A Ratio Model of <i>L</i>₁/<i>L</i>₂ Norm for Sound Source Identification

Abstract

In the field of sound source identification, robust and accurate identification of the targeted source could be a challenging task. Most of the existing methods select the regularization parameters whose value could directly affect the accuracy of sound source identification during the solving processing. In this paper, we introduced the ratio model ℓ1/ℓ2 norm to identify the sound source(s) in the engineering field. Using the alternating direction method of multipliers solver, the proposed approach could avoid the selection of the regularization parameter and localize sound source(s) with robustness at low and medium frequencies. Compared with other three methods employing classical penalty functions, including the Tikhonov regularization method, the iterative zoom-out-thresholding algorithm and the fast iterative shrinkage-thresholding algorithm, the Monte Carlo Analysis shows that the proposed approach with ℓ1/ℓ2 model leads to stable sound pressure reconstruction results at low and medium frequencies. The proposed method demonstrates beneficial distance-adaptability and signal-to-noise ratio (SNR)-adaptability for sound source identification inverse problems.

Keywords

• microphone array
• near-field acoustical holography
• sound source identification
• sparse regularization