Pseudolocal tomography

SIAM Journal on Applied Mathematics

Volumn 56, Issue 1, 1996, Pages 167-191

  Katsevich, Alexander I ^a   Ramm, Alexander G ^a,b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b KANSAS STATE UNIVERSITY   (United States)

Author keywords

Detection of discontinuities; Image enhancement; Local; Tomography

Indexed keywords

IMAGE ENHANCEMENT; IMAGE QUALITY; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; PROBABILITY DENSITY FUNCTION;

CAUCHY KERNEL; DISCONTINUITY DETECTION; PSEUDOLOCAL TOMOGRAPHY; RADON TRANSFORM INVERSION FORMULA;

IMAGING TECHNIQUES;

EID: 0030083211     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139994266116     Document Type: Article

References (18)

1. S. CHOW AND J. HALE, Methods of Bifurcation Theory, Springer-Verlag, New York, 1982.
2. A. FARIDANI, F. KEINERT, F. NATTERER, E. L. RITMAN, AND K.T. SMITH, Local and global tomography, in Signal Processing, IMA Vol. Math. Appl., Vol. 23, Springer-Verlag, New York, 1990, pp. 241-255.
3. A. FARIDANI, E. L. RITMAN, AND K. T. SMITH, Local tomography, SIAM J. Appl. Math., 52 (1992), pp. 459-484, 1193-1198.
4. I. GELFAND, M. GRAEV, AND N. VILENKIN, Integral Geometry and Representation Theory, Academic Press, New York, 1965.
5. I. S. GHADSHTEYN AND I. M. RYZHIK, Table of Integrals. Series, and Products, 5th ed., Academic Press, Boston, 1994.
6. A. I. KATSEVICH AND A. G. RAMM, A method for finding discontinuities of functions from the tomographic data, in Proceedings of the 1993 AMS-SIAM Summer Seminar on the Mathematics of Tomography, Impedance Imaging and Integral Geometry, M. Oheney, P. Kuchment, and E. T. Quinto, eds., 1994.
7. _, Finding Singular Support of a Function From Its Tomographic Data, Preprint, Los Alamos National Laboratory, Los Alamos, NM, 1994.
8. _, Asymptotics of PDO on discontinuous functions near singular support, Preprint, Los Alamos National Laboratory, Los Alamos, NM, 1994.
9. F. NATTERER, The Mathematics of Computerized Tomography, J. Wiley, New York, 1986.
10. V. P. PALAMODOV, Some singular problems in tomography, in Mathematical Problems of Tomography, I.M. Gelfand and S.G. Gindikin. eds., Amer. Math. Soc., Providence, RI, 1990, pp. 123-140.
11. D. A. POPOV, On convergence of a class of algorithms for the inversion of the numerical Radon transform, in Mathematical Problems of Tomography, I. M. Gelfand and S. G. Gindikin, eds., Amer. Math. Soc., Providence, RI, 1990, pp. 7-65.
12. 3, SIAM J. Math. Anal., 24 (1993), pp. 1215-1225.
13. A. G. RAMM AND A. I. ZASLAVSKY, Singularities of the Radon transform. Bull. Amer. Math. Soc., 25 (1993), pp. 109-115.
14. _, Reconstructing singularities of a function given its Radon transform. Math. Comput. Modelling, 18, 1 (1993), pp. 109-138.
15. _, Asymptotics of the Fourier transform of piecewise-smooth functions, C. R. Acad. Sci Paris Ser. I Math., 316 (1993), pp. 541-545.
16. K. T. SMITH AND F. KEINERT, Mathematical foundations of computed tomography, Appl. Optics (1985), pp. 3950-3957.
17. F. TREVES, Introduction to Pseudodifferential and Fourier Integral operators, Vol. I: Pseudodifferential Operators, Plenum, New York, 1980.
18. E. I. VAINBERG, I. A. KAZAK, AND V. P. KURCZAEV, Reconstruction of the internal three-dimensional structure of objects based on real-time integral projections, Soviet J. Non-dest. Test., 17 (1981), pp. 415-423.