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A multiscattering series for impedance tomography in layered media. (English) Zbl 0926.35156

Summary: We introduce an inversion algorithm for tomographic images of layered media. The algorithm is based on a multiscattering series expansion of the Green function that, unlike the Born series, converges unconditionally. Our inversion algorithm obtains images of the medium that improves iteratively as we use more and more terms in the multiscattering series. We present the derivation of the multiscattering series, formulate the inversion algorithm and demonstrate its performance through numerical experiments.

MSC:

35R30 Inverse problems for PDEs
35J25 Boundary value problems for second-order elliptic equations
86A22 Inverse problems in geophysics
78A45 Diffraction, scattering
78A40 Waves and radiation in optics and electromagnetic theory
78M25 Numerical methods in optics (MSC2010)
92C55 Biomedical imaging and signal processing
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