### Abstract

Layer stripping based on the Riccati equation for the scattering matrix is a natural approach to the solution of the inverse scattering problem for the Helmholtz equation. But it has so far failed to work in two and three dimensions. This paper examines a cause of failure and establishes a Riccati equation for the scattering matrix on the level surfaces of the index of refraction. The new Riccati equation overcomes a common drawback shared by the traditional Riccati equations - the waves are unnaturally forced to propagate with a Green's function of an artificially fixed background wave number, and this man-made mismatch will mix and deform the propagating and evanescent modes, which skews the regularization of the backward solve of the Riccati equations for layer stripping.

Original language | English (US) |
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Pages (from-to) | 1745-1756 |

Number of pages | 12 |

Journal | Inverse Problems |

Volume | 21 |

Issue number | 5 |

DOIs | |

State | Published - Oct 1 2005 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Mathematical Physics
- Computer Science Applications
- Applied Mathematics