Two-Stage Filtered Higher Order Delay Multiply and Sum Beamformer for Ultrasound Plane Wave Imaging with Linear Complexity

Current ultrasound imaging research trends involve the utilization of extended delay multiply and sum (DMAS) beamformer, often incorporating a second stage. For instance, the third-degree DMAS beamformer utilizes triplets for the multiplication process, artificially enlarging the aperture. The combination of two stages, coupled with the elevation in polynomial order, enhances the contrast-to-noise ratio (CNR) and imaging resolution. In this study, we investigate the feasibility of employing a variable quantity of elements per multiplication with the adoption of a second stage. This original approach leads to incremental improvements in CNR and resolution with each additional stage and polynomial degree. However, the conventional implementation of this approach is associated with time-consuming computational complexity and frequency artifacts. Therefore, we present a novel recursive framework for linear complexity implementation for arbitrary DMAS order and an additional filtering stage in the post-processing step, mitigating computational overhead and artifacts. In addition, a second stage is added to further improve image quality. The implemented beamformer was evaluated on a simulated point scatterer using the MATLAB Ultrasound Toolbox (MUST) and real measurements on a commercial ultrasound phantom (CIRS Model 040 GSE).