Pith. sign in

REVIEW 1 major objections 2 minor 270 references

V-Line Tensor Tomography in a Disk: Theoretical and Numerical Reconstruction

T0 review · 1 major / 2 minor · reviewed 2026-07-01 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The kernel of V-line transforms on symmetric m-tensor fields inside a disk is explicitly characterized, yielding a new inversion formula via decomposition.

desk verdict The paper adds an explicit kernel characterization and inversion formula for V-line tensor transforms in the disk under strict interior support, with numerics validating the authors' own prior algorithms. read the letter →

arxiv 2606.31632 v1 pith:U4HSVZKR submitted 2026-06-30 math.NA cs.NAmath.AP

Rahul Bhardwaj , Madhu Gupta This is my paper
classification math.NAcs.NAmath.AP
keywords V-linetransformtensortomographykernelcharacterizationinversionformulasymmetricfieldsnumericalreconstruction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper characterizes the kernel of the V-line transforms applied to symmetric m-tensor fields supported inside a disk of radius R. It then applies a decomposition result to produce an explicit inversion formula that recovers the tensor field from the transform data. The work also supplies numerical reconstructions for the cases of vector fields and symmetric 2-tensor fields, testing the formulas on phantoms both with and without added noise. A reader cares because V-line data arise in imaging geometries that follow broken lines, and an exact kernel description identifies which tensor features remain invisible to the measurements.

What carries the argument

Explicit kernel characterization of the V-line transform on symmetric m-tensor fields, together with the decomposition result that produces the inversion formula.

What would settle it

A symmetric m-tensor field inside the disk whose V-line transform vanishes but lies outside the stated kernel, or a numerical test phantom whose reconstruction by the derived formula deviates from the known ground truth beyond discretization error.

Watch

Extended reading notes

Core claim

We provide an explicit characterization of the kernel of the V-line transforms acting on a symmetric m-tensor field and derive a new inversion formula using a decomposition result. Numerical verification confirms the algorithms for vector fields and symmetric 2-tensor fields on various phantoms, including under noise.

Load-bearing premise

The symmetric m-tensor field has compact support strictly inside the disk of radius R centered at the origin.

Editorial extensions

If this is right

  • The kernel consists precisely of those symmetric m-tensor fields that produce zero V-line data.
  • The decomposition-based inversion recovers the field uniquely from complete V-line measurements.
  • The same numerical schemes remain stable for both m=1 and m=2 when moderate noise is present.
  • Reconstruction quality holds across multiple phantom geometries tested in the disk.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The kernel description may supply stability bounds for the inversion when data are incomplete.
  • The decomposition technique could be tested on V-line transforms defined on other bounded domains.
  • Numerical implementations might extend directly to higher-order symmetric tensors once the kernel formula is available.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 2 minor

Summary. The paper investigates V-line transforms acting on symmetric m-tensor fields with compact support inside a disk of radius R centered at the origin. It claims an explicit characterization of the kernel of these transforms, derives a new inversion formula via a decomposition result, and provides numerical verification and validation of inversion algorithms (for vector fields and symmetric 2-tensor fields) taken from the authors' prior work, demonstrating effectiveness and noise robustness on various phantoms.

Significance. If the kernel characterization and inversion formula are correct under the stated hypotheses, the work advances V-line tensor tomography by supplying explicit theoretical tools for higher-order tensors together with concrete numerical evidence of practical reconstruction quality. The numerical experiments on multiple phantoms, including noisy data, constitute a clear strength.

major comments (1)
  1. [Abstract, §2] Abstract and §2 (setting and assumptions): The explicit kernel characterization and the new inversion formula are derived under the hypothesis that the symmetric m-tensor field has compact support strictly inside the disk. The manuscript supplies no analysis, extension, or counter-example for the case in which support reaches or touches the boundary, where V-line integration paths can interact with the boundary in ways excluded by the strict-interior hypothesis; this precondition is load-bearing for the central theoretical claims.
minor comments (2)
  1. [§5] §5 (numerical section): The description of phantom construction and data-selection criteria should be expanded so that the reported reconstruction results can be reproduced from the given information.
  2. Notation: The distinction between the new inversion formula derived in this paper and the algorithms validated numerically (taken from the cited prior works) should be made explicit in the text and in the figure captions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and the positive evaluation of the paper's contributions. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Abstract, §2] Abstract and §2 (setting and assumptions): The explicit kernel characterization and the new inversion formula are derived under the hypothesis that the symmetric m-tensor field has compact support strictly inside the disk. The manuscript supplies no analysis, extension, or counter-example for the case in which support reaches or touches the boundary, where V-line integration paths can interact with the boundary in ways excluded by the strict-interior hypothesis; this precondition is load-bearing for the central theoretical claims.

    Authors: The strict-interior compact support hypothesis is explicitly required for the kernel characterization and the decomposition-based inversion formula, because it guarantees that every V-line segment lies entirely in the open disk where the tensor field is supported and avoids any boundary interaction that would alter the integral geometry. This setting is stated in the abstract and Section 2 and is the natural domain for the theoretical tools developed. Extending the results to the case of support touching the boundary would demand a separate analysis of modified path behaviors and possible singularities, which lies outside the scope of the present work. We therefore do not revise the manuscript to include such an extension or counter-examples. revision: no

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in derivation chain

full rationale

The paper states new theoretical results: an explicit kernel characterization for the V-line transform on symmetric m-tensor fields and a new inversion formula derived via a decomposition result, under the explicit assumption of compact support strictly inside the disk. The self-citations to bhardwaj_2024 and bhardwaj2025tensor apply only to the numerical verification and validation of previously developed algorithms for the vector and 2-tensor cases; they do not supply the kernel characterization or the claimed new inversion formula. No equations, definitions, or steps in the provided abstract reduce the central claims to fitted inputs, self-definitions, or a self-citation chain by construction. The support assumption is stated as a precondition but does not create a circular reduction in the derivation itself. This is a standard extension of prior work with independent theoretical content.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

No free parameters, invented entities, or non-standard axioms are visible from the abstract; the work relies on standard properties of symmetric tensor fields and integral transforms in the plane.

assumptions (1)
  • standard math Standard properties of symmetric tensor fields and line integrals in Euclidean space hold without additional restrictions.
    Invoked implicitly as the background for defining V-line transforms on tensors.

how reviews work

0 comments
Cite this review

Pith. "Pith review of V-Line Tensor Tomography in a Disk: Theoretical and Numerical Reconstruction." pith.science (2026). https://pith.science/paper/U4HSVZKR

@misc{pith2026260631632,
  author       = {Pith},
  title        = {Pith review of: V-Line Tensor Tomography in a Disk: Theoretical and Numerical Reconstruction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/U4HSVZKR}},
  note         = {Machine review of arXiv:2606.31632}
}
abstract

In this article, we investigate V-line transforms for symmetric $m$-tensor fields whose support lies inside a disk of radius $R$ and centered at the origin. We provide an explicit characterization of the kernel of the V-line transforms acting on a symmetric $m$-tensor field and derive a new inversion formula using a decomposition result. In addition, we present a comprehensive numerical verification and validation of the inversion algorithms for these V-line transforms for vector fields and symmetric $2$-tensor fields, which were recently developed in \cite{bhardwaj_2024,bhardwaj2025tensor}. The reconstruction results obtained for various phantoms demonstrate the effectiveness and robustness of the proposed numerical methods, including in the presence of noise.

Figures

Figures reproduced from arXiv: 2606.31632 by the authors.

