Computational Complexity Reduction of Synthetic-aperture Focus in Ultrasound Imaging Using Frequency-domain Reconstruction

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A new frequency-domain implementation of a synthetic aperture focusing technique is presented in the paper. The concept is based on synthetic aperture radar (SAR) and sonar that is a developed version of the convolution model in the frequency domain. Compared with conventional line-by-line imaging, synthetic aperture imaging has a better resolution and contrast at the cost of more computational load. To overcome this problem, point-by-point reconstruction methods have been replaced by block-processing algorithms in radar and sonar; however, these techniques are relatively unknown in medical imaging. In this paper, we extended one of these methods called wavenumber to medical ultrasound imaging using a simple model of synthetic aperture focus. The model, derived here for monostatic mode, can be generalized to multistatic as well. The method consists of 4 steps: a 2D fast Fourier transform of the data, frequency shift of the data to baseband, interpolation to convert polar coordinates to rectangular ones, and returning the data to the spatial-domain using a 2D inverse Fourier transform. We have also used chirp pulse excitation followed by matched filtering and spotlighting algorithm to compensate the effect of differences in parameters between radar and medical imaging. Computational complexities of the two methods, wavenumber and delay-and-sum (DAS), have been calculated. Field II simulated point data have been used to evaluate the results in terms of resolution and contrast. Evaluations with simulated data show that for typical phantoms, reconstruction by the wavenumber algorithm is almost 20 times faster than classical DAS while retaining the resolution.

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