Algebraic and Analytic Inversion of Acoustic Data Prom Partially or Fully Enclosing Apertures

  • Steven A. Johnson
  • James F. Greenleaf
  • Balasubramanian Rajagopalan
  • Mitsuo Tanaka
Part of the Acoustical Imaging book series (ACIM, volume 8)

Abstract

Several methods are presented for inversion of both reflection and transmission data (i.e., produce an image from the data) collected from transducers distributed on a sphere or portions of a surface surrounding a distribution of scatterers. These methods are based on finding approximate forms of the true generalized inversion of the linear operator which transforms the particular distributions of scatterers, transducer arrangement, and transmitted waveforms into the corresponding collected data. Thus, reflection and transmission data collection may be written as linear operations AMx=b where A is an attenuation operation and M is a time varying spatial integrating operator, b is data and x is the desired image. One such iterative method is presented which uses a Kacmarz-like inversion technique which is analogous to the ART reconstruction algorithm used in x-ray reconstructive tomography. This iterative method is well suited for partially enclosing apertures. Progress in formulation of non-iterative or analytic methods is presented. These methods are analogous to the Radon inversion formulae for x-ray density reconstruction. A comparison is made of the images produced by these new methods and the “synthetic focus” method previously developed in our laboratory.

Keywords

Attenuation Convolution Radon Sine Refraction 

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References

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Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Steven A. Johnson
    • 1
  • James F. Greenleaf
    • 1
  • Balasubramanian Rajagopalan
    • 1
  • Mitsuo Tanaka
    • 1
  1. 1.Department of Physiology and Biophysics Biodynamics Research UnitMayo Foundation RochesterUSA

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