Data-adaptive pattern-coupled Bayesian compressive sensing for sparse sound field reconstruction

Pattern-coupled Bayesian compressive sensing shows great potential in sound field reconstruction by leveraging structural sparsity, but its fixed coupling patterns for sparsity hyperparameters limit adaptability to non-uniform correlation distributions. To overcome this limitation, this paper proposes an enhanced method termed data-adaptive pattern-coupled Bayesian compressive sensing for high-accuracy sound field reconstruction. In this method, a hierarchical Gaussian-Gamma prior model is established based on the equivalent source method within the compressive sensing framework, achieving reconstruction by solving for the sparse coefficient vector of equivalent source strengths. A set of adaptive coupling parameters is introduced via a learnable transformation matrix, dynamically regulating the interrelationships between hyperparameters and thereby substantially enhancing the adaptability of the prior model. Furthermore, both the coupling parameters and hyperparameters are iteratively updated with a data-driven method, enabling adaptive mutual influence of sparsity patterns among elements within the sparse coefficient vector. This process promotes clustering of non-zero coefficients and concentration of zero-valued coefficients, inducing a physically meaningful block-sparse structure reflecting the spatial continuity of actual sound sources. By fully exploiting the intrinsic statistical correlations between elements of the sparse coefficient vector without requiring knowledge of the block structure, it achieves superior sound field reconstruction accuracy. Numerical simulations and experimental results demonstrate that the proposed method outperforms existing approaches in terms of reconstruction accuracy and noise robustness, thereby validating its effectiveness and superiority in sound field reconstruction.