Sound Field Reconstruction Using Compressed Separable Projection-Based Equivalent Source Method

The compressive-equivalent source method (C-ESM) has been developed for the sound field reconstruction by solving the l1 minimization with the predetermined sparsity of the equivalent source strengths. However, the C-ESM would reconstruct the sound field with the error proportional to the measurement noise-related data fidelity constraint that increases with the decrease of the signal-to-noise ratio. Apart from that, the reconstruction stability of the C-ESM would not be guaranteed due to the existence of the measurement noise. To address such problem, the present paper proposes a compressed separable projection-based equivalent source method. In the method, the projections of the measured pressures in the predesigned basis that combines the priors of the sound radiation of the equivalent sources and the measurement noise are obtained by solving the l1 minimization. This not only leads to the data fidelity constraint being small and unrelated to the measurement noise, but also separates the measurement noise from the measured sound field. Therefore, the proposed method can theoretically reconstruct the sound field more accurately and stably than the C-ESM. Numerical simulations and experiments are carried out to verify the effectiveness of the proposed method.