Optimization strategies and neighbor pair complementary codes for massively parallel focal zone ultrafast ultrasound

Plane wave methods for ultrafast ultrasound imaging suffer from a low signal to noise ratio (SNR) and a limited field of view at greater imaging depths. Imaging using multiple focused coded beams in parallel is one strategy for high speed imaging that may improve on these limitations. However, the SNR and resolution of this strategy are degraded by the interference between the beams transmitted in parallel. We aim to reduce this interference while retaining acceptable axial resolution by careful design of the coded beams. To ensure good axial resolution and to increase flexibility of code design, we use two transmit events to form each set of lines in the image. This implies an increase in imaging speed of approximately K=2, where K is the number of beams fired in parallel. To decode channel data we use a matched filter, summing cross-correlation results over each pair of transmit events. As a result, the interference between two beams fired in parallel is dictated by the magnitude of the sum of cross-correlations between parallel beam encoding patterns. We have constructed a metric based on this idea, and optimized coded beams for this metric using the sequential quadratic programming capabilities of MATLAB's nonlinear optimization toolbox. Using our optimization framework, we have generated codes that allow for very low interference between two simultaneously transmitted parallel beams. Our optimization framework also enables generation of lowerinterference codes for many simultaneous parallel focal zones, compared to randomly selected codes. In simulation, we found that using optimized codes reduces the clutter associated with parallel transmission, and that the optimized coded imaging strategy is capable of generating images with higher contrast than those acquired at the same frame rate by plane wave imaging.