Model-based deep learning for ultrasound beamforming

Recently, the ultrasound signal processing pipeline has shifted from hardware-based solutions to the digital domain, enabling more intricate reconstruction techniques. We highlight several beamforming methods from a statistical inference perspective, connecting deep learning techniques to established signal processing models grounded in fundamental principles. The ultrasound acquisition process can be modeled as a linear combination of scatterers x (i.e. tissue reflectivity) which amounts to the received channel data y, captured by a forward model y = Hx + n, with the measurement matrix H. Solving this system relies heavily on priors to yield a unique and anatomically feasible solution. A naive linear estimator for x is H T y, also known as the delay-and-sum beamformer, which crudely disregards all off-axis scattering as zero-mean white noise. Based on the structured-noise assumption for off-axis scattering in the minimum variance beamformer, ABLE implements fast statistical inference of the optimal linear beamformer through deep learning. In addition, we can infuse prior knowledge on the distribution of x resulting in the neural maximum-a-posteriori beamformer. All aforementioned methods assume no dependency between individual pixels. Ultimately, the use of generative models allows us to extend the methods with more informative spatial priors.