Ray transform on Sobolev spaces of symmetric tensor fields, I: Higher order Reshetnyak formulas, with Vladimir A. Sharafutdinov, Inverse Probl. Imaging 16 (2022), no. 4, 787 - 826.

High frequency stability estimates for a partial data inverse problem, with Anupam Pal Choudhury, Math. Methods Appl. Sci. 45 (2022), no. 3, 1573–1586.

A method for large diffeomorphic registration via broken geodesics, with Alphin J. Thottupattu and Jayanthi Sivaswamy.

Stability for a formally determined inverse problem for a hyperbolic PDE with space and time dependent coefficients, with Rakesh and Soumen Senapati, SIAM J. Math. Anal. 53 (2021), no. 6, 6822–6846.

Microlocal inversion of a 3-dimensional restricted transverse ray transform of symmetric m-tensor fields, with Rohit Kumar Mishra and Suman Kumar Sahoo, J. Math. Anal. Appl. 495 (2021), no. 1, 124700, 13 pp.

Scientific opinion article with mathematical simulations related to COVID-19 on the usage of masks, with Subhashini Sadasivam, The Wire Science, June 19, 2020.

A uniqueness result for light ray transform on symmetric 2-tensor fields, with Soumen Senapati and Manmohan Vashisth, J. Fourier Anal. Appl., 26 (2020), no. 3, 40.

Momentum ray transforms, II: Range characterization in the Schwartz space, with Suman Kumar Sahoo, Ramesh Manna and Vladimir Sharafutdinov, Inverse Problems 36 (2020), no. 4, 045009, 33 pp.

On s-injective and injective ray transforms of tensor fields on surfaces, with Rohit Kumar Mishra and François Monard, J. Inverse Ill-Posed Probl. 27 (2019), no 4, 527–538.

Momentum ray transforms, with Suman Kumar Sahoo, Ramesh Manna and Vladimir Sharafutdinov, Inverse Probl. Imaging 13 (2019), no. 3, 679–701.

An inverse problem for the relativistic Schrödinger equation with partial boundary data, with Manmohan Vashisth, Accepted for publication in Applicable Analysis.

Microlocal analysis of a restricted ray transform on symmetric m-tensor fields in R^n, with Rohit Kumar Mishra, SIAM J. Math. Anal. 50 (2018), no. 6, 6230–6254.

Inverse diffusivity problem via homogenization theory, with Tuhin Ghosh and M. Vanninathan.

A fully non-linear optimization approach to acousto-electric tomography, with Bolaji Adesokan, Kim Knudsen and Souvik Roy, Inverse Problems, 34 (2018), no. 10, 104004, 16 pp.

Image reconstruction from radially incomplete spherical Radon data, with Gaik Ambartsoumian, Souvik Roy and Rim Gouia-Zarrad, European J. Appl. Math., 29 (2018), no. 3, 470–493.

Singular FIOs in SAR imaging, II: Transmitter and receiver at different speeds, with Gaik Ambartsoumian, Raluca Felea, Cliff Nolan and Eric Todd Quinto, SIAM J. Math. Anal., 50 (2018), no. 1, 591–621.

Numerical inversion of arc Radon transform, with Syed Tabish Abbas and Jayanthi Sivaswamy, IEEE Trans. Comput. Imaging, 2 (2016), no. 4, 540–549.

Determination of Lower Order Perturbations of the Polyharmonic Operator from Partial Boundary Data, with Tuhin Ghosh, Applicable Analysis, 95 (2016), no. 11, 2444–2463.

Common midpoint versus common offset acquisition geometry in seismic imaging, with Raluca Felea, Cliff Nolan and Eric Todd Quinto, Inverse Probl. Imaging, 10 (2016), no. 1, 87–102.

Stability estimates for an inverse boundary value problem for the biharmonic operator with bounded potentials, with Anupam Pal Choudhury, Journal of Mathematical Analysis and Applications, 431 (2015), no.1, 300-316.

An efficient numerical algorithm for the inversion of an integral transform arising in ultrasound imaging, with Souvik Roy, Praveen Chandrasekhar and A. S. Vasudeva Murthy, Journal of Mathematical Imaging and Vision, 53 (2015), no.1, 78-91.

Inversion of a class of circular and elliptical Radon transforms, with Gaik Ambartsoumian, Complex analysis and dynamical systems VI. Part 1, 1–12, Contemp. Math., 653, Israel Math. Conf. Proc., Amer. Math. Soc., Providence, RI, 2015.

Microlocal analysis of an ultrasound transform with circular source and receiver trajectories, with Gaik Ambartsoumian, Jan Boman and Eric Todd Quinto. Geometric analysis and integral geometry, 45–58, Contemp. Math., 598, Amer. Math. Soc., Providence, RI, 2013.

A class of singular Fourier integral operators in synthetic aperture radar imaging, with Gaik Ambartsoumian, Raluca Felea, Cliff Nolan and Eric Todd Quinto. J. Funct. Anal., 264 (2013), no. 1, 246–269.

Microlocal analysis of elliptical Radon transforms with foci on a line, with Howard Levinson and Eric Todd Quinto, in "The Mathematical Legacy of Leon Ehrenpreis," Springer 2012.

Microlocal aspects of common offset synthetic aperture radar imaging, with Eric Todd Quinto. Inverse Probl. Imaging, 5 (2011), no. 3, 659-674.

Synthetic aperture radar imaging exploiting multiple scattering, with Birsen Yazici. Inverse Problems, 27 (2011), no. 5, 055004, 25 pp.

On the inversion formulas of Pestov and Uhlmann for the geodesic ray transform. J. Inverse Ill-Posed Probl. 18 (2010), no. 4, 401–408.

Multistatic synthetic aperture radar image formation, with John Swoboda, Can Evren Yarman and Birsen Yazici. IEEE Trans. Image Process., 19 (2010), no. 5, 1290–1306.

A support theorem for the geodesic ray transform of symmetric tensor fields, with Plamen Stefanov. Inverse Probl. Imaging, 3 (2009), no. 3, 453–464.

A support theorem for the geodesic ray transform on functions. J. Fourier Anal. Appl., 15 (2009), no. 4, 515–520.

# Book Chapters

Microlocal analysis of some synthetic aperture radar imaging problems. Mathematical models, methods and applications, 55–75, Ind. Appl. Math., Springer, Singapore, 2015.

Microlocal analysis in tomography, with Eric Todd Quinto, In Handbook of Mathematical Methods in Imaging, 2e.

Microlocal analysis and imaging, with Gaik Ambartsoumian, Raluca Felea, Cliff Nolan and Eric Todd Quinto, In SIAM Mathematics of Planet Earth 2013 publication.