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Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
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A representation for Green's function retrieval by multidimensional deconvolution.

Kees Wapenaar1, Joost van der Neut

  • 1Department of Geotechnology, Delft University of Technology, PO Box 5048, 2600 GA Delft, The Netherlands. c.p.a.wapenaar@tudelft.nl

The Journal of the Acoustical Society of America
|January 12, 2011
PubMed
Summary
This summary is machine-generated.

Multidimensional deconvolution (MDD) improves Green's function retrieval by addressing source irregularities. This method overcomes limitations of traditional cross-correlation, providing a clearer, deblurred, and deghosted source function.

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Area of Science:

  • Geophysics
  • Seismology
  • Wave propagation

Background:

  • Green's function retrieval using cross-correlation is susceptible to issues like uneven source distribution and signal attenuation.
  • These limitations can obscure the true source characteristics in geophysical data.

Purpose of the Study:

  • To propose a unified representation for Green's function retrieval using Multidimensional Deconvolution (MDD).
  • To demonstrate how MDD overcomes the limitations inherent in the traditional cross-correlation method.

Main Methods:

  • A unified mathematical framework for Green's function retrieval via MDD was developed.
  • The space-time point-spread function (PSF) characterizing source smearing in cross-correlation was identified and quantified.
  • MDD was applied to remove the PSF, effectively deblurring and deghosting the retrieved Green's function.

Main Results:

  • The traditional cross-correlation method results in a Green's function with a spatially and temporally smeared source.
  • A space-time point-spread function (PSF) was successfully retrieved from receiver array measurements, quantifying this smearing.
  • MDD effectively removed the PSF, yielding a deblurred and deghosted Green's function.

Conclusions:

  • MDD offers a superior approach to Green's function retrieval compared to standard cross-correlation.
  • The proposed unified representation clarifies the advantages of MDD in geophysical data processing.
  • Deblurring and deghosting the Green's function source are key benefits of employing MDD.