Generalized Apodization Design with Learned Complex-Valued Weights for High-Frame-Rate Ultrasound Beamforming

High-frame-rate ultrasound imaging, using unfocused transmissions that insonify the entire imaging view, have spurred the development of novel ultrasound modes such as vector flow imaging or shear wave elastography. Nonetheless, the image quality suffers when each image is formed from a single transmit, and image compounding for quality improvement reduces the effective frame rate. Here, we propose a novel supervised learning framework to design generalized receive apodizations with complex-valued weights for delay-and-sum (DAS) beamforming that can produce high-quality images with only a few unfocused transmissions. Apodization weights are determined pixel-wise using selected pre-beamformed 1- or 3- angle RF data paired with reference 31-angle compounded images. We use a closed-form expression to find the mean-square optimal apodizations on a 6000 acquisition (38 individuals) musculoskeletal data set. On a test set consisting of phantom, musculoskeletal, and carotid data, the 3-angle complex apodizations resulted in 46.3% lower normalized mean-squared image error and 13.3% narrower lateral resolution compared to using a conventional Hanning apodization with a receive F-number of 1.25. The learned weights demonstrated observable structure in the orthogonality, symmetry, and aperture of the complex apodizations. Lastly, we demonstrated the live imaging readiness of our framework by substituting the generalized apodizations into a pre-existing real-time DAS framework. Compared to deep learning approaches for the same task (improving image quality with few transmits), our framework is both computationally efficient and fully interpretable. Overall, we demonstrate that our generalized apodization design approach achieved high DAS image quality using only 3 steered plane wave transmits in various imaging scenarios.