Resolution enhancement of two-dimensional grid-free compressive beamforming

Area of Science:

• Acoustics
• Signal Processing
• Array Signal Processing

Background:

• Conventional grid-based compressive beamforming suffers from basis mismatch.
• Atomic norm minimization (ANM) based grid-free beamforming improves source reconstruction but has limited resolution for closely spaced sources.
• The atomic norm is not a direct sparsity metric, limiting its effectiveness when sources are not sufficiently separated.

Purpose of the Study:

• To overcome the resolution limitations of ANM-based grid-free beamforming for two-dimensional acoustic source reconstruction.
• To develop a novel sparse metric that promotes greater sparsity than the atomic norm.
• To enhance the resolution of acoustic source localization, particularly for closely spaced sources.

Main Methods:

• Proposed a new sparse metric superior to the atomic norm for promoting sparsity.
• Formulated a minimization problem using the proposed sparse metric.
• Introduced the majorization-minimization (MM) algorithm, iteratively applying ANM with a reweighting strategy, termed iterative reweighted atomic norm minimization (IRANM).

Main Results:

• IRANM effectively overcomes the resolution limitations of standard ANM.
• Enhanced resolution was demonstrated using both simulations and experimental data.
• The method shows effectiveness with both uniform rectangular arrays and non-uniform microphone arrays.

Conclusions:

• IRANM significantly enhances the resolution of two-dimensional acoustic source reconstruction compared to traditional ANM.
• The proposed sparse metric and MM algorithm provide a robust solution for localizing closely spaced acoustic sources.
• The developed technique offers improved performance for various microphone array configurations.