Zero source insertion technique to account for undersampling in GPR imaging
First Claim
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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Accused Products
Abstract
A method and system for detecting the presence of subsurface objects within a medium is provided. In some embodiments, the imaging and detection system operates in a multistatic mode to collect radar return signals generated by an array of transceiver antenna pairs that is positioned across the surface and that travels down the surface. The imaging and detection system pre-processes the return signal to suppress certain undesirable effects. The imaging and detection system then generates synthetic aperture radar images from real aperture radar images generated from the pre-processed return signal. The imaging and detection system then post-processes the synthetic aperture radar images to improve detection of subsurface objects. The imaging and detection system identifies peaks in the energy levels of the post-processed image frame, which indicates the presence of a subsurface object.
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Citations
20 Claims
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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:
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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. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A computer-readable storage device storing computer-executable instructions for controlling a computing device to generate a contribution image frame for a transmitter based on return signals acquired by multiple receivers from a signal emitted by the transmitter, the receivers being at locations, the return signal for each receiver including a number of samples indicating amplitude of the return signal, each sample corresponding to a fast time delay at which the signal emitted by the transmitter was acquired by that receiver, by a method comprising:
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transforming the return signal of each receiver from a time domain into a frequency domain to generate first transformed return signals; augmenting the first transformed return signals with zero return signals to represent virtual receivers to account for under-sampling by the receivers to generate zero inserted return signals; transforming the zero inserted return signals across the receivers for each fast time delay in a frequency domain to generate second transformed return signals; inversely transforming the zero inserted return signals across the receivers for each fast time delay to generate first inverse transformed return signals; inversely transforming the first inverse transformed return signals for each receiver from the frequency domain to a time domain to generate second inverse transformed return signals; and creating the contribution image frame from elements of the inverse transformed return signals. - View Dependent Claims (9, 10, 11, 12, 13, 14, 15)
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16. 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, comprising:
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a data store that stores a matrix of the return signals with each column representing a receiver and each row representing a fast time delay; a component that applies a fast Fourier transform to each column of the matrix to generate a column transformed matrix; a component that inserts columns of zeros into the column transformed matrix to account for under-sampling in a cross-track direction to generate a zero inserted matrix; a component that applies a fast Fourier transform to each row of the matrix to generate a row transformed matrix; a component that applies an inverse fast Fourier transform to each row of the zero inserted matrix to generate a inverse row transformed matrix; a component that modifies the matrix based on a field from the transmitter to generate a modified inverse row transformed matrix; a component that applies an inverse fast Fourier transform to each column of the modified inverse row transformed matrix to generate an inverse column transformed matrix; and a component that creates the contribution image frame from elements of the inverse column transformed matrix. - View Dependent Claims (17, 18, 19, 20)
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Specification