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Stability in diffraction tomography and a nonlinear “basic theorem”

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Abstract

The stability problem is studied for reconstruction of the refraction coefficient from boundary measurements of solutions of the Helmholtz equation at a fixed time-frequency. An answer is given in terms of Gabor means of the coefficient. A domain in the phase space is shown where the Gabor means can be stably reconstructed. As a corollary, a rigorous form is given to the basic theorem of diffraction tomography.

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  1. School of Mathematical Sciences Tel Aviv University Ramat Aviv, Tel Aviv 69978, Israel

    V. P. Palamodov

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  1. V. P. Palamodov
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Palamodov, V.P. Stability in diffraction tomography and a nonlinear “basic theorem”. J. Anal. Math. 91, 247–268 (2003). https://doi.org/10.1007/BF02788790

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  • DOI: https://doi.org/10.1007/BF02788790

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