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Zero source insertion technique to account for undersampling in GPR imaging

  • US 8,659,467 B1
  • Filed: 08/26/2011
  • Issued: 02/25/2014
  • Est. Priority Date: 08/26/2010
  • Status: Active Grant
First Claim
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1. A method performed by a computing device for generating a contribution image frame for a transmitter based on return signals acquired by multiple receivers from a signal emitted by the transmitter at a down-track location, the receivers being at cross-track locations, the method comprising:

  • providing a matrix of the return signals with each column representing a receiver and each row representing a fast time delay;

    applying a fast Fourier transform separately to each column of the matrix to generate a column transformed matrix;

    inserting columns of zeros into the column transformed matrix to account for under-sampling in a cross-track direction to generate a zero inserted matrix;

    applying a fast Fourier transform separately to each row of the zero inserted matrix to generate a row transformed matrix;

    multiplying the row transformed matrix by a factor to propagate the matrix to a specific depth to generate a propagated row transformed matrix;

    applying an inverse fast Fourier transform separately to each row of the propagated row transformed matrix to generate an inverse row transformed matrix;

    multiplying elements of the inverse row transformed matrix by a factor representing a field emitted by the transmitter to generate a modified inverse row transformed matrix;

    applying an inverse fast Fourier transform separately to each column of the modified inverse row transformed matrix to generate an inverse column transformed matrix; and

    creating the contribution image frame from elements of the inverse column transformed matrix.

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