Fast Sparse Reconstruction of Sound Field Via Bayesian Compressive Sensing

To overcome the contradiction between the resolution and the measurement cost, various algorithms for reconstructing the sound field with sparse measurement have been developed. However, limited attention is paid to the computation efficiency. In this study, a fast sparse reconstruction method is proposed based on the Bayesian compressive sensing. First, the reconstruction problem is modeled by a sparse decomposition of the sound field via singular value decomposition. Then, the Bayesian compressive sensing is adapted to reconstruct the sound field with sparse measurement of sound pressure. Numerical results demonstrate that the proposed method is applicable to either the spatially sparse distributed sound sources or the spatially extended sound sources. And comparisons with other two sparse reconstruction methods show that the proposed one has the advantages in terms of reconstruction accuracy and computational efficiency. In addition, as it is developed in the framework of multitask compressive sensing, the method can use multiple snapshots to perform reconstruction, which greatly enhances the robustness to noise. The validity and the advantage of the proposed method are further proved by experimental results.