Figure 1
Figure 1. (a) Construction of the V-line BR(β, d) & (b) Configuration of broken rays used for data collection. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. displays the results for this smooth test case. The first column shows the ground-truth scalar components f1 and f2. The second column illustrates the simulated forward data Lf (β, d) and T f (β, d) plotted against the angular variable β (in degrees) and the distance parameter d. The final column displays the reconstructed components obtained via the proposed inversion method. We see that the reconstructed scalar co… view at source ↗
Figure 3
Figure 3. Reconstructed components of f with different levels of noise. We now consider another phantom, which we refer to as Ph2. In this class, each component of the phantom is represented as a weighted combination of three characteristic functions of disks having different radii r and centers (a, b). The values of these parameters are given in [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Original components of the vector field f (first column), the associated V-line transform data Lf and T f (second column), and the reconstructed vector field components (third column). Extending the validation of the inversion scheme, [PITH_FULL_IMAGE:figures/full_fig…
Figure 5
Figure 5. Figure 5: Reconstructed components of f with different levels of noise. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 6
Figure 6. Figure 6: Original components of the vector field f (first column), the associated V-line transform data Lf and T f (second column), and the reconstructed vector field components (third column). Further, [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]
Figure 7
Figure 7. Figure 7: Reconstructed components of f with different levels of noise. Phantoms f No noise 5% noise 10% noise 20% noise PH1 f1 1.29% 5.33% 10.40% 20.82% PH1 f2 1.57% 8.38% 16.46% 33.04% PH2 f1 8.29% 31.72% 62.25% 123.26% PH2 f2 9.52% 60.84% 120.30% 239.77% PH3 f1 15.62% 39.04% …
Figure 8
Figure 8. Figure 8: Reconstructed components of f (Phantom 2) for different angles (θ = 15◦ to 75◦ ) [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]
Figure 9
Figure 9. Figure 9: Reconstructed components of f (Phantom 3) for different angles (θ = 15◦ to 75◦ ). 5.2 Reconstruction of Tensor Fields To generate the data, we will follow the same procedure as discussed in subsection 5.1. The only difference is that we will now consider the three comp…
Figure 10
Figure 10. Figure 10: and 12 shows the reconstruction of the f11, f12 and f22 for Ph2 and Ph3 in the absence of noise. This shows that the algorithm can reconstruct sharp discontinuities for both convex and non-convex geometries with almost no artifacts [PITH_FULL_IMAGE:figures/full_fig_p…
Figure 11
Figure 11. Figure 11: Reconstructed 2-tensor field f (Phantom 2) from Lf , T f , and Mf with noisy data [PITH_FULL_IMAGE:figures/full_fig_p023_11.png]
Figure 12
Figure 12. Figure 12: Reconstructed 2-tensor field f (Phantom 3) from Lf , T f , and Mf . 23 [PITH_FULL_IMAGE:figures/full_fig_p023_12.png]
Figure 13
Figure 13. Figure 13: Reconstructed 2-tensor field f (Phantom 3) from Lf , T f , and Mf with noisy data. 6 Acknowledgements Rahul Bhardwaj gratefully acknowledges the partial financial support provided by the FIST programme of the Department of Science and Technology (DST), Government of I…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

270 extracted references · 270 canonical work pages

  1. [1]

    Communications in Analysis and Geometry , year=

    Broken ray tensor tomography with one reflecting obstacle , author=. Communications in Analysis and Geometry , year=

    work page

  2. [2]

    The Journal of Geometric Analysis , year=

    Broken Ray Transform for Twisted Geodesics on Surfaces with a Reflecting Obstacle , author=. The Journal of Geometric Analysis , year=

    work page

  3. [3]

    Communications in Analysis and Geometry , FJOURNAL =

    Ilmavirta, Joonas and Salo, Mikko , TITLE =. Communications in Analysis and Geometry , FJOURNAL =. 2016 , NUMBER =. doi:10.4310/CAG.2016.v24.n2.a6 , URL =

    work page doi:10.4310/cag.2016.v24.n2.a6 2016

  4. [4]

    Inverse Problems , FJOURNAL =

    Ilmavirta, Joonas , TITLE =. Inverse Problems , FJOURNAL =. 2013 , NUMBER =. doi:10.1088/0266-5611/29/3/035008 , URL =

    work page doi:10.1088/0266-5611/29/3/035008 2013

  5. [5]

    and Purohit, Anamika and Zamindar, Indrani , TITLE =

    Mishra, Rohit K. and Purohit, Anamika and Zamindar, Indrani , TITLE =. Analysis and Mathematical Physics , FJOURNAL =. 2025 , NUMBER =. doi:10.1007/s13324-025-01014-4 , URL =

    work page doi:10.1007/s13324-025-01014-4 2025

  6. [6]

    SIAM Journal on Imaging Sciences , year=

    V-line tensor tomography: numerical results , author=. SIAM Journal on Imaging Sciences , year=

    work page

  7. [7]

    Combined Modalities of

    Ga. Combined Modalities of. IEEE Transactions on Nuclear Science , year=

    work page

  8. [8]

    Gullberg , journal=

    Roman Basko and Gengsheng Larry Zeng and Grant T. Gullberg , journal=. Fully three dimensional image reconstruction from ". 1997 , volume=

    work page 1997

Show all 270 references
  1. [9]

    Eurasian Journal of Mathematical and Computer Applications , volume=

    Tomography of tensor fields in the plain , author=. Eurasian Journal of Mathematical and Computer Applications , volume=

  2. [10]

    and Vashisth, Manmohan , journal=

    Bhardwaj, Rahul and Mishra, Rohit K. and Vashisth, Manmohan , journal=. On the Inversion of Generalized. 2025 , doi =

    2025

  3. [11]

    Tensor tomography for a set of generalized

    Bhardwaj, Rahul , journal=. Tensor tomography for a set of generalized. 2025 , publisher=

    2025

  4. [12]

    IEEE Transactions on Computational Imaging , volume=

    Inversion of the attenuated v-line transform with vertices on the circle , author=. IEEE Transactions on Computational Imaging , volume=. 2017 , publisher=

    2017

  5. [13]

    SIAM Journal on imaging sciences , volume=

    Analytic inversion of a conical Radon transform arising in application of Compton cameras on the cylinder , author=. SIAM Journal on imaging sciences , volume=. 2017 , publisher=

    2017

  6. [14]

    Inversion of the

    Gaik Ambartsoumian , keywords =. Inversion of the. Computers & Mathematics with Applications , volume =. 2012 , note =. doi:https://doi.org/10.1016/j.camwa.2012.01.059 , url =

    2012 doi

  7. [15]

    Generalized

    Ambartsoumian, Gaik , year=. Generalized

  8. [16]

    Gaik Ambartsoumian , editor =. The

  9. [17]

    , journal=

    Ambartsoumian, Gaik and Latifi, Mohammad J. , journal=. The. 2019 , publisher=

    2019

  10. [18]

    The Journal of Geometric Analysis , volume=

    Inversion and symmetries of the star transform , author=. The Journal of Geometric Analysis , volume=. 2021 , publisher=

    2021

  11. [19]

    and Mishra, Rohit K

    Ambartsoumian, Gaik and Latifi, Mohammad J. and Mishra, Rohit K. , journal=. Numerical implementation of generalized

  12. [20]

    and Mishra, Rohit K

    Ambartsoumian, Gaik and Latifi, Mohammad J. and Mishra, Rohit K. , journal=. Generalized. 2020 , publisher=

    2020

  13. [21]

    Computers & Mathematics with Applications , VOLUME =

    Gaik Ambartsoumian and Sunghwan Moon , title =. Computers & Mathematics with Applications , VOLUME =. 2013 , NUMBER =

    2013

  14. [22]

    2017 , publisher=

    Partial Differential Equations with Fourier Series and Boundary Value Problems: Third Edition , author=. 2017 , publisher=

    2017

  15. [23]

    2003 , publisher=

    Selected Topics in Integral Geometry , author=. 2003 , publisher=

    2003

  16. [24]

    Radon, Johann , biburl =. Akad. Wiss. , keywords =

  17. [25]

    Exact solution of

    André Liemert and Alwin Kienle , keywords =. Exact solution of. Applied Mathematics and Computation , volume =. 2014 , issn =. doi:https://doi.org/10.1016/j.amc.2014.04.003 , url =

