By Guillaume Bal, David Finch, Visit Amazon's Peter Kuchment Page, search results, Learn about Author Central, Peter Kuchment, , John Schotland, Plamen Stefanov

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Title: Tomography and Inverse shipping Theory
Author: Bal, Guillaume (EDT)/ Finch, David (EDT)/ Kuchment, Peter (EDT)/ Schotland, John (EDT)/ Stefanov, P
Publisher: Amer Mathematical Society
Publication Date: 2012/01/01
Number of Pages: 180
Binding variety: PAPERBACK
Library of Congress: 2011033070

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De Gournay, and O. Kavian. Imaging by modification: numerical reconstruction of local conductivities from corresponding power density measurements. SIAM J. Imaging Sciences, 2:1003–1030, 2009. [11] D. Gilbarg and N. S. Trudinger. Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin, 1977. [12] P. Kuchment and L. Kunyansky. 2D and 3D reconstructions in acousto-electric tomography. submitted. [13] K. Lin and J. McLaughlin. An error estimate on the direct inversion model in shear stiffness imaging.

677–700. [11] A. Puro, Cormack-type inversion of exponential Radon transform, Inverse Problems, 17(1) (2001), pp. 179–188. [12] R. Ramlau, R. Clackdoyle, F. Noo, and G. Bal, Accurate attenuation correction in SPECT imaging using optimization of bilinear functions and assuming an unknown spatiallyvarying attenuation distribution, ZAMM Z. Angew. Math. , 80 (2000), pp. 613–621. [13] D. Solmon, The identification problem for the exponential Radon transform, Math. Methods in the Applied Sciences, 18 (1995), pp.

We show in Fig. 3 the results of the reconstruction in the disc X defined above. 95 is the lowest eigenvalue of (−Δ)−1 σ. 36 8 GUILLAUME BAL AND KUI REN Figure 2. Same as Fig. 1 but in the two-dimensional case. Figure 3. From left to right: original absorption coefficient σ, reconstructed σδ and reconstructed σ−δ . The non-uniqueness results that we have seen above are all constructed when only one set of interior data is available. It turns out that with two sets of interior data, we can uniquely reconstruct two coefficients as presented in Section 4.

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