Stability in diffraction tomography and a nonlinear “basic theorem”
VP Palamodov - Journal d'Analyse Mathématique, 2003 - Springer
Journal d'Analyse Mathématique, 2003•Springer
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.
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.
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.
Springer
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