Complex approximate message passing equivalent source method for sparse acoustic source reconstruction

Acoustic source reconstruction techniques are an essential technical basis for noise source identification and fault diagnosis. How to computationally efficiently obtain the accurate estimation of acoustic source location and strength remains a fundamental challenge for acoustic source reconstruction techniques. To accommodate the needs of processing complex-valued signals, complex approximate message passing algorithm (CAMP) is considered. Benefiting from the Onsager correction term, the reconstruction performance and convergence speed of CAMP are enhanced. The computational complexity of CAMP is significantly reduced by avoiding matrix inversion in each iteration. Therefore, a sparse Equivalent Source Method (ESM) based on CAMP is proposed in this paper and named CAMP-ESM for achieving acoustic source reconstruction with increased accuracy and computational efficiency. Simulation results show in the mid-high frequency range, CAMP-ESM achieves the best reconstruction results in the shortest time compared to other ℓ₁-based ESM. In addition, the proposed method achieves a good balance between reconstruction accuracy and computational efficiency compared to other state-of-the-art ESM methods. Two experiments verified that CAMP-ESM can accurately localize the acoustic source and quantify the acoustic power.