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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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Scattered Far-Field Sampling in Multi-Static Multi-Frequency Configuration.

Maria Antonia Maisto1, Mehdi Masoodi1, Giovanni Leone1

  • 1Department of Engineering, University of Campania, 81031 Aversa, CE, Italy.

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|July 24, 2021
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Summary
This summary is machine-generated.

This study develops a sampling strategy for inverse scattering problems, reducing measurement points and frequencies while maintaining reconstruction performance. A practical, albeit suboptimal, approach simplifies data acquisition in multi-static/multi-frequency configurations.

Keywords:
field samplinginverse scatteringradar imaging

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Area of Science:

  • Electromagnetics and Wave Propagation
  • Computational Physics
  • Signal Processing

Background:

  • Inverse scattering problems are crucial for characterizing objects from scattered wave data.
  • Multi-static/multi-frequency configurations offer rich information but pose data acquisition challenges.
  • Reducing data acquisition complexity without compromising reconstruction accuracy is a key objective.

Purpose of the Study:

  • To determine an optimal sampling strategy for inverse scattering problems in multi-static/multi-frequency configurations.
  • To reduce the number of measurement points and frequencies required for accurate object reconstruction.
  • To develop a practical measurement configuration for data acquisition.

Main Methods:

  • Linearized scattering model and 2D scalar geometry are employed.
  • Analysis of the scattering operator's singular value spectrum to determine the number of degrees of freedom (NDF).
  • Development of a sampling strategy based on approximating the significant singular spectrum, followed by an iterative procedure to enforce a rectangular grid in the angle-frequency domain.

Main Results:

  • A sampling strategy is derived by identifying data points that capture the essential singular spectrum.
  • An initial optimal strategy leads to a complex measurement configuration.
  • A suboptimal, iterative strategy simplifies the configuration by using a rectangular grid, reducing distinct angles and frequencies.

Conclusions:

  • The proposed suboptimal sampling strategy offers a practical approach to data acquisition for inverse scattering problems.
  • This method balances the need for reduced measurement complexity with the requirement for accurate reconstruction.
  • The findings are validated through numerical examples, demonstrating the effectiveness of the simplified measurement configuration.