Stability in diffraction tomography and a nonlinear "basic theorem"

V. P. Palamodov

doi:10.1007/BF02788790

Stability in diffraction tomography and a nonlinear "basic theorem"

V. P. Palamodov^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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.

Original language	English
Pages (from-to)	247-268
Number of pages	22
Journal	Journal d'Analyse Mathematique
Volume	91
DOIs	https://doi.org/10.1007/BF02788790
State	Published - 2003

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10.1007/BF02788790

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Stability in diffraction tomography and a nonlinear "basic theorem"

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