Integral geometry in hyperbolic spaces and electrical impedance tomography

SIAM Journal on Applied Mathematics

Volumn 56, Issue 3, 1996, Pages 755-764

  Berenstein, Carlos A ^a   Casadio Tarabusi, Enrico ^b,c  

^a UNIVERSITY OF MARYLAND   (United States)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

^c UNIVERSITY OF MARYLAND   (United States)

Author keywords

Convolution operators; Electrical impedance tomography; Hyperbolic space; Inverse conductivity problem; Radon transform; Totally geodesic submanifolds

Indexed keywords

COMPUTERIZED TOMOGRAPHY; ELECTRIC CONDUCTIVITY; ELECTRIC IMPEDANCE; INVERSE PROBLEMS; LINEARIZATION; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS;

CONVOLUTION OPERATORS; HYPERBOLIC SPACE; POINCARE METRIC; RADAR TRANSFORM; TOTALLY GEODESIC SUBMANIFOLDS; X RAY TRANSFORM;

GEOMETRY;

EID: 0030167925     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139994277348     Document Type: Article

References (16)

1. D. C. BARBER AND B. H. BROWN, Applied potential tomography, J. Phys. E, 17 (1984), pp. 723-733.
2. _, Progress in electrical impedance tomography, in Inverse Problems in Partial Differential Equations, 1989 Arcata Conference Proceedings, D. Colton, R. Ewing, and W. Rundell, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990, pp. 151-164.
3. C. A. BERENSTEIN AND E. CASADIO TARABUSI, Inversion formulas for the k-dimensional Radon transform in real hyperbolic spaces, Duke Math. J., 62 (1991), pp. 613-631.
4. _, On the Radon and Riesz transforms in real hyperbolic spaces, in Geometric Analysis, E. L. Grinberg, ed., Contemp. Math. 140, American Mathematical Society, Providence, RI, 1992, pp. 1-21.
5. C. A. BERENSTEIN AND E. CASADIO TARABUSI, Range of the k-dimensional Radon transform in real hyperbolic spaces, Forum Math., 5 (1993), pp. 603-616.
6. _. The inverse conductivity problem and the hyperbolic X-ray transform, in 75 Years of Radon Transform, S. G. Gindikin and P. Michor, eds., International Press, Hong Kong, 1994, pp. 31-36.
7. G. BEYLKIN, The inversion problem and applications of the generalized Radon transform, Comm. Pure Appl. Math., 37 (1984), pp. 579-599.
8. I. S. GRADSHTEYN AND I. M. RYZHIK, Table of Integrals, Series, and Products, corrected and enlarged edition, Academic Press, Orlando, FL, 1980.
9. S. HELGASON, Differential operators on homogeneous spaces, Acta Math., 102 (1959), pp. 239-299.
10. _, Groups and Geometric Analysis: Integral Geometry, Invariant Differential Operators, and Spherical Functions, Pure and Appl. Math. 113, Academic Press, Orlando, FL, 1984.
11. _, The totally-geodesic Radon transform on constant curvature spaces, in Integral Geometry and Tomography, E. Grinberg and E. T. Quinto, eds., Contemp. Math. 113, American Mathematical Society, Providence, RI, 1990, pp. 141-149.
12. G. E. MARTIN, The Foundations of Geometry and the Non-Euclidean Plane, Undergrad. Texts Math., Springer, New York, 1975.
13. A. I. NACHMAN, Reconstructions from boundary measurements, Ann. of Math. (2), 128 (1988), pp. 531-587.
14. _, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math. (2), (to appear).
15. F. SANTOSA AND M. VOGELIUS, A backprojection algorithm for electrical impedance imaging, SIAM J. Appl. Math., 50 (1990), pp. 216-243.
16. J. SYLVESTER AND G. UHLMANN, The Dirichlet to Neumann map and applications, in Inverse Problems in Partial Differential Equations, 1989 Arcata Conference Proceedings, D. Colton. R. Ewing, and W. Rundell, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990, pp. 101-139.