    2014 doi

  18. [26]

    Photons Plus Ultrasound: Imaging and Sensing 2007: The Eighth Conference on Biomedical Thermoacoustics, Optoacoustics, and Acousto-optics , volume=

    Thermoacoustic tomography: numerical results , author=. Photons Plus Ultrasound: Imaging and Sensing 2007: The Eighth Conference on Biomedical Thermoacoustics, Optoacoustics, and Acousto-optics , volume=. 2007 , organization=

    2007

  19. [27]

    IEEE Transactions on Computational Imaging , volume=

    Numerical inversion of a broken ray transform arising in single scattering optical tomography , author=. IEEE Transactions on Computational Imaging , volume=. 2016 , publisher=

    2016

  20. [28]

    Inverse Problems , VOLUME =

    Andersson, Fredrik , TITLE =. Inverse Problems , VOLUME =. 2005 , NUMBER =

    2005

  21. [29]

    Range description of a conical

    Baines, Weston , journal=. Range description of a conical

  22. [30]

    Inversion of the generalized

    Denisjuk, Alexander , journal=. Inversion of the generalized. 1994 , publisher=

    1994

  23. [31]

    Inversion of the x-ray transform for

    Denisjuk, Alexander , journal=. Inversion of the x-ray transform for. 2006 , publisher=

    2006

  24. [32]

    Inverse Problems , abstract =

    Aleksander Denisiuk , title =. Inverse Problems , abstract =. 2023 , publisher =. doi:10.1088/1361-6420/acef52 , url =

    2023 doi

  25. [33]

    Numerical Analysis and Applications , volume=

    Reconstruction of vector fields and their singularities from ray transforms , author=. Numerical Analysis and Applications , volume=. 2011 , publisher=

    2011

  26. [34]

    Derevtsov, E. Yu. , TITLE =. J. Inverse Ill-Posed Probl. , FJOURNAL =. 2005 , NUMBER =

    2005

  27. [35]

    Eurasian Journal of Mathematical and Computer Applications , volume=

    Tomography of tensor fields in the plane , author=. Eurasian Journal of Mathematical and Computer Applications , volume=

  28. [36]

    Inverse Problems , VOLUME =

    Desbat, Laurent , TITLE =. Inverse Problems , VOLUME =. 1995 , NUMBER =

    1995

  29. [37]

    1979 , publisher=

    Transport Theory , author=. 1979 , publisher=

    1979

  30. [38]

    Radiation Physics and Chemistry , volume=

    Polarization effects on multiple scattering gamma transport , author=. Radiation Physics and Chemistry , volume=. 1993 , publisher=

    1993

  31. [39]

    Polarisation effects in multiple scattering photon calculations using the

    Fern. Polarisation effects in multiple scattering photon calculations using the. Radiation Physics and Chemistry , volume=. 1999 , publisher=

    1999

  32. [40]

    Physical Review E , volume =

    Single-scattering optical tomography , author =. Physical Review E , volume =. 2009 , month =

    2009

  33. [41]

    Physical Review E , volume =

    Single-scattering optical tomography: Simultaneous reconstruction of scattering and absorption , author =. Physical Review E , volume =. 2010 , month =

    2010

  34. [42]

    and Schotland, John C

    Florescu, Lucia and Markel, Vadim A. and Schotland, John C. , TITLE =. Inverse Problems , VOLUME =. 2011 , NUMBER =

    2011

  35. [43]

    Inverse Problems , volume=

    Nonreciprocal broken ray transforms with applications to fluorescence imaging , author=. Inverse Problems , volume=. 2018 , publisher=

    2018

  36. [44]

    Analytical reconstruction formula for n -dimensional conical

    Gouia-Zarrad, Rim , journal=. Analytical reconstruction formula for n -dimensional conical. 2014 , publisher=

    2014

  37. [45]

    Inverse Problems , volume=

    Rim Gouia-Zarrad and Gaik Ambartsoumian , title=. Inverse Problems , volume=

  38. [46]

    and Schmiedecke, Christian , TITLE =

    Griesmaier, Roland and Mishra, Rohit K. and Schmiedecke, Christian , TITLE =. SIAM J. Sci. Comput. , FJOURNAL =. 2018 , NUMBER =

    2018

  39. [47]

    Journal of Geometric Analysis , volume=

    Generic local uniqueness and stability in polarization tomography , author=. Journal of Geometric Analysis , volume=. 2013 , publisher=

    2013

  40. [48]

    Inverse Problems , volume=

    Alexander Katsevich and Roman Krylov , title=. Inverse Problems , volume=

  41. [49]

    Physics in Medicine & Biology , volume=

    Roman Krylov and Alexander Katsevich , title=. Physics in Medicine & Biology , volume=

  42. [50]

    Inverse Problems , volume=

    An exact inversion formula for cone beam vector tomography , author=. Inverse Problems , volume=. 2013 , publisher=

    2013

  43. [51]

    and Bukhgeim, Alexander A

    Kazantsev, Sergey G. and Bukhgeim, Alexander A. , TITLE =. J. Inverse Ill-Posed Probl. , FJOURNAL =. 2004 , NUMBER =

    2004

  44. [52]

    Mathematical Methods in the Applied Sciences , volume=

    Three-dimensional vector field inversion formula using first moment transverse transform in quaternionic approaches , author=. Mathematical Methods in the Applied Sciences , volume=. 2020 , publisher=

    2020

  45. [53]

    and Mishra, Rohit K

    Krishnan, Venkateswaran P. and Mishra, Rohit K. , journal=. Microlocal analysis of a restricted ray transform on symmetric m -tensor fields in. 2018 , publisher=

    2018

  46. [54]

    Inverse Problems & Imaging , volume=

    Momentum ray transforms , author=. Inverse Problems & Imaging , volume=. 2019 , publisher=

    2019

  47. [55]

    and Manna, Ramesh and Sahoo, Suman K

    Krishnan, Venkateswaran P. and Manna, Ramesh and Sahoo, Suman K. and Sharafutdinov, Vladimir A. , journal=. Momentum ray transforms,. 2020 , publisher=

    2020

  48. [56]

    Journal of Inverse and Ill-posed Problems , volume=

    On solenoidal-injective and injective ray transforms of tensor fields on surfaces , author=. Journal of Inverse and Ill-posed Problems , volume=

  49. [57]

    Journal of Mathematical Analysis and Applications , volume=

    Microlocal inversion of a 3-dimensional restricted transverse ray transform on symmetric tensor fields , author=. Journal of Mathematical Analysis and Applications , volume=. 2021 , publisher=

    2021

  50. [58]

    Inverse Problems & Imaging , volume=

    A support theorem for the geodesic ray transform of symmetric tensor fields , author=. Inverse Problems & Imaging , volume=. 2009 , publisher=

    2009

  51. [59]

    Ray transform on

    Krishnan, Venky P and Sharafutdinov, Vladimir A , journal=. Ray transform on. 2021 , publisher=

    2021

  52. [60]

    , journal=

    Kunyansky, Leonid A. , journal=. A new. 2001 , publisher=

    2001

  53. [61]

    Louis , title =

    Alfred K. Louis , title =. Inverse Problems , abstract =. 2022 , publisher =. doi:10.1088/1361-6420/ac6379 , url =

    2022 doi

  54. [62]

    , journal=

    Mishra, Rohit K. , journal=. Full reconstruction of a vector field from restricted

  55. [63]

    and Monard, Fran

    Mishra, Rohit K. and Monard, Fran. Range characterizations and. J. Spectr. Theory , FJOURNAL =. 2021 , NUMBER =

    2021

  56. [64]

    and Sahoo, Suman K

    Mishra, Rohit K. and Sahoo, Suman K. , title =. SIAM Journal on Mathematical Analysis , volume =

