Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the injectivity of the attenuated Radon transform


Author: Alexander Hertle
Journal: Proc. Amer. Math. Soc. 92 (1984), 201-205
MSC: Primary 44A15; Secondary 65R10, 92A07
DOI: https://doi.org/10.1090/S0002-9939-1984-0754703-0
MathSciNet review: 754703
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the attenuated (exponential) Radon transform $ {R_\mu }$, where $ \mu $ is assumed to be linear in the space variable, is injective on compactly supported distributions. Moreover, a limited angle reconstruction is possible and a hole theorem holds. We review the well-known special case of constant attenuation.


References [Enhancements On Off] (What's this?)

  • [1] E. M. Cirka, Approximation of holomorphic functions on smooth manifolds in $ {C^n}$, Math. USSR Sb. 7 (1969), 95-114.
  • [2] S. Helgason, The Radon transform, Birkhäuser, Boston, Mass., 1980. MR 1723736 (2000m:44003)
  • [3] A. Markoe, Fourier inversion of the attenuated X-ray transform, SIAM J. Math. Anal. (to appear). MR 747431 (86a:44006)
  • [4] A. Markoe and E. T. Quinto, An elementary proof of local invertibility for generalized and attenuated Radon transforms, Preprint 1983. MR 800800 (87f:44009)
  • [5] F. Natterer, On the inversion of the attenuated Radon transform, Numer. Math. 32 (1979), 431-438. MR 542205 (80e:65122)
  • [6] E. T. Quinto, The invertibility of rotation invariant Radon transforms, J. Math. Anal. Appl. 91 (1983), 510-522. MR 690884 (84j:44007a)
  • [7] R. S. Strichartz, Radon inversion--variations on a theme, Amer. Math. Monthly 89 (1982), 377-384. MR 660917 (83m:44008)
  • [8] O. J. Tretiak, Attenuated and exponential Radon transforms, Proc. Sympos. Appl. Math., vol. 27, Amer. Math. Soc. Providence, R.I., 1982. MR 692051 (84c:92010)
  • [9] O. J. Tretiak and C. L. Metz, The exponential Radon transform, SIAM J. Appl. Math. 39 (1980), 341-354. MR 588505 (82a:44004)
  • [10] J. Wermer, Banach algebras and several complex variables, 2nd ed., Springer, Berlin and New York, 1976. MR 0394218 (52:15021)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 44A15, 65R10, 92A07

Retrieve articles in all journals with MSC: 44A15, 65R10, 92A07


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0754703-0
Keywords: Attenuated Radon transform, generalized Radon transform, Fourier transform
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society