PDF: DeepWave: A Recurrent Neural-Network for Real-Time Acoustic Imaging (neurips.cc)

Code: https://github.com/imagingofthings/DeepWave

Last updated: October 2024

Contributions

Previous work: Delay-And-Sum (DAS) beamformer [1, Chapter 5].

Idea: Real-time reconstruction of acoustic spherical maps based on LISTA [2].

Limitations: It can reconstruct only high resolution microphone arrays

Methods

Background: Steering matrix

Signals can arrive to the microphones from different positions and angles. A direction can be parametrized as:

• Azimuth ($\theta$): The horizontal angle of arrival.
• Elevation ($\phi$): The vertical angle of arrival.

The vector that stores the phase shifts or time delays of the signal to each microphone in the array is the steering vector. The steering vector is a complex 1D vector of M elements (microphones), $a(\theta) \in \mathbb{C}^{M}:$

$$ \mathbf{a}(\theta) = \begin{pmatrix} 1 \\ e^{-j k d \sin(\theta)} \\ e^{-j 2 k d \sin(\theta)} \\ \vdots \\ e^{-j (M-1) k d \sin(\theta)} \end{pmatrix} $$

where:

• $d$: distance between microphones.
• k: The wavenumber. $k = 2\pi / \lambda$, where $\lambda$ is the wavelength of the signal.