2-D and 3-D Reconstruction Algorithms in the Fourier Domain for Plane-Wave Imaging in Nondestructive Testing

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.