Adaptive sparse basis compressive equivalent source method for sound field reconstruction

An overcomplete dictionary is constructed by combining two sparse bases, designed for the spatially sparse and extended source cases, respectively. By utilizing this dictionary, the compressive equivalent source method is expected to achieve sparse reconstruction of sound fields radiated by unknown sources. However, prior studies and numerical simulations presented in this paper reveal that an unsuitable sparse basis would be selected for sound field representation, thereby degrading reconstruction performance. To address this limitation, this paper proposes an adaptive sparse basis compressive equivalent source method by introducing joint sparsity and low-rank constraints. The method adjusts the sparse representation by formulating the reconstruction as a Bayesian optimization problem that simultaneously promotes sparsity and low-rank structures of source strength coefficients. Both numerical simulations and experimental results across three source cases demonstrate that the proposed method can effectively select suitable sparse bases. Consequently, higher reconstruction accuracy than the conventional compressive equivalent source method using the overcomplete dictionary can be achieved (particularly in spatially sparse and combined source cases). Moreover, the reconstructions obtained by the proposed method exhibit greater robustness. This method provides a solution for reconstruction without prior knowledge of source characteristics, offering practical advantages for noise source identification applications.