Wideband 2-D sparse array optimization combined with multiline reception for real-time 3-D medical ultrasound

Three-dimensional (3-D) ultrasound medical imaging provides advantages over a traditional 2-D visualization method. However, the use of a 2-D array to acquire 3-D images may result in a transducer composed of thousands of elements and a large amount of data in the front-end, making it impractical to implement high volume rate imaging and individually control all elements with the scanner. This paper proposes an original approach, valid for wideband operations centered on the design center frequency, to maintain a limited number of active elements and firing events, while preserving high resolution and volume rate. A 7 MHz 2-D array is composed of two circular concentric subparts. In the inner footprint the elements are distributed following a regular grid, while in the outer subpart a sparse non-grid solution is adopted. The inner circular dense array is composed of 256 elements with a pitch of 0.5λ. The overall footprint, delimited by the outer subpart, is equivalent to a 256-element array with a pitch of 1.5λ. All the elements of the inner subpart are activated in transmission. Following an optimization procedure, both subparts, including a subset of the elements placed in the inner footprint (i.e., sparse on-the-grid array) and the elements spread over the outer subpart (i.e., sparse off-the-grid array) are used to receive. A total number of 256 elements, defined by the sum of elements distributed in the inner and outer subparts, is fixed in reception. The proposed approach implies a multiline reception strategy, where for each transmission 3 × 3 firing events occur in reception. The sparse receive array is optimized by using a simulated annealing optimization. An original cost function is designed specifically to achieve successful results in wideband conditions. The receive array is optimized in order to obtain consistent results for different signal bandwidths of the excitation pulse. For all the desired bandwidths, the optimized array will provide the recovery of the lower lateral resolution of the transmission phase and, at the same time, a significant reduction of the undesired side lobe raised in the 3-D two-way beam pattern. The 3-D two-way beam pattern analysis reveals that the proposed solution is able to guarantee a lateral resolution of 1.35 mm at a focus depth of 25 mm for the three fractional signal bandwidths of interest (i.e., 30%, 50% and 70%) considered in the optimization process. The undesired side lobes are successfully suppressed especially when, as a consequence of the multiline strategy, non-coincident steering angles are used in transmission and reception. Moreover, thanks to the firing scheme adopted, a high-volume rate of 63 volumes per second may be achieved at the focus depth. The volume rate decreases to 32 volumes per second at twice the focal depth. Phantom image simulations show that the proposed method maintains a satisfactory and almost uniform image quality in terms of resolution and contrast for all the signal bandwidths of interest.