Designing a sparse sensor array for sound field reconstruction using compressive-equivalent source method

The compressive-equivalent source method (C-ESM) can reconstruct the sound field radiated by sparsely distributed sound sources with a reduced number of sensors. To ensure the performance of the C-ESM, the transfer matrix between the sensors and equivalent point sources should exhibit sufficient incoherence. Given that the configuration of the sensor array affects this incoherence condition, concern regarding the sensor array design would arise. To address such concern, this paper proposes a sensor array design approach. The primary objective of this approach is to minimize the mean coherence of the transfer matrix within the developed iterative framework, providing the incoherence condition required by the C-ESM. Subsequently, the designed sensor array is utilized by the C-ESM for the reconstructions. The effectiveness and practicality of the proposed approach are validated through numerical simulations and experiments.