Delay-Multiply-and-Sum Beamforming for Real-Time In-Air Acoustic Imaging

In-air acoustic imaging systems demand beamforming techniques that offer high dynamic range and spatial resolution while remaining robust, yet conventional Delay-and-Sum (DAS) beamforming suffers from high sidelobes and low contrast. Conversely, advanced adaptive methods are typically too computationally expensive for real-time field operation. To overcome this trade-off, we propose a higher-order non-linear beamforming method using the Delay-Multiply-and-Sum (DMAS) technique with Coherence Factor weighting, specifically adapted for in-air microphone arrays. By leveraging Newton-Girard binomial expansion, we reduce the complexity ofn-th order DMAS to O(N), enabling GPU-accelerated, real-time performance on embedded platforms, with the implementation also made available as open-source. Through validation against simulated and real-world data, we demonstrate that the proposed 5th-order DMAS with CF achieves a dynamic range improvement of nearly 40 dB over DAS, alongside significantly higher image SNR and artifact suppression. We demonstrate real-time viability on various GPU platforms, establishing this approach as a practical, high-performance solution for 3D in-air sonar and industrial acoustic imaging.