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A Multi-Frequency Tomographic Inverse Scattering Using Beam Basis Functions.

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Summary

This study introduces a novel beam-based method for ultra-wide band tomographic inverse scattering, offering localized imaging and data processing as an alternative to traditional approaches. The beam frame technique enables efficient multi-frequency or time-domain implementation for advanced imaging applications.

Keywords:
beam summation methodsimaginginverse scatteringwave propagation

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Area of Science:

  • Electromagnetics and wave propagation
  • Computational imaging and inverse problems
  • Signal processing

Background:

  • Conventional ultra-wide band (UWB) tomographic inverse scattering relies on plane-wave or Green's function methods.
  • These methods can be computationally intensive and may lack localization in data processing and imaging.
  • A need exists for alternative approaches offering improved efficiency and localized analysis.

Purpose of the Study:

  • To present a beam-based approach for UWB tomographic inverse scattering.
  • To introduce the concept of a "beam frame" for localized data processing and imaging.
  • To demonstrate the implementation of this method in the frequency domain (FD) using Fourier-based tools.

Main Methods:

  • Utilizes a phase-space set of iso-diffracting beam-waves forming a "beam frame".
  • Employs windowed phase-space transformations to map scattering data to the beam domain.
  • Applies backpropagation of beams to the target domain for image reconstruction.
  • Leverages local Radon transform (RT) properties for imaging.

Main Results:

  • The beam frame is an overcomplete basis applicable across frequencies, enabling both FD and time-domain (TD) implementations.
  • Beam-domain data is localized, compressed, and related to the local RT of the scatterer.
  • The imaging process is framed as an inverse local RT, applicable to specific domains of interest (DoI).

Conclusions:

  • The presented beam-based method offers a viable and efficient alternative for UWB tomographic inverse scattering.
  • The frequency-domain implementation utilizes simpler Fourier-based processing tools.
  • This approach facilitates localized imaging and data analysis, advancing the field of inverse scattering.