### Abstract

The integral transform, F( mu , nu )= integral _{-infinity} ^{infinity} D( eta mu , eta + nu ) exp(i mu eta ^{2})d eta applied to functions D(x, y) on the plane, arises when one applies tomographic reconstruction techniques to problems in radar detection. The authors show that this transform can be inverted to reconstruct the superposition D+D composed with A, where A is a fixed linear transformation of the plane. In the case relevant to applications, where D(x, y) is real valued and vanishes on the half plane x<0, D itself can be reconstructed.

Original language | English (US) |
---|---|

Article number | 008 |

Pages (from-to) | 405-411 |

Number of pages | 7 |

Journal | Inverse Problems |

Volume | 2 |

Issue number | 4 |

DOIs | |

State | Published - 1986 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Applied Mathematics

### Cite this

*Inverse Problems*,

*2*(4), 405-411. [008]. https://doi.org/10.1088/0266-5611/2/4/008

**Inversion of an integral transform associated with tomography in radar detection.** / Feig, E.; Greenleaf, F. P.

Research output: Contribution to journal › Article

*Inverse Problems*, vol. 2, no. 4, 008, pp. 405-411. https://doi.org/10.1088/0266-5611/2/4/008

}

TY - JOUR

T1 - Inversion of an integral transform associated with tomography in radar detection

AU - Feig, E.

AU - Greenleaf, F. P.

PY - 1986

Y1 - 1986

N2 - The integral transform, F( mu , nu )= integral -infinity infinity D( eta mu , eta + nu ) exp(i mu eta 2)d eta applied to functions D(x, y) on the plane, arises when one applies tomographic reconstruction techniques to problems in radar detection. The authors show that this transform can be inverted to reconstruct the superposition D+D composed with A, where A is a fixed linear transformation of the plane. In the case relevant to applications, where D(x, y) is real valued and vanishes on the half plane x<0, D itself can be reconstructed.

AB - The integral transform, F( mu , nu )= integral -infinity infinity D( eta mu , eta + nu ) exp(i mu eta 2)d eta applied to functions D(x, y) on the plane, arises when one applies tomographic reconstruction techniques to problems in radar detection. The authors show that this transform can be inverted to reconstruct the superposition D+D composed with A, where A is a fixed linear transformation of the plane. In the case relevant to applications, where D(x, y) is real valued and vanishes on the half plane x<0, D itself can be reconstructed.

UR - http://www.scopus.com/inward/record.url?scp=36149034150&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36149034150&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/2/4/008

DO - 10.1088/0266-5611/2/4/008

M3 - Article

VL - 2

SP - 405

EP - 411

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 4

M1 - 008

ER -