Two-dimensional grid-free compressive beamforming.

Area of Science:

• Acoustics
• Signal Processing
• Array Processing

Background:

• Conventional compressive beamforming relies on a grid assumption for direction-of-arrival (DOA) estimation.
• This grid assumption leads to performance degradation due to basis mismatch when source DOAs deviate from the grid.
• Plane microphone arrays are commonly used, but limitations exist with non-uniform arrays and noisy data.

Purpose of the Study:

• To develop a two-dimensional grid-free compressive beamforming method for acoustic source DOA estimation and strength quantification.
• To overcome the limitations of conventional grid-based compressive beamforming, particularly basis mismatch.
• To enable accurate and fast acoustic source imaging using non-uniform microphone arrays and noisy measurements.

Main Methods:

• Defined a continuum-based atomic norm minimization for denoising measured pressure and isolating source pressures.
• Formulated a positive semidefinite programming to approximate the atomic norm minimization.
• Developed a fast algorithm using the alternating direction method of multipliers to solve the optimization problem.
• Employed matrix enhancement and matrix pencil methods for source distribution reconstruction.

Main Results:

• The grid-free compressive beamforming method demonstrated high-resolution and low-contamination imaging.
• Accurate and fast estimation of two-dimensional DOAs was achieved.
• Effective quantification of acoustic source strengths was obtained.
• The method proved robust with non-uniform arrays and noisy measurements.

Conclusions:

• The developed grid-free compressive beamforming method effectively addresses the limitations of traditional grid-based approaches.
• This technique offers a significant advancement in acoustic source localization and strength quantification.
• The method provides a powerful tool for analyzing complex acoustic environments with improved accuracy and speed.