Support

Support from NSF grants DMS-1814104 and NSF CAREER grant DMS-1943580 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.

Coauthors

Yernat Assylbekov, Guillaume Bal, Cédric Bellis, Jan Bohr, Éric Bonnetier, Matias Courdurier, Colin Guillarmou, Chenxi Guo, Sean Holman, Joonas Ilmavirta, Sébastien Imperiale, Alexandre Jollivet, Venkateswaran P. Krishnan, Ian Langmore, Rafe Mazzeo, Rohit K. Mishra, Richard Nickl, Axel Osses, Gabriel P. Paternain, Donsub Rim, Francisco Romero, Plamen Stefanov, Faouzi Triki, Gunther Uhlmann, Yuzhou (Joey) Zou.

Supported Articles

  • [S1]. Steven Flynn, Injectivity of the Heisenberg X-ray Transform, Journal of Functional Analysis, Volume 280, Issue 5, 1 March 2021, 108886. article - DOI

Preprints and Publications

[J*] = accepted for publication/published
[P*] = preprint or submitted
  • [P39]. Local and global blow-downs of transport twistor space (with Jan Bohr and Gabriel P. Paternain)
    preprint (2024) arxiv
  • [P38]. (review article) Non-standard Sobolev scales and the mapping properties of the X-ray transform on manifolds with strictly convex boundary,
    preprint (2023) arxiv
  • [P37]. Boundary triples for a family of degenerate elliptic operators of Keldysh type (with Yuzhou (Joey) Zou),
    Pure and Applied Analysis (to appear) (2024) arxiv
  • [J36]. The $C^\infty$-isomorphism property for a class of singularly-weighted X-ray transforms (with Rohit K. Mishra and Yuzhou (Joey) Zou),
    Inverse Problems 39.2 (2022): 024001. Special Issue "Emerging Talents 2021"
    arxiv - DOI
  • [P35]. Double b-fibrations and desingularization of the X-ray transform on manifolds with strictly convex boundary (with Rafe Mazzeo),
    preprint (2021) arxiv
  • [J34]. Sampling the X-ray transform on simple surfaces (with Plamen Stefanov),
    SIAM Journal on Mathematical Analysis 55.3 (2023): 1707-1736 - arxiv - DOI
  • [J33]. Statistical guarantees for Bayesian uncertainty quantification in non-linear inverse problems with Gaussian process priors (with Richard Nickl and Gabriel P. Paternain),
    Annals of Statistics 2021, Vol. 49, No. 6, 3255-3298. arxiv - DOI
  • [J32]. Functional relations, sharp mapping properties and regularization of the X-ray transform on disks of constant curvature,
    SIAM Journal of Mathematical Analysis, 52(6), 5675-5702. (28 pages). arxiv - DOI
  • [P31]. Inverse source problems in transport via attenuated tensor tomography (with Guillaume Bal),
    preprint (2019). arxiv
  • [J30]. Range characterizations and Singular Value Decomposition of the geodesic X-ray transform on disks of constant curvature (with Rohit K. Mishra),
    Journal of Spectral Theory, 11(3), pp. 1005--1041 (2020). arxiv
  • [J29]. Consistent Inversion of Noisy Non-Abelian X-Ray Transforms (with Richard Nickl and Gabriel P. Paternain),
    Communications in Pure and Applied Mathematics, 74(5), pp. 1045-1099 (2020). arxiv - DOI
  • [J28]. On solenoidal-injective and injective ray transforms of tensor fields on surfaces (with Venkateswaran P. Krishnan and Rohit K. Mishra),
    Journal of Inverse and Ill-posed Problems 27.4 (2019): 527-538. arxiv
  • [J27]. (review article) Integral geometry on manifolds with boundary and applications (with Joonas Ilmavirta),
    The Radon Transform: the first 100 years and beyond. Radon series on computations and applied mathematics 22 (2019). Editors: R. Ramlau, O. Scherzer, arxiv
  • [J26]. Imaging of isotropic and anisotropic conductivities from power densities in three dimensions (with Donsub Rim),
    Inverse Problems 34.7 (2018): 075005. arxiv
  • [J25]. Efficient Nonparametric Bayesian Inference For X-Ray Transforms (with Richard Nickl and Gabriel P. Paternain),
    Annals of Statistics 2019, Vol. 47, No. 2, 1113-1147. arxiv
  • [J24]. The attenuated geodesic X-ray transform (with Sean Holman and Plamen Stefanov),
    Inverse Problems 34.6 (2018): 064003. 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),
    The Journal of Geometric Analysis 30.3 (2020): 2515-2557. arxiv
  • [J21]. Inversion formulas and range characterizations for the attenuated geodesic ray transform (with Yernat Assylbekov and Gunther Uhlmann),
    Journal des 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