Compressive sensing based spherical harmonics decomposition of a low frequency sound field within a cylindrical cavity

A low frequency sound field within a cylindrical cavity can be well approximated by a sparse set of Fourier−Bessel series in a spherical coordinate system. The approximation accuracy can be guaranteed as long as the series coefficients are well estimated by use of spherical microphone arrays (SMA). Conventional methods like spherical Fourier transform and Helmholtz equation least square require a large number of sensors, and it is difficult to estimate the high order coefficients in the presence of sensor noise. To cope with these issues, compressive sensing (CS) is utilized and compared with the conventional methods. In this study, the estimate of the high order coefficients from contaminated measurements is examined, and the effect of modal behavior is analyzed. Numerical simulations show that sensors can be significantly saved especially for high order cavity modes due to the low sparsity of coefficients which is also stable as the modal frequency increases, and the overall accuracy is also improved. The optimal SMA configuration for the use of CS is studied. A large SMA with omni-microphone deployed by the Fliege sampling scheme is suggested. The CS results are finally validated through the good simulated reconstructions of cylindrical cavity modes.