Design and Evaluation of a Weighted Periodic Sparse Array for Low-Complexity 1-D Phased Array Ultrasound Imaging Systems

A sparse array offers a significant reduction in the complexity of ultrasonic imaging systems by decreasing the number of active elements and associated electrical circuits needed to form a focused beam. Consequently, for 1-D arrays, it has been adopted in the development of miniaturized systems such as portable, handheld, or smartphone-based systems. Previously, we developed an analytic method that can design a pair of 1-D periodic sparse arrays (PSAs) satisfying three specific constraints, which are the array size, desired grating lobe level, and sparseness factor (SF). In this study, we further developed our method by incorporating aperture weighting functions, which take the form of tapered rectangular functions to introduce null points on the beam pattern. These null points effectively suppress grating lobes generated by a matching pair of arrays. The design process commences with determining transmit and receive PSA patterns, followed by deriving corresponding aperture weighting functions. First, aperture functions of a base and weighting arrays are convolved, which is then upsampled to the targeted array size. Finally, the upsampled aperture is convolved to an aperture function of a subarray, resulting in weighted PSAs (wPSAs). Pulsed wave (PW) simulation confirmed improved grating lobe suppression with wPSAs compared to PSAs. Phantom imaging experiments using a 1-D phased array validated the enhanced contrast due to suppressed grating lobes but at the cost of small degradation in lateral resolution. The signal-to-noise ratio (SNR) also gradually declined with the greater SFs, but no significant difference in SNR was observed between wPSAs and PSAs. Finally, in vivo echocardiography imaging highlighted the clinical potential of wPSAs, particularly with high SFs. Overall, these results suggest that wPSAs can effectively enhance contrast compared to PSAs under the given SF or, alternatively, wPSA with greater SFs can achieve comparable image quality to PSAs with lower SFs. In conclusion, the wPSA approach holds promise for further reducing the complexity of ultrasound imaging systems.