UWB Beam-Based Local Diffraction Tomography-Part I: Phase-Space Processing and Physical Interpretation

Ram Tuvi, Ehud Heyman, Timor Melamed

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this two-part article, we study the ultrawideband beam-based schemes for tomographic inverse scattering. The theory utilizes discrete phase-space sets of beam waves, which constitute overcomplete frames everywhere in the propagation domain, and thus can be considered as a local alternative to the conventional plane-wave or Green's function integrals used in conventional diffraction tomography. Specifically, we formulate two inversion schemes, a multi-frequency domain scheme, and a time domain scheme. The former utilizes isodiffracting Gaussian beams, while the latter utilizes isodiffracting pulsed beams. Both schemes consist of two phases: In the preprocessing phase, the scattering data are expanded as a sum of beams whose amplitudes, referred to as the 'beam-domain data,' are extracted from the data using local beam-based transforms. In the imaging phase, the beam data are backpropagated and used for local reconstruction. In this Part I we discuss the preprocessing phase. We define the beam-based transforms, and then use the Born approximation to establish a cogent physical interpretation of the beam-domain data. Specifically, we show that these data are related to the local Radon transform of the medium, which is interpreted physically as a local Snell's law. This relation will be used in Part II to reconstruct the medium.

Original languageEnglish
Article number9091932
Pages (from-to)7144-7157
Number of pages14
JournalIEEE Transactions on Antennas and Propagation
Volume68
Issue number10
DOIs
StatePublished - 1 Oct 2020

Keywords

  • Beam summation methods
  • diffraction tomography (DT)
  • inverse scattering

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