  57. [65]

    Numerical implementation of geodesic

    Monard, Fran. Numerical implementation of geodesic. SIAM Journal on Imaging Sciences , volume=. 2014 , publisher=

    2014

  58. [66]

    Inverse Problems , volume=

    On an integral transform and its inverse in nuclear imaging , author=. Inverse Problems , volume=. 2002 , publisher=

    2002

  59. [67]

    IEEE Transactions on Image Processing , volume=

    Unique tomographic reconstruction of vector fields using boundary data , author=. IEEE Transactions on Image Processing , volume=

  60. [68]

    Inverse Problems , volume=

    On the problem of polarization tomography: I , author=. Inverse Problems , volume=. 2007 , publisher=

    2007

  61. [69]

    Inverse Problems , volume=

    Victor Palamodov , title=. Inverse Problems , volume=

  62. [70]

    2023 , publisher=

    Geometric Inverse Problems: With Emphasis on Two Dimensions , author=. 2023 , publisher=

    2023

  63. [71]

    2000 , publisher =

    Thomas Schuster , title =. 2000 , publisher =

    2000

  64. [72]

    Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (

    Schuster, Thomas , TITLE =. Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (. 2008 , MRCLASS =

    2008

  65. [73]

    and Sahoo, Suman K

    Mishra, Rohit K. and Sahoo, Suman K. , TITLE =. Proc. Amer. Math. Soc. , FJOURNAL =. 2023 , NUMBER =. doi:10.1090/proc/16080 , URL =

    2023 doi

  66. [74]

    , title =

    Vertgeim, Lev B. , title =. Journal of Inverse and Ill-posed Problems , year =

  67. [75]

    On the X-ray transform of planar symmetric 2-tensors , journal =

    Kamran Sadiq and Otmar Scherzer and Alexandru Tamasan , keywords =. On the X-ray transform of planar symmetric 2-tensors , journal =. 2016 , issn =. doi:https://doi.org/10.1016/j.jmaa.2016.04.018 , url =

    2016 doi

  68. [76]

    and Salo, Mikko and Uhlmann, Gunther , TITLE =

    Paternain, Gabriel P. and Salo, Mikko and Uhlmann, Gunther , TITLE =. Chinese Ann. Math. Ser. B , FJOURNAL =. 2014 , NUMBER =. doi:10.1007/s11401-014-0834-z , URL =

    2014 doi

  69. [77]

    and Salo, Mikko and Uhlmann, Gunther , TITLE =

    Paternain, Gabriel P. and Salo, Mikko and Uhlmann, Gunther , TITLE =. Invent. Math. , FJOURNAL =. 2013 , NUMBER =. doi:10.1007/s00222-012-0432-1 , URL =

    2013 doi

  70. [78]

    Efficient tensor tomography in fan-beam coordinates

    Monard, Fran. Efficient tensor tomography in fan-beam coordinates. Inverse Probl. Imaging , year =

  71. [79]

    Inverse Problems , FJOURNAL =

    Denisjuk, Alexander , TITLE =. Inverse Problems , FJOURNAL =. 2006 , NUMBER =

    2006

  72. [80]

    , journal=

    Sharafutdinov, Vladimir A. , journal=. The problem of polarization tomography:. 2008 , publisher=

    2008

  73. [81]

    Brian Sherson , title =

  74. [82]

    Inverse Problems , volume=

    Fatma Terzioglu , title=. Inverse Problems , volume=

  75. [83]

    and Thakkar, Chandni , TITLE =

    Mishra, Rohit K. and Thakkar, Chandni , TITLE =. Inverse Problems , FJOURNAL =. 2024 , NUMBER =

    2024

  76. [84]

    Inverse Problems , volume=

    Fatma Terzioglu and Peter Kuchment and Leonid Kunyansky , title=. Inverse Problems , volume=

  77. [85]

    Inverse Problems , volume=

    The broken ray transform: additional properties and new inversion formula , author=. Inverse Problems , volume=. 2019 , publisher=

    2019

  78. [86]

    IEEE Transactions on Computational Imaging , volume=

    Iterative algorithms for joint scatter and attenuation estimation from broken ray transform data , author=. IEEE Transactions on Computational Imaging , volume=. 2021 , publisher=

    2021

  79. [87]

    Mathematical Methods in the Applied Sciences , volume=

    Vector field reconstruction via quaternionic setting , author=. Mathematical Methods in the Applied Sciences , volume=. 2018 , publisher=

    2018

  80. [88]

    Schotland and Vadim A

    Fan Zhao and John C. Schotland and Vadim A. Markel , title=. Inverse Problems , volume=

  81. [89]

    2019 , month =

    G Ambartsoumian and M J Latifi Jebelli , title =. 2019 , month =. doi:10.1088/1361-6420/aafcf3 , url =

    2019 doi

  82. [90]

    Latifi and Mishra, Rohit K

    Ambartsoumian, Gaik and Jebelli, Mohammad J. Latifi and Mishra, Rohit K. , title =. SIAM Journal on Imaging Sciences , volume =. 2024 , doi =

    2024

  83. [91]

    and Zamindar, Indrani , TITLE =

    Ambartsoumian, Gaik and Mishra, Rohit K. and Zamindar, Indrani , TITLE =. Inverse Problems , FJOURNAL =. 2024 , NUMBER =. doi:10.1088/1361-6420/ad1f83 , URL =

    2024 doi

  84. [92]

    Numerical Inversion of a Broken Ray Transform Arising in Single Scattering Optical Tomography , year=

    Ambartsoumian, Gaik and Roy, Souvik , journal=. Numerical Inversion of a Broken Ray Transform Arising in Single Scattering Optical Tomography , year=

  85. [93]

    2019 , lastchecked =

    Gaik Ambartsoumian , publisher =. 2019 , lastchecked =. doi:doi:10.1515/9783110560855-007 , isbn =

    2019 doi

  86. [94]

    Inverse Problems , abstract =

    Fatma Terzioglu and Peter Kuchment and Leonid Kunyansky , title =. Inverse Problems , abstract =. 2018 , month =. doi:10.1088/1361-6420/aab0ab , url =

    2018 doi

  87. [95]

    Pestov, L. N. and Sharafutdinov, V. A. , TITLE =. Sibirsk. Mat. Zh. , FJOURNAL =. 1988 , NUMBER =. doi:10.1007/BF00969652 , URL =

    1988 doi

  88. [96]

    75 years of

    Radon, Johann , TITLE =. 75 years of. 1994 , MRCLASS =

    1994

  89. [97]

    Cormack, A. M. , TITLE =. J. Appl. Phys. , VOLUME =. 1963 , PAGES =

    1963

  90. [98]

    The inverse problem for the local geodesic ray transform , JOURNAL =

    Uhlmann, Gunther and Vasy, Andr. The inverse problem for the local geodesic ray transform , JOURNAL =. 2016 , NUMBER =. doi:10.1007/s00222-015-0631-7 , URL =

    2016 doi

  91. [99]

    Mukhometov, R. G. , TITLE =. Linear and nonlinear problems in computer tomography (. 1985 , MRCLASS =

    1985

  92. [101]

    Sharafutdinov, V. A. , TITLE =. Sibirsk. Mat. Zh. , FJOURNAL =. 1992 , NUMBER =. doi:10.1007/BF00970902 , URL =

    1992 doi

  93. [102]

    Sharafutdinov, V. A. , TITLE =. Sibirsk. Mat. Zh. , FJOURNAL =. 1983 , NUMBER =

    1983

  94. [103]

    Inverse Problems , FJOURNAL =

    Denisjuk, Alexander , TITLE =. Inverse Problems , FJOURNAL =. 2006 , NUMBER =. doi:10.1088/0266-5611/22/2/001 , URL =

    2006 doi

  95. [104]

    , TITLE =

    Sharafutdinov, Vladimir A. , TITLE =. 1994 , PAGES =. doi:10.1515/9783110900095 , URL =

