×
Al-Omari, S. K. Q.; Kılıçman, A.

On the exponential Radon transform and its extension to certain functions spaces. (English) Zbl 1474.44003

Abstr. Appl. Anal. 2014, Article ID 612391, 6 p. (2014).
Summary: We investigate the exponential Radon transform on a certain function space of generalized functions. We establish certain space of generalized functions for the cited transform. The transform that is obtained is well defined. More properties of consistency, convolution, analyticity, continuity, and sufficient theorems have been established.

Cited in 4 Documents

MSC:

44A12 Radon transform
46F12 Integral transforms in distribution spaces
PDF BibTeX XML Cite
\textit{S. K. Q. Al-Omari} and \textit{A. Kılıçman}, Abstr. Appl. Anal. 2014, Article ID 612391, 6 p. (2014; Zbl 1474.44003)
Full Text: DOI

References:

[1] Robinson, E. A., Spectral approach to geophysical inversion by Lorentz, Fourier and Radon transforms, Proceedings of the IEEE Institute of Electrical and Electronics Engineers, 70, 9, 1039-1054 (1982)
[2] Chapman, C. H., Generalized Radon transforms and slant stacks, Geophysical Journal, Royal Astronomical Society, 66, 2, 445-453 (1981) · Zbl 0464.73132
[3] Mikusiński, P.; Zayed, A., The Radon transform of Boehmians, Proceedings of the American Mathematical Society, 118, 2, 561-570 (1993) · Zbl 0774.44004
[4] Roopkumar, R., Generalized Radon transform, The Rocky Mountain Journal of Mathematics, 36, 4, 1375-1390 (2006) · Zbl 1135.46020
[5] Ludwig, D., The Radon transform on euclidean space, Communications on Pure and Applied Mathematics, 19, 49-81 (1966) · Zbl 0134.11305
[6] Deans, S. R., The Radon Transform and Some of Its Applications (1973), New York, NY, USA: John Wiley & Sons, New York, NY, USA
[7] Kurusa, Á., A characterization of the Radon transform and its dual of Euclidean space, Acta Universitatis Szegediensis, 54, 3-4, 273-276 (1990) · Zbl 0732.44001
[8] Hertle, A., A characterization of Fourier and Radon transforms on Euclidean space, Transactions of the American Mathematical Society, 273, 2, 595-607 (1982) · Zbl 0569.44004
[9] Hertle, A., Continuity of the Radon transform and its inverse on Euclidean space, Mathematische Zeitschrift, 184, 2, 165-192 (1983) · Zbl 0507.46036
[10] Beylkin, G., Discrete Radon transform, Institute of Electrical and Electronics Engineers. Transactions on Acoustics, Speech, and Signal Processing, 35, 2, 162-172 (1987)
[11] Fishburn, P.; Schwander, P.; Shepp, L.; Vanderbei, R. J., The discrete Radon transform and its approximate inversion via linear programming, Discrete Applied Mathematics, 75, 1, 39-61 (1997) · Zbl 0879.68103
[12] Clough, A. V.; Barrett, H. H., Attenuated radon and abel transforms, Journal of the Optical Society of America, 73, 11, 1590-1595 (1983)
[13] Bal, G.; Moireau, P., Fast numerical inversion of the attenuated Radon transform with full and partial measurements, Inverse Problems, 20, 4, 1137-1164 (2004) · Zbl 1094.65130
[14] Yarman, C. E.; Yazici, B., A new exact inversion method for exponential Radon transform using the harmonic analysis of the Euclidean motion group, Inverse Problems and Imaging, 1, 3, 457-479 (2007) · Zbl 1133.44002
[15] Sidky, E. Y.; Kao, C.-M.; LaRiviere, P. J.; Pan, X., Noise properties of the inverse \(π\)-scheme exponential radon transform, Medical Imaging: Image Processing
[16] Tretiak, O.; Metz, C., The exponential Radon transform, SIAM Journal on Applied Mathematics, 39, 2, 341-354 (1980) · Zbl 0459.44003
[17] Al-Omari, S. K. Q., Hartley transforms on a certain space of generalized functions, Georgian Mathematical Journal, 20, 3, 415-426 (2013) · Zbl 1277.42003
[18] Al-Omari, S. K. Q.; Kılıçman, A., Note on Boehmians for class of optical Fresnel wavelet transforms, Journal of Function Spaces and Applications, 2012 (2012) · Zbl 1266.46030
[19] Al-Omari, S. K. Q.; Kılıçman, A., On generalized Hartley-Hilbert and Fourier-Hilbert transforms, Advances in Difference Equations, 2012, article 232 (2012) · Zbl 1381.42006
[20] Boehme, T. K., The support of Mikusiński operators, Transactions of the American Mathematical Society, 176, 319-334 (1973) · Zbl 0268.44005
[21] Al-Omari, S. K. Q.; Kılıçman, A., On diffraction Fresnel transforms for Boehmians, Abstract and Applied Analysis, 2011 (2011) · Zbl 1243.46032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.