Application of X-Y separable 2-D array beamforming for increased frame rate and energy efficiency in handheld devices

Two-dimensional arrays present significant beamforming computational challenges because of their high channel count and data rate. These challenges are even more stringent when incorporating a 2-D transducer array into a battery-powered hand-held device, placing significant demands on power efficiency. Previous work in sonar and ultrasound indicates that 2-D array beamforming can be decomposed into two separable line-array beamforming operations. This has been used in conjunction with frequency-domain phase-based focusing to achieve fast volume imaging. In this paper, we analyze the imaging and computational performance of approximate near-field separable beamforming for high-quality delay-and-sum (DAS) beamforming and for a low-cost, phase-rotation-only beamforming method known as direct-sampled in-phase quadrature (DSIQ) beamforming. We show that when high-quality time-delay interpolation is used, separable DAS focusing introduces no noticeable imaging degradation under practical conditions. Similar results for DSIQ focusing are observed. In addition, a slight modification to the DSIQ focusing method greatly increases imaging contrast, making it comparable to that of DAS, despite having a wider main lobe and higher side lobes resulting from the limitations of phase-only time-delay interpolation. Compared with non-separable 2-D imaging, up to a 20-fold increase in frame rate is possible with the separable method. When implemented on a smart-phone-oriented processor to focus data from a 60 x 60 channel array using a 40 x 40 aperture, the frame rate per C-mode volume slice increases from 16 to 255 Hz for DAS, and from 11 to 193 Hz for DSIQ. Energy usage per frame is similarly reduced from 75 to 4.8 mJ/ frame for DAS, and from 107 to 6.3 mJ/frame for DSIQ. We also show that the separable method outperforms 2-D FFT-based focusing by a factor of 1.64 at these data sizes. This data indicates that with the optimal design choices, separable 2-D beamforming can significantly improve frame rate and battery life for hand-held devices with 2-D arrays.