    1994 doi

  96. [105]

    1999 , PAGES =

    Helgason, Sigurdur , TITLE =. 1999 , PAGES =. doi:10.1007/978-1-4757-1463-0 , URL =

    1999 doi

  97. [106]

    Sharafutdinov, V. A. , TITLE =. Dokl. Akad. Nauk SSSR , FJOURNAL =. 1986 , NUMBER =

    1986

  98. [107]

    Introduction to pseudodifferential and

    Tr. Introduction to pseudodifferential and. 1980 , PAGES =

    1980

  99. [108]

    Gaik Ambartsoumian and Venkateswaran Krishnan and Eric Todd Quinto , title=

  100. [109]

    Inverse Problems , volume = 21, pages =

    Gaik Ambartsoumian and Peter Kuchment , title =. Inverse Problems , volume = 21, pages =

  101. [110]

    Gaik Ambartsoumian and Peter Kuchment , title =. SIAM J. Math. Anal. , volume = 38, number = 2, pages =

  102. [111]

    Katsevich, Alexander , TITLE =. J. Fourier Anal. Appl. , FJOURNAL =. 2002 , NUMBER =. doi:10.1007/s00041-002-0020-7 , URL =

    2002 doi

  103. [112]

    Duke Math

    Boman, Jan and Quinto, Eric Todd , TITLE =. Duke Math. J. , FJOURNAL =. 1987 , NUMBER =. doi:10.1215/S0012-7094-87-05547-5 , URL =

    1987 doi

  104. [113]

    Guillemin, Victor and Sternberg, Shlomo , TITLE =. Amer. J. Math. , FJOURNAL =. 1979 , NUMBER =. doi:10.2307/2373923 , URL =

    1979 doi

  105. [114]

    Nolan and Margaret Cheney , title =

    Clifford J. Nolan and Margaret Cheney , title =. Inverse Problems , volume = 20, number = 2, pages =

  106. [115]

    Duistermaat, J. J. and Guillemin, V. W. , TITLE =. Invent. Math. , FJOURNAL =. 1975 , NUMBER =

    1975

  107. [116]

    Eric Todd Quinto and Tania Bakhos and Sohhyun Chung , title =

  108. [117]

    Gaik Ambartsoumian and Rim Gouia-Zarrad and Matthew Lewis , title =

  109. [118]

    Krishnan and Eric Todd Quinto , title =

    Venkateswaran P. Krishnan and Eric Todd Quinto , title =. 2011 , NOTE =

    2011

  110. [120]

    Near-field Ultrasound Tomography , year=

    Mensah, Serge and Franceschini, Emilie , journal=. Near-field Ultrasound Tomography , year=. doi:10.1109/TIP.2009.2039662 , ISSN=

    2009 doi

  111. [121]

    Norton , title =

    S.J. Norton , title =. J. Acoust. Soc. Am. , year =

  112. [122]

    2010 , institution=

    Eric Todd Quinto and Hans Rullg. 2010 , institution=

    2010

  113. [123]

    Inverse Problems and Imaging , volume = 4, number = 4, pages =

    Hans Rullg. Inverse Problems and Imaging , volume = 4, number = 4, pages =

  114. [124]

    2011 , note=

    Raluca Felea and Eric Todd Quinto , title =. 2011 , note=

    2011

  115. [125]

    , TITLE =

    Krishnan, Venkateswaran P. , TITLE =. J. Fourier Anal. Appl. , FJOURNAL =. 2009 , NUMBER =. doi:10.1007/s00041-009-9061-5 , URL =

    2009 doi

  116. [126]

    Louis and Eric Todd Quinto , title =

    Alfred K. Louis and Eric Todd Quinto , title =. Surveys on Solution Methods for Inverse Problems , editor =

  117. [127]

    International Mathematics Research Notices , pages =

    Eric Todd Quinto , title =. International Mathematics Research Notices , pages =. 2006 , note=

    2006

  118. [128]

    and Stefanov, Plamen , TITLE =

    Krishnan, Venkateswaran P. and Stefanov, Plamen , TITLE =. Inverse Problems and Imaging , VOLUME =. 2009 , NUMBER =

    2009

  119. [129]

    and Cheney, Margaret and Dowling, Thomas and Gaburro, Romina , TITLE =

    Nolan, Clifford J. and Cheney, Margaret and Dowling, Thomas and Gaburro, Romina , TITLE =. Inverse Problems , FJOURNAL =. 2006 , NUMBER =. doi:10.1088/0266-5611/22/5/017 , URL =

    2006 doi

  120. [130]

    Lars-Erik Andersson , title =. SIAM J. Math. Anal. , volume = 19, year = 1988, pages =

    1988

  121. [131]

    Journal of Computational and Applied Mathematics , pages=

    Eric Todd Quinto , title =. Journal of Computational and Applied Mathematics , pages=

  122. [132]

    Eric Todd Quinto and Ozan. SIAM J. Appl. Math. , volume = 68, pages =

  123. [133]

    2010 , institution=

    Hans Rullg. 2010 , institution=

    2010

  124. [134]

    Eric Todd Quinto and Ulf Skoglund and Ozan. Proc. Nat. Acad. Sci. USA , note=

  125. [135]

    , title =

    Fawcett, J. , title =. SIAM J. Appl. Math. , volume =. 1985 , pages =

    1985

  126. [136]

    2004 , journal =

    David Finch and Sarah Patch and Rakesh , title =. 2004 , journal =

    2004

  127. [137]

    2005 , journal =

    Thomas Schuster and Eric Todd Quinto , title =. 2005 , journal =

    2005

  128. [138]

    2010 , institution=

    Eric Todd Quinto and Andreas Rieder and Thomas Schuster , title =. 2010 , institution=

    2010

  129. [139]

    Felea, Raluca , TITLE =. Comm. Partial Differential Equations , FJOURNAL =. 2005 , NUMBER =. doi:10.1080/03605300500299968 , URL =

    2005 doi

  130. [140]

    Inside Out, Inverse Problems and Applications , series =

    David Victor Finch and Ih-Ren Lan and Gunther Uhlmann , title =. Inside Out, Inverse Problems and Applications , series =. 2003 , pages =

    2003

  131. [141]

    Inverse Problems , FJOURNAL =

    Felea, Raluca , TITLE =. Inverse Problems , FJOURNAL =. 2007 , NUMBER =. doi:10.1088/0266-5611/23/4/009 , URL =

    2007 doi

  132. [142]

    and Cheney, Margaret , TITLE =

    Nolan, Clifford J. and Cheney, Margaret , TITLE =. J. Fourier Anal. Appl. , FJOURNAL =. 2004 , NUMBER =. doi:10.1007/s00041-004-8008-0 , URL =

    2004 doi

  133. [143]

    Microlocal analysis for differential operators , SERIES =

    Grigis, Alain and Sj. Microlocal analysis for differential operators , SERIES =. 1994 , PAGES =

    1994

  134. [144]

    2009 , PAGES =

    Cheney, Margaret and Borden, Brett , TITLE =. 2009 , PAGES =

    2009

  135. [145]

    SIAM Rev

    Cheney, Margaret , TITLE =. SIAM Rev. , FJOURNAL =. 2001 , NUMBER =. doi:10.1137/S0036144500368859 , URL =

    2001 doi

  136. [146]

    Krishnan, Venkateswaran P. and Yaz

  137. [147]

    On reconstruction formulas for the ray transform acting on symmetric differentials on surfaces , JOURNAL =

    Monard, Fran. On reconstruction formulas for the ray transform acting on symmetric differentials on surfaces , JOURNAL =. 2014 , NUMBER =. doi:10.1088/0266-5611/30/6/065001 , URL =

    2014 doi

  138. [148]

