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A new exact inversion method for exponential Radon transform using the harmonic analysis of the Euclidean motion group
1. | Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, NY 12180, United States, United States |
[1] |
Simon Gindikin. A remark on the weighted Radon transform on the plane. Inverse Problems and Imaging, 2010, 4 (4) : 649-653. doi: 10.3934/ipi.2010.4.649 |
[2] |
Alberto Ibort, Alberto López-Yela. Quantum tomography and the quantum Radon transform. Inverse Problems and Imaging, 2021, 15 (5) : 893-928. doi: 10.3934/ipi.2021021 |
[3] |
Michael Krause, Jan Marcel Hausherr, Walter Krenkel. Computing the fibre orientation from Radon data using local Radon transform. Inverse Problems and Imaging, 2011, 5 (4) : 879-891. doi: 10.3934/ipi.2011.5.879 |
[4] |
Sunghwan Moon. Inversion of the spherical Radon transform on spheres through the origin using the regular Radon transform. Communications on Pure and Applied Analysis, 2016, 15 (3) : 1029-1039. doi: 10.3934/cpaa.2016.15.1029 |
[5] |
Ali Gholami, Mauricio D. Sacchi. Time-invariant radon transform by generalized Fourier slice theorem. Inverse Problems and Imaging, 2017, 11 (3) : 501-519. doi: 10.3934/ipi.2017023 |
[6] |
Hans Rullgård, Eric Todd Quinto. Local Sobolev estimates of a function by means of its Radon transform. Inverse Problems and Imaging, 2010, 4 (4) : 721-734. doi: 10.3934/ipi.2010.4.721 |
[7] |
Gareth Ainsworth. The attenuated magnetic ray transform on surfaces. Inverse Problems and Imaging, 2013, 7 (1) : 27-46. doi: 10.3934/ipi.2013.7.27 |
[8] |
Gareth Ainsworth. The magnetic ray transform on Anosov surfaces. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 1801-1816. doi: 10.3934/dcds.2015.35.1801 |
[9] |
Jean-François Crouzet. 3D coded aperture imaging, ill-posedness and link with incomplete data radon transform. Inverse Problems and Imaging, 2011, 5 (2) : 341-353. doi: 10.3934/ipi.2011.5.341 |
[10] |
James W. Webber, Sean Holman. Microlocal analysis of a spindle transform. Inverse Problems and Imaging, 2019, 13 (2) : 231-261. doi: 10.3934/ipi.2019013 |
[11] |
Yang Zhang. Artifacts in the inversion of the broken ray transform in the plane. Inverse Problems and Imaging, 2020, 14 (1) : 1-26. doi: 10.3934/ipi.2019061 |
[12] |
Dan Jane, Gabriel P. Paternain. On the injectivity of the X-ray transform for Anosov thermostats. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 471-487. doi: 10.3934/dcds.2009.24.471 |
[13] |
Yiran Wang. Parametrices for the light ray transform on Minkowski spacetime. Inverse Problems and Imaging, 2018, 12 (1) : 229-237. doi: 10.3934/ipi.2018009 |
[14] |
Gareth Ainsworth, Yernat M. Assylbekov. On the range of the attenuated magnetic ray transform for connections and Higgs fields. Inverse Problems and Imaging, 2015, 9 (2) : 317-335. doi: 10.3934/ipi.2015.9.317 |
[15] |
Siamak RabieniaHaratbar. Support theorem for the Light-Ray transform of vector fields on Minkowski spaces. Inverse Problems and Imaging, 2018, 12 (2) : 293-314. doi: 10.3934/ipi.2018013 |
[16] |
François Rouvière. X-ray transform on Damek-Ricci spaces. Inverse Problems and Imaging, 2010, 4 (4) : 713-720. doi: 10.3934/ipi.2010.4.713 |
[17] |
Jan Boman. Unique continuation of microlocally analytic distributions and injectivity theorems for the ray transform. Inverse Problems and Imaging, 2010, 4 (4) : 619-630. doi: 10.3934/ipi.2010.4.619 |
[18] |
Venkateswaran P. Krishnan, Plamen Stefanov. A support theorem for the geodesic ray transform of symmetric tensor fields. Inverse Problems and Imaging, 2009, 3 (3) : 453-464. doi: 10.3934/ipi.2009.3.453 |
[19] |
Mark Hubenthal. The broken ray transform in $n$ dimensions with flat reflecting boundary. Inverse Problems and Imaging, 2015, 9 (1) : 143-161. doi: 10.3934/ipi.2015.9.143 |
[20] |
Daniel Fusca. The Madelung transform as a momentum map. Journal of Geometric Mechanics, 2017, 9 (2) : 157-165. doi: 10.3934/jgm.2017006 |
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