A minimum variance (MV) approach for near-field beamforming of broadband data is proposed. The approach is implemented in the frequency domain, and it provides a set of adapted, complex apodization weights for each frequency subband. The performance of the proposed MV beamformer is tested on simulated data obtained using Field II. The method is validated using synthetic aperture data and data obtained from a plane wave emission. Data for 13 point targets and a circular cyst with a radius of 5 mm are simulated. The performance of the MV beamformer is compared with delay-an sum (DS) using boxcar weights and Harming weights and is quantified by the full width at half maximum (FWHM) and the peak-side-lobe level (PSL). Single emission {DS boxcar, DS Harming, MV} provide a PSL of {-16, -36, -49} dB and a FWHM of {0.79, 1.33, 0.08} mm. Using all 128 emissions, {DS boxcar, DS Harming, MV} provides a PSL of {-32, -49, -65} dB, and a FWHM of {0.63, 0.97, 0.08} rum. The contrast of the beamformed single emission responses of the circular cyst was calculated as {-18, -37, -40} dB. The simulations have shown that the frequency subband MV beamformer provides a significant increase in lateral resolution compared with DS, even when using considerably fewer emissions. An increase in resolution is seen when using only one single emission. Furthermore, the effect of steering vector errors is investigated. The steering vector errors are investigated by applying an error of the sound speed estimate to the ultrasound data. As the error increases, it is seen that the MV beamformer is not as robust compared with the DS beamformer with boxcar an Harming weights. Nevertheless, it is noted that the DS does not outperform the MV beamformer. For errors of 2% and 4% of the correct value, the FWHM are {0.81, 1.25, 0.34) mm and {0.89, 1.44, 0.46} min, respectively.
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