    , TITLE =

    Krishnan, Venkateswaran P. , TITLE =. J. Inverse Ill-Posed Probl. , FJOURNAL =. 2010 , NUMBER =. doi:10.1515/JIIP.2010.017 , URL =

    2010 doi

  139. [149]

    Anikonov, Yu. E. and Romanov, Vladimir G. , TITLE =. J. Inverse Ill-Posed Probl. , FJOURNAL =. 1997 , NUMBER =. doi:10.1515/jiip.1997.5.6.487 , URL =

    1997 doi

  140. [150]

    Pestov, Leonid and Uhlmann, Gunther , TITLE =. Ann. of Math. (2) , FJOURNAL =. 2005 , NUMBER =. doi:10.4007/annals.2005.161.1093 , URL =

    2005 doi

  141. [151]

    Pestov, Leonid and Uhlmann, Gunther , TITLE =. Int. Math. Res. Not. , FJOURNAL =. 2004 , NUMBER =. doi:10.1155/S1073792804142116 , URL =

    2004 doi

  142. [152]

    Duke Math

    Greenleaf, Allan and Uhlmann, Gunther , TITLE =. Duke Math. J. , FJOURNAL =. 1989 , NUMBER =. doi:10.1215/S0012-7094-89-05811-0 , URL =

    1989 doi

  143. [153]

    1977 , PAGES =

    Guillemin, Victor and Sternberg, Shlomo , TITLE =. 1977 , PAGES =

    1977

  144. [154]

    Duke Math

    Stefanov, Plamen and Uhlmann, Gunther , TITLE =. Duke Math. J. , FJOURNAL =. 2004 , NUMBER =. doi:10.1215/S0012-7094-04-12332-2 , URL =

    2004 doi

  145. [155]

    Stefanov, Plamen and Uhlmann, Gunther , TITLE =. J. Amer. Math. Soc. , FJOURNAL =. 2005 , NUMBER =. doi:10.1090/S0894-0347-05-00494-7 , URL =

    2005 doi

  146. [156]

    Stefanov, Plamen and Uhlmann, Gunther , TITLE =. Amer. J. Math. , FJOURNAL =. 2008 , NUMBER =. doi:10.1353/ajm.2008.0003 , URL =

    2008 doi

  147. [157]

    Sur la rigidit\'e impos\'ee par la longueur des g\'eod\'esiques , JOURNAL =

    Michel, Ren. Sur la rigidit\'e impos\'ee par la longueur des g\'eod\'esiques , JOURNAL =. 1981/82 , NUMBER =. doi:10.1007/BF01389295 , URL =

    1981 doi

  148. [158]

    The analysis of linear partial differential operators

    H. The analysis of linear partial differential operators. 2003 , PAGES =

    2003

  149. [159]

    Synthetic-aperture inversion in the presence of noise and clutter , JOURNAL =

    Yaz. Synthetic-aperture inversion in the presence of noise and clutter , JOURNAL =. 2006 , NUMBER =. doi:10.1088/0266-5611/22/5/011 , URL =

    2006 doi

  150. [160]

    Synthetic aperture hitchhiker imaging , JOURNAL =

    Yaz. Synthetic aperture hitchhiker imaging , JOURNAL =. 2008 , NUMBER =

    2008

  151. [161]

    Inverse Problems , FJOURNAL =

    Cheney, Margaret and Borden, Brett , TITLE =. Inverse Problems , FJOURNAL =. 2003 , NUMBER =. doi:10.1088/0266-5611/19/1/310 , URL =

    2003 doi

  152. [162]

    , TITLE =

    de Hoop, Maarten V. , TITLE =. Inside out: inverse problems and applications , SERIES =. 2003 , MRCLASS =

    2003

  153. [163]

    Felea, Raluca and Greenleaf, Allan , TITLE =. Comm. Partial Differential Equations , FJOURNAL =. 2008 , NUMBER =. doi:10.1080/03605300701318716 , URL =

    2008 doi

  154. [164]

    Felea, Raluca and Greenleaf, Allan and Pramanik, Malabika , TITLE =

  155. [165]

    Inverse Problems , FJOURNAL =

    Agranovsky, Mark and Kuchment, Peter , TITLE =. Inverse Problems , FJOURNAL =. 2007 , NUMBER =. doi:10.1088/0266-5611/23/5/016 , URL =

    2007 doi

  156. [166]

    and de Hoop, Maarten V

    Stolk, Christiaan C. and de Hoop, Maarten V. , TITLE =. Wave Motion , FJOURNAL =. 2006 , NUMBER =. doi:10.1016/j.wavemoti.2006.05.003 , URL =

    2006 doi

  157. [167]

    Ulander, Lars M. H. and Hellsten, H. and Stenstr\"om, G. , TITLE =. IEEE Transactions on Aerospace and Electronic Systems , VOLUME =. 2006 , NUMBER =

    2006

  158. [168]

    Bistatic synthetic aperture radar imaging for arbitrary flight trajectories , JOURNAL =

    Yarman, Can Evren and Yaz. Bistatic synthetic aperture radar imaging for arbitrary flight trajectories , JOURNAL =. 2008 , NUMBER =. doi:10.1109/TIP.2007.911812 , URL =

    2008 doi

  159. [169]

    Singularit\'es analytiques microlocales , BOOKTITLE =

    Sj. Singularit\'es analytiques microlocales , BOOKTITLE =. 1982 , MRCLASS =

    1982

  160. [170]

    Helgason, Sigur. The. Acta Math. , FJOURNAL =. 1965 , PAGES =

    1965

  161. [171]

    Duke Math

    Guillemin, Victor and Uhlmann, Gunther , TITLE =. Duke Math. J. , FJOURNAL =. 1981 , NUMBER =

    1981

  162. [172]

    Greenleaf, Allan and Uhlmann, Gunther , TITLE =. J. Funct. Anal. , FJOURNAL =. 1990 , NUMBER =. doi:10.1016/0022-1236(90)90011-9 , URL =

    1990 doi

  163. [173]

    and Uhlmann, G

    Greenleaf, A. and Uhlmann, G. , TITLE =. Ann. Inst. Fourier (Grenoble) , FJOURNAL =. 1990 , NUMBER =

    1990

  164. [174]

    Integral geometry and tomography (

    Greenleaf, Allan and Uhlmann, Gunther , TITLE =. Integral geometry and tomography (. 1990 , MRCLASS =

    1990

  165. [175]

    and Uhlmann, Gunther A

    Melrose, Richard B. and Uhlmann, Gunther A. , TITLE =. Comm. Pure Appl. Math. , FJOURNAL =. 1979 , NUMBER =. doi:10.1002/cpa.3160320403 , URL =

    1979 doi

  166. [176]

    Duistermaat, J. J. , TITLE =. 2011 , PAGES =

    2011

  167. [177]

    Fourier integral operators

    H. Fourier integral operators. Acta Math. , FJOURNAL =. 1971 , NUMBER =

    1971

  168. [178]

    1989 , PAGES =

    Guillemin, Victor , TITLE =. 1989 , PAGES =

    1989

  169. [179]

    1977 , author =

    Acoustical Holography , publisher =. 1977 , author =

    1977

  170. [180]

    The Journal of the Acoustical Society of America , year =

    Sato, Takuso and Aoki, Hisayuki and Ikeda, Osamu , title =. The Journal of the Acoustical Society of America , year =

  171. [181]

    Applied Optics , year =

    Faris, Gregory W and Byer, Robert L , title =. Applied Optics , year =

  172. [182]

    Deep Sea Research Part A

    Munk, Walter and Wunsch, Carl , title =. Deep Sea Research Part A. Oceanographic Research Papers , year =

  173. [183]

    Journal of Geophysical Research: Oceans , year =

    Howe, Bruce M and Worcester, Peter F and Spindel, Robert C , title =. Journal of Geophysical Research: Oceans , year =

  174. [184]

    Journal of Fourier Analysis and Applications , year =

    Ramaseshan, Karthik , title =. Journal of Fourier Analysis and Applications , year =

