Sparse reconstruction of sound field using pattern-coupled Bayesian compressive sensing.

Area of Science:

• Acoustics
• Signal Processing
• Computational Physics

Background:

• Conventional near-field acoustic holography (NAH) using compressive sensing (CS) struggles with accurately reconstructing sound fields.
• Existing methods often fail to fully leverage block-sparse signal structures or require predefined block partitions, leading to reconstruction inaccuracies.

Purpose of the Study:

• To propose a pattern-coupled Bayesian compressive sensing (BCS) method for improved sparse reconstruction of sound fields in NAH.
• To address the limitations of conventional CS-based NAH by enabling effective block-sparse recovery without prior knowledge of block structures.

Main Methods:

• Developed a hierarchical Gaussian-Gamma probability model with a pattern-coupled prior, integrating the equivalent source method.
• Transformed sound field reconstruction into recovering sparse coefficients of equivalent source strengths within the CS framework.
• Introduced hyperparameters to control element sparsity, influenced by neighboring elements to promote block-sparse solutions.

Main Results:

• The proposed pattern-coupled BCS method effectively promotes block-sparse solutions for equivalent source strengths.
• Demonstrated superior performance in sound field reconstruction compared to conventional methods, validated through simulations and experiments.
• Achieved accurate reconstruction without requiring prior information on block partitions.

Conclusions:

• The pattern-coupled Bayesian compressive sensing method offers a significant advancement in near-field acoustic holography.
• This technique provides a more robust and accurate approach to sound field reconstruction, particularly for signals with inherent block-sparse characteristics.
• The method's effectiveness is confirmed, paving the way for enhanced acoustic analysis and noise control applications.