Acoustic source identification: Experimenting the ℓ1 minimization approach

Abstract

This work experiments and investigates the problem of acoustic sources identification from a limited number of measurements delivered by a microphone array as a Basis Pursuit problem. The basic idea beyond Basis Pursuit is to search for a solution that minimizes the ℓ1 norm of the solution rather than the usual sum of squares (ℓ2 norm) of the residual error. Basis Pursuit has been developed in the context of Compressed Sensing (CS), and has already proved to be efficient in a great number of applications. However, the quality of the obtained results is subdued to restricted conditions whose fulfillment in acoustics are investigated in this paper depending on geometrical parameters such as the source/array distance or the array aperture. This leads to the proposition of several practical guidelines for the experimenter as how to select a microphone array and how to optimaly position it w.r.t the radiating source of interest. Simulations and experimental data are used to demonstrate the relevance and limitations of this approach. The results proved to be better than those obtained by conventional Beamforming (BF), even in its near-field focusing version based on spherical waves.