# Variational Bayesian Compressive Sensing with Equivalent Source Modeling for Sound Field Reconstruction

## TL;DR

This paper introduces a faster and more accurate method for reconstructing sound fields using Bayesian compressive sensing and equivalent source modeling.

## Contribution

A variational Bayesian compressive sensing framework integrated with equivalent source modeling for efficient and accurate sound field reconstruction.

## Key findings

- The proposed method achieves superior reconstruction accuracy compared to conventional Bayesian compressive sensing.
- It significantly reduces computational burden and improves robustness in low signal-to-noise ratio scenarios.
- Numerical simulations and experiments validate the method's effectiveness.

## Abstract

While conventional Bayesian compressive sensing exploits signal sparsity for accurate sound field reconstruction from under-sampled measurements, its practicality is limited by high computational complexity and slow convergence. To address these limitations, this paper proposes a variational Bayesian compressive sensing framework integrated with equivalent source modeling for sound field reconstruction. The approach first establishes a sparse representation of the sound field using the equivalent source method, and then assigns hierarchical prior distributions to the equivalent source strengths and the noise precision within this Bayesian model. Mean-field variational inference is adopted to derive an analytically tractable approximation to the true posterior distribution by minimizing the Kullback–Leibler divergence, thus enabling efficient estimation of the equivalent source strengths and subsequent high-accuracy sound field reconstruction. This proposed method retains the desirable statistical advantages of Bayesian modeling while enhancing computational efficiency. Numerical simulations and experiments validate that the proposed method achieves superior reconstruction accuracy compared with conventional Bayesian compressive sensing and orthogonal matching pursuit algorithm, with significantly reduced computational burden and enhanced robustness in low signal-to-noise ratio scenarios.