Research On Sound Field Reconstruction Method Based On Compressive Sensing Equivalent Source Using Spherical Array

Plane near-field acoustic holography（NAH）can only identify the sound source ahead of the array,but not the sound source behind the array.Spherical near-field acoustic holography（S-NAH）can identify the sound source in any direction and realize the reconstruction of three-dimensional sound field.The equivalent source method（ESM）is an efficient and popular calculation and analysis method for NAH.Spherical array equivalent source method（S-ESM）formed by the combination of equivalent source method and spherical array can effectively realize sound field reconstruction and sound source identification.However,this method also has some shortcomings,such as narrow application range of sound source frequency and low reconstruction accuracy.This paper attempts to combine the compressive sensing algorithm（CS）with the S-ESM,and uses the open microphone spherical array as the measurement front end to study the sound field reconstruction method of the spherical array compressive sensing equivalent source method（CS~2-ESM）.Numerical simulation and experimental results show the feasibility and effectiveness of the CS~2-ESM.The structure of the full text is as follows:（1）The sound field reconstruction principles of equivalent source method and spherical array equivalent source method are introduced,and the shortcomings of spherical array equivalent source method are analyzed.Using the sparsity of sound field signal and introduces CS to improve the S-ESM.When solving the ill posed problem,this paper uses the minimization of L₁-norm to better promote the sparse solution and obtain the global optimal solution.（2）The numerical simulation of CS~2-ESM is carried out.The monopole sound source is used to reconstruct the sound field under the conditions of changing the sound source frequency,sound source position,reconstruction surface radius and different signal-to-noise ratio,and the accuracy of sound field reconstruction is analyzed.The simulation results show that CS~2-ESM has wider sound source frequency application range,strong noise anti-interference ability and high sound field reconstruction accuracy than S-ESM.（3）Further,the experimental verification of the sound field reconstruction method of CS~2-ESM in the full anechoic chamber is carried out.The experimental device is built.By changing the speaker frequency and its position relative to the spherical array,the two sound field reconstruction methods of CS~2-ESM and S-ESM are experimentally verified and compared.The sound field reconstruction value and theoretical sound pressure value are given respectively,and the sound field reconstruction error is analyzed accordingly.The experimental results show that the spherical source array reconstruction method is more effective than S-ESM.