2-D and 3-D Reconstruction Algorithms in the Fourier
Domain for Plane-Wave Imaging in Nondestructive Testing
Abstract:
Time-domain plane-wave imaging (PWI)
has recently emerged in medical imaging and is now taking to nondestructive
testing (NDT) due to its ability to provide images of good resolution and
contrast with only a few steered plane waves. Insonifying a medium with plane
waves is a particularly interesting approach in 3-D imaging with matrix arrays
because it allows to tremendously reduce the volume of data to be stored and
processed as well as the acquisition time. However, even if the data volume is reduced
with plane wave emissions, the image reconstruction in the time domain with a
delay-and-sum algorithm is not sufficient to achieve low computation times in
3-D due to the number of voxels. Other reconstruction algorithms take place in
the wavenumber-frequency (f-k) domain and have been shown to accelerate
computation times in seismic imaging and in synthetic aperture radar. In this
paper, we start from time-domain PWI in 2-D and compare it to two algorithms in
the f-k domain, coming from the Stolt migration in seismic imaging and the Lu
theory of limited diffraction beams in medical imaging. We then extend them to
immersion testing configurations where a linear array is facing a plane
water-steel interface. Finally, the reconstruction algorithms are generalized
to 3-D imaging with matrix arrays. A comparison dwelling on image quality and
algorithmic complexities is provided, as well as a theoretical analysis of the
image amplitudes and the limits of each method. We show that the reconstruction
schemes in the f-k domain improve the lateral resolution and offer a
theoretical and numerical computation gain of up to 36 in 3-D imaging in a
realistic NDT configuration.
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