Sensor array design for sparse sound field reconstruction

The compressive-equivalent source method can reconstruct the sound field of the sparsely distributed sound sources through promoting the sparsity of the equivalent source strengths. To reduce the mutual coherence of the sensing matrix, the spatially random sampling is performed. However, different samplings would make the reconstruction results instable, and a fixed sampling would not guarantee satisfied reconstruction results when reconstructing the sound field at different frequencies. To handle this issue, the present paper proposes a sensor array design method for sparse sound field reconstruction. After obtaining the matrix by the sum of the frequency-dependentsensing matrices, the optimization problem of the proposed method is formulated based on the mutual coherence minimization principle, and the solutions indicating the selected positions of the sensors are solved by the gradient projection. Numerical simulation and experimental results show that lower reconstruction errors can be obtained with the designed senor array compared to the spatially random sampling.