  175. [185]

    Serdica Math

    Stefanov, Plamen , title =. Serdica Math. J , year =

  176. [186]

    Journal of Soviet Mathematics , year =

    Gel'Fand, IM and Gindikin, SG and Graev, MI , title =. Journal of Soviet Mathematics , year =

  177. [187]

    Alexander Denisjuk , title =. Am. Math. Soc. Trans , year =

  178. [188]

    SIAM Journal on Mathematical Analysis , year =

    Palamodov, Victor , title =. SIAM Journal on Mathematical Analysis , year =

  179. [189]

    Muhometov, R. G. , title =. Sibirsk. Mat. Zh. , year =

  180. [190]

    SIAM Journal on Applied Mathematics , year =

    Tuy, Heang K , title =. SIAM Journal on Applied Mathematics , year =

  181. [191]

    Journal of Inverse and Ill-posed Problems , year =

    Vertgeim, LB , title =. Journal of Inverse and Ill-posed Problems , year =

  182. [192]

    Inverse Problems , year =

    Katsevich, Alexander and Schuster, Thomas , title =. Inverse Problems , year =

  183. [193]

    Inverse Problems , year =

    Schuster, Thomas , title =. Inverse Problems , year =

  184. [194]

    Mathematical methods in tomography , publisher =

    Grangeat, Pierre , title =. Mathematical methods in tomography , publisher =. 1991 , pages =

    1991

  185. [195]

    Inside Out, Inverse Problems and Applications , year =

    Lan, Ih-Ren and Finch, David V and Uhlmann, Gunther , title =. Inside Out, Inverse Problems and Applications , year =

  186. [196]

    Transactions of the American Mathematical Society , year =

    Boman, Jan and Quinto, Eric Todd , title =. Transactions of the American Mathematical Society , year =

  187. [197]

    American Mathematical Society, Series Contemporary Mathematics , year =

    Ambartsoumian, Gaik and Boman, Jan and Krishnan, Venkateswaran P and Quinto, Eric Todd , title =. American Mathematical Society, Series Contemporary Mathematics , year =

  188. [198]

    Quinto, Eric Todd , title =. Radon Transforms and Tomography: 2000 AMS-IMS-SIAM Joint Summer Research Conference on Radon Transforms and Tomography, Mount Holyoke College, South Hadley, Massachusetts, June 18-22, 2000 , year =

    2000

  189. [199]

    Grangeat, Pierre , title =

  190. [200]

    and Almqvist, M

    Jansson, T. and Almqvist, M. and Eriksson, R. and Strahlen, K. and Sparr, G. and Persson, H. W. and Lindstrom, K. , title =

  191. [201]

    Krishnan and Rohit K

    Venkateswaran P. Krishnan and Rohit K. Mishra , title =

  192. [202]

    SIAM Journal on Applied Mathematics , year =

    Katsevich, Alexander and Kapralov, Mikhail , title =. SIAM Journal on Applied Mathematics , year =

  193. [203]

    Inverse Problems , year =

    Katsevich, Alexander , title =. Inverse Problems , year =

  194. [204]

    Inverse Problems

    Sharafutdinov, Vladimir , title =. Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data , year =. doi:10.1088/0266-5611/23/6/021 , keywords =

    doi

  195. [205]

    Svetov, I. E. , title =. Numerical Analysis and Applications , year =. doi:10.1134/S1995423912030093 , issn =

    doi

  196. [206]

    Inverse Problems , year =

    Desai, Naeem M and Lionheart, William RB , title =. Inverse Problems , year =

  197. [207]

    Inverse Problems , year =

    W R B Lionheart and P J Withers , title =. Inverse Problems , year =. doi:10.1088/0266-5611/31/4/045005 , publisher =

    doi

  198. [208]

    Inverse Problems , year =

    Roman Novikov and Vladimir Sharafutdinov , title =. Inverse Problems , year =. doi:10.1088/0266-5611/23/3/023 , publisher =

    doi

  199. [209]

    Inverse Problems , year =

    Vladimir Sharafutdinov , title =. Inverse Problems , year =. doi:10.1088/0266-5611/24/3/035010 , publisher =

    doi

  200. [210]

    and Mishra, Rohit K

    Krishnan, Venkateswaran P. and Mishra, Rohit K. , title =. SIAM J. Math. Anal. , year =. doi:10.1137/18M1178530 , fjournal =

    doi

  201. [211]

    Efficient tensor tomography in fan-beam coordinates , journal =

    Monard, Fran. Efficient tensor tomography in fan-beam coordinates , journal =. 2016 , volume =. doi:10.3934/ipi.2016007 , fjournal =

    2016 doi

  202. [212]

    Efficient tensor tomography in fan-beam coordinates

    Monard, Fran. Efficient tensor tomography in fan-beam coordinates. Inverse Probl. Imaging , year =. doi:10.3934/ipi.2018019 , fjournal =

    doi

  203. [213]

    and Mishra, Rohit K

    Krishnan, Venkateswaran P. and Mishra, Rohit K. and Monard, Fran. On solenoidal-injective and injective ray transforms of tensor fields on surfaces. , journal =. 2019 , volume =

    2019

  204. [214]

    Mishra , title =

    Rohit K. Mishra , title =. Arxiv , year =

  205. [215]

    Imaging microstructures , publisher =

    Lionheart, William and Sharafutdinov, Vladimir , title =. Imaging microstructures , publisher =. 2009 , volume =. doi:10.1090/conm/494/09648 , mrclass =

    2009 doi

  206. [216]

    and Schmiedecke, Christian , title =

    Griesmaier, Roland and Mishra, Rohit K. and Schmiedecke, Christian , title =. SIAM J. Sci. Comput. , year =. doi:10.1137/17M1150943 , fjournal =

    doi

  207. [217]

    Krishnan and Rohit K

    Venkateswaran P. Krishnan and Rohit K. Mishra and Suman K. Sahoo , title =

  208. [218]

    Inverse Problems , year =

    S Holman , title =. Inverse Problems , year =. doi:10.1088/0266-5611/25/3/035009 , publisher =

    doi

  209. [219]

    , title =

    William RB Lionheart. , title =

  210. [220]

    Patcharee Wongsason , title =

  211. [221]

    Physical Review E , volume =

    Single-scattering optical tomography , author =. Physical Review E , volume =. 2009 , month =. doi:10.1103/PhysRevE.79.036607 , url =

    2009 doi

  212. [222]

    Physical Review E , volume =

    Single-scattering optical tomography: Simultaneous reconstruction of scattering and absorption , author =. Physical Review E , volume =. 2010 , month =. doi:10.1103/PhysRevE.81.016602 , url =

    2010 doi

  213. [223]

    Markel and John C

    Lucia Florescu and Vadim A. Markel and John C. Schotland , title =. Inverse Problems , abstract =. 2011 , month =. doi:10.1088/0266-5611/27/2/025002 , url =

    2011 doi

  214. [224]

    and Greenleaf, James F

    Johnson, Steven A. and Greenleaf, James F. and M. Tanaka and G. Flandro. Reconstructing three-dimensional temperature and fluid velocity vector fields from acoustic transmission measurements. ISA Transactions. 1977

    1977

  215. [225]

    Faris and Robert L

    Gregory W. Faris and Robert L. Byer , journal =. Three-dimensional beam-deflection optical tomography of a supersonic jet , volume =. 1988 , url =. doi:10.1364/AO.27.005202 , abstract =

    1988 doi

  216. [226]

    and Worcester, Peter F

    Howe, Bruce M. and Worcester, Peter F. and Spindel, Robert C. , title =. Journal of Geophysical Research: Oceans , volume =. doi:https://doi.org/10.1029/JC092iC04p03785 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/JC092iC04p03785 , abstract =

    doi

  217. [227]

