Abstract
We give a sharp upper estimate for the response of boundary current-voltage measurements to perturbations of the admittivity in a body that are localized in space and frequency. We calculate the differential of the measurement mapping and study theGabor symbol of this operator.
Similar content being viewed by others
References
Alessandrini, G., Stable determination of conductivity by boundary measurements,Appl. Anal. 27 (1988), 153–172.
Boone, K., Barber, D. andBrown, B., Imaging with electricity: Report of the European Concerted Action on Impedance Tomography,J. Med. Eng. 21 (1997), 201–232.
Calderón, A. P., On an inverse boundary value problem, inSeminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980), pp. 65–73, Soc. Brasil. Mat., Rio de Janeiro, 1980.
Cheney, M., Isaacson, D. andNewel, J. C., Electrical impedance tomography,SIAM Rev. 41 (1999), 85–101.
Cordoba, A. andFefferman, C., Wave packets and Fourier integral operators,Comm. Partial Differential Equations 3 (1978), 979–1005.
Gabor, D., Theory of communication,J. Inst. El. Eng. 93:3 (1946), 429–457.
Hadamard, J.,Lectures on Cauchy's Problem in Linear Partial Differential Equations, Dover, New York, 1953.
Iagolnitzer, D. andStapp, H. P., Macroscopic causalty and physical region analyticity in S-matrix theory,Comm. Math. Phys. 14 (1969), 15–55.
Nachman, A. I., Reconstruction from boundary measurements,Ann. of Math. 128 (1988), 531–576.
Santosa, F. andVogelius, M., A backprojection algorithm for electrical impedance imaging,SIAM J. Appl. Math. 50 (1990), 216–243.
Sylvester, J. andUhlmann, G., A global uniqueness theorem for an inverse boundary value problem,Ann. of Math. 125 (1987), 153–169.
Uhlmann, G., Inverse boundary value problems and applications,Astérisque 207 (1992), 6, 153–211.
Zhdanov, M. S. andKeller, G. V.,The Geoelectrical Methods in Geophysical Exploration, Methods in Geochemistry and Geophysics31, Elsevier, Amsterdam-London, 1994.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Palamodov, V.P. Gabor analysis of the continuum model for impedance tomography. Ark. Mat. 40, 169–187 (2002). https://doi.org/10.1007/BF02384508
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02384508