Optimal sensor arrangement in random array for compressive-sensing based sound source identification

Abstract This paper adopts the theory of compressive sensing (CS) for the identification of sound source with attention on the sensor arrangement in the random array. As a lower Restricted Isometry Constant (RIC) is anticipated for satisfying the Restricted Isometry Property (RIP) that assures a stable recovery with CS, an objective function is established with the RIC averaging over the array’s intended frequency range. Monte-Carlo based statistical method enables an estimation of RIC in the course of the minimization process, thereby proper sensor positions could be determined. The demonstration through numerical simulations and experimental measurements examines an optimal arrangement of 24 sensors for a given aperture, which is compared to two different types of random arrays. It is shown that the sensor configuration obtained by the proposed approach offers an improved performance as the frequency decreases and/or signal-to-noise ratio gets worse.