    1979 , issn =

    Ocean acoustic tomography: a scheme for large scale monitoring , journal =. 1979 , issn =. doi:https://doi.org/10.1016/0198-0149(79)90073-6 , url =

    1979 doi

  218. [228]

    The Journal of the Acoustical Society of America , volume =

    Sato, Takuso and Aoki, Hisayuki and Ikeda, Osamu , title = ". The Journal of the Acoustical Society of America , volume =. 1985 , month =. doi:10.1121/1.391734 , url =

    1985 doi

  219. [229]

    Florescu, J.C

    L. Florescu, J.C. Schotland and V.A. Markel , title=. Physical Review E , volume=. 2009 , publisher=

    2009

  220. [230]

    Florescu, J.C

    L. Florescu, J.C. Schotland and V.A. Markel , title=. Physical Review E , volume=. 2010 , publisher=

    2010

  221. [231]

    Florescu, J.C

    L. Florescu, J.C. Schotland and V.A. Markel , title=. Inverse Problems , volume=. 2011 , publisher=

    2011

  222. [232]

    Computers & Mathematics with Applications , volume=

    Gaik Ambartsoumian , title=. Computers & Mathematics with Applications , volume=. 2012 , publisher=

    2012

  223. [233]

    Ambartsoumian, R

    G. Ambartsoumian, R. Gouia-Zarrad and Matthew A. Lewis , title=. Inverse Problems , volume=. 2010 , publisher=

    2010

  224. [234]

    Ambartsoumian and S

    G. Ambartsoumian and S. Moon , title=. Computers & Mathematics with Applications , volume=. 2013 , publisher=

    2013

  225. [235]

    Allmaras, D.P

    M. Allmaras, D.P. Darrow, Y. Hristova, G. Kanschat and P. Kuchment , title=. arXiv preprint arXiv:1012.3373 , year=

    arXiv

  226. [236]

    and Gullberg, Grant T

    Basko, Roman and Zeng, Gengsheng L. and Gullberg, Grant T. , title=. IEEE Transactions on Nuclear Science , volume=. 1997 , publisher=

    1997

  227. [237]

    Morvidone, Marcela and Nguyen, Ma. On the. Journal of Biomedical Imaging , volume=. 2010 , publisher=

    2010

  228. [238]

    and Truong, Tuong T

    Nguyen, Mai K. and Truong, Tuong T. , title=. Journal of Physics A: Mathematical and Theoretical , volume=. 2011 , publisher=

    2011

  229. [239]

    Hansen , title=

    E.W. Hansen , title=. JOSA , volume=. 1981 , publisher=

    1981

  230. [240]

    Natterer , title=

    F. Natterer , title=. 2001 , publisher=

    2001

  231. [241]

    Natterer and F

    F. Natterer and F. W. Mathematical methods in image reconstruction , year=

  232. [242]

    Sneddon , title=

    I.N. Sneddon , title=. Glasgow Mathematical Journal , volume=. 1968 , publisher=

    1968

  233. [243]

    Verly , title=

    J.G. Verly , title=. JOSA , volume=. 1981 , publisher=

    1981

  234. [244]

    Titchmarsh , title=

    E.C. Titchmarsh , title=. 1948 , publisher=

    1948

  235. [245]

    Quinto , title=

    E.T. Quinto , title=. SIAM Journal on Mathematical Analysis , volume=. 1993 , publisher=

    1993

  236. [246]

    Y. Xu, L.H. Wang, G. Ambartsoumian and P. Kuchment , title=. Photoacoustic imaging and spectroscopy , pages=. 2017 , publisher=

    2017

  237. [247]

    Translations of the American Mathematical Society-Series 2 , volume=

    Aleksander Denisyuk , title=. Translations of the American Mathematical Society-Series 2 , volume=. 1994 , publisher=

    1994

  238. [248]

    Inverse problems , volume=

    Aleksander Denisyuk , title=. Inverse problems , volume=. 2006 , publisher=

    2006

  239. [249]

    Inverse Problems , volume=

    Alexander Katsevich , title=. Inverse Problems , volume=. 2006 , publisher=

    2006

  240. [250]

    Schuster , title=

    Alexander Katsevich and Thomas. Schuster , title=. Inverse Problems , volume=. 2013 , publisher=

    2013

  241. [251]

    Krishnan and R.K

    V.P. Krishnan and R.K. Mishra , title=. SIAM Journal on Mathematical Analysis , volume=. 2018 , publisher=

    2018

  242. [252]

    Monard , title=

    F. Monard , title=. arXiv preprint arXiv:1510.05132 , year=

    arXiv

  243. [253]

    SIAM journal on mathematical analysis , volume=

    Victor Palamodov , title=. SIAM journal on mathematical analysis , volume=. 2009 , publisher=

    2009

  244. [254]

    Paternain, M

    G.P. Paternain, M. Salo and G. Uhlmann , title=. Inventiones mathematicae , volume=. 2013 , publisher=

    2013

  245. [255]

    Inverse Problems , volume=

    Thomas Schuster , title=. Inverse Problems , volume=. 2000 , publisher=

    2000

  246. [256]

    Sharafutdinov , title=

    Vladimir A. Sharafutdinov , title=. 2012 , publisher=

    2012

  247. [257]

    Sharafutdinov , title=

    Vladimir A. Sharafutdinov , title=. Inverse problems , volume=. 2007 , publisher=

    2007

  248. [258]

    Tuy , title=

    H.K. Tuy , title=. SIAM Journal on Applied Mathematics , volume=. 1983 , publisher=

    1983

  249. [259]

    Mishra, Suman K

    Rohit K. Mishra, Suman K. Sahoo , title=. SIAM Journal on Mathematical Analysis , volume=. 2021 , publisher=

    2021

  250. [260]

    Mishra , title=

    Rohit K. Mishra , title=. Journal of Inverse and Ill-posed Problems , volume=

  251. [261]

    Ambartsoumian, M.J.L

    G. Ambartsoumian, M.J.L. Jebelli and R.K. Mishra , title=. Inverse Problems , volume=. 2020 , publisher=

    2020

  252. [262]

    Ambartsoumian, R.K

    G. Ambartsoumian, R.K. Mishra and I. Zamindar , title=. arXiv preprint arXiv:2306.13245 , year=

  253. [263]

    Krishnan, Rohit K

    Venkateswaran P. Krishnan, Rohit K. Mishra and Francois Monard , title=. Journal of Inverse and Ill-posed Problems , volume=

  254. [264]

    Kim and P

    D. Kim and P. Wongsason , title=. Mathematical Methods in the Applied Sciences , volume=. 2020 , publisher=

    2020

  255. [265]

    Pickalov , title=

    Evgeny Yu Derevtsov, V.V. Pickalov , title=. Numerical Analysis and Applications , volume=. 2011 , publisher=

    2011

  256. [266]

    Svetov , title=

    Derevtsov Yu Derevtsov and Ivon E. Svetov , title=. Eurasian Journal of Mathematical and Computer Applications , volume=

  257. [267]

    Sparr, K

    G. Sparr, K. Strahlen, K. Lindstrom and H.W. Persson , title=. Inverse Problems , volume=. 1995 , publisher=

    1995

  258. [268]

    Lee , title=

    J.M. Lee , title=. 2003 , publisher=

    2003

  259. [269]

    Sahoo and M

    S.K. Sahoo and M. Vashisth , title=. arXiv preprint arXiv:1901.08026 , year=

    1901

  260. [270]

    Flajolet, X

    P. Flajolet, X. Gourdon and P. Dumas , title=. Theoretical computer science , volume=. 1995 , publisher=

    1995

  261. [271]

    2012 , publisher=

    John M Lee , title=. 2012 , publisher=

    2012

  262. [272]

    Vashisth , title=

    M. Vashisth , title=. Journal of Inverse and Ill-posed Problems , volume=

Pith tools

Reviewed July 1, 2026 · model on record in the stance chip above.