Support

Support from NSF grant DMS-1712790 (formerly 1634544, formerly 1514820) is gratefully acknowledged.

Ph.D. thesis

Defended April 27th, 2012.
Title: Taming unstable inverse problems. Mathematical routes toward high-resolution medical imaging modalities. (with distinction) pdf
Adviser: Guillaume Bal.

Submitted

Published/In Press

  • [J27, review article]. "Integral geometry on manifolds with boundary and applications" (with Joonas Ilmavirta), Inverse Problems (to appear) (2018), arxiv
  • [J26]. "Imaging of isotropic and anisotropic conductivities from power densities in three dimensions" (with Donsub Rim), Inverse Problems (to appear) (2018) arxiv
  • [J25]. "Efficient Nonparametric Bayesian Inference For X-Ray Transforms" (with Richard Nickl and Gabriel P. Paternain), Annals of Statistics (to appear) (2018) arxiv
  • [J24]. "The attenuated geodesic X-ray transform" (with Sean Holman and Plamen Stefanov), Inverse Problems (to appear) (2018) arxiv
  • [J23]. "Efficient tensor tomography in fan-beam coordinates. II: Attenuated transforms", Inverse Problems and Imaging, 12 (2): 433-460 (2018) arxiv
  • [J22]. "The geodesic X-ray transform with a GL(n,C)-connection" (with Gabriel P. Paternain), Journal of Geometric Analysis (to appear) (2017) arxiv
  • [J21]. "Inversion formulas and range characterizations for the attenuated geodesic ray transform" (with Yernat Assylbekov and Gunther Uhlmann), Journal of Math. Pures et Appliquees, 111, 161-190 (March 2018) arxiv
  • [J20]. "Reconstruction formulas for X-ray transforms in negative curvature" (with Colin Guillarmou), Annales Inst. Fourier, 67 (4): 1353-1392 (2017) arxiv
  • [J19]. "Efficient tensor tomography in fan-beam coordinates", Inverse Problems and Imaging, 10:2 (2016), 433-459. arxiv
  • [J18]. "Inversion of the attenuated geodesic X-ray transform over functions and vector fields on simple surfaces", SIAM J. on Math. Anal., 48:2 (2016), 1155-1177 arxiv - pdf
  • [J17]. "Reconstruction of a fully anisotropic elasticity tensor from knowledge of displacement fields" (with Guillaume Bal and Gunther Uhlmann), SIAM Journal on Applied Mathematics, Vol. 75, No. 5, pp. 2214-2231 (2015). arXiv
  • [J16]. "Simultaneous source and attenuation reconstruction in SPECT using ballistic and single scattering data" (with Matias Courdurier, Axel Osses and Francisco Romero), Inverse Problems 31 (2015) 095002. arxiv
  • [J15]. "The geodesic ray transform on Riemannian surfaces with conjugate points" (with Plamen Stefanov and Gunther Uhlmann), Communications in Mathematical Physics, 337 (2015), 1491-1513. arxiv - Springerlink
  • [J14]. "On reconstruction formulas for the ray transform acting on symmetric differentials on surfaces", Inverse Problems 30 (2014) 065001. arXiv
  • [J13]. "Numerical implementation of geodesic X-ray transforms and their inversion", SIAM J. Imaging Sciences, Vol. 7, No. 2, pp. 1335-1357 (2014). arXiv
  • [J12]. "Imaging of anisotropic conductivities from current densities in two dimensions" (with Guillaume Bal and Chenxi Guo), SIAM J. on Imaging Sciences, Vol. 7, Issue 4 (2014). reprint
  • [J11]. "Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurements" (with Guillaume Bal, Cédric Bellis and Sébastien Imperiale), Inverse Problems 30 (2014) 125004. arXiv
  • [J10]. "Linearized internal functionals for anisotropic conductivities" (with Guillaume Bal and Chenxi Guo), Inv. Probl. and Imaging Vol 8. No. 1 (Feb. 2014). arXiv
  • [J9]. "Inverse anisotropic conductivity from internal current densities" (with Guillaume Bal and Chenxi Guo), Inverse Problems 30 (2) (2014) 025001. arXiv
  • [J8]. "Inverse anisotropic conductivity from power densities in dimension $n\ge 3$" (with Guillaume Bal), Comm. PDE, Vol. 38, Issue 7 (2013). arXiv
  • [J7]. "Inverse anisotropic diffusion from power density measurements in two dimensions" (with Guillaume Bal), Inverse Problems 28 (2012) 084001. arXiv
  • [J6]. "Inverse diffusion problems with redundant internal information" (with Guillaume Bal), Inv. Probl. Imaging, Vol. 6 (May 2012), No. 2. arXiv
  • [J5]. "Inverse diffusion from knowledge of power densities" (with Guillaume Bal, Éric Bonnetier and Faouzi Triki), Inv. Probl. Imaging, Vol 7 (May 2013), No. 2. arXiv
  • [J4]. "Inverse transport with isotropic time-harmonic sources" (with Guillaume Bal), SIAM J. Math. Anal., Vol. 44, No. 1, pp. 134-161 (2012). pdf
  • [J3]. "Angular average of time-harmonic transport solutions" (with Guillaume Bal, Alexandre Jollivet and Ian Langmore), Communications in Partial Differential Equations, 1532-4133, Vol. 36, Issue 6, 2011, Pages 1044 - 1070. pdf
  • [J2]. "An accurate solver for forward and inverse transport" (with Guillaume Bal), Journal of Computational Physics, Vol. 229, Issue 13, July, 2010. pdf
  • [J1]. "Inverse Transport with isotropic sources and angularly-averaged measurements" (with Guillaume Bal and Ian Langmore), Inv. Probl. Imaging, Vol.2 (2008), No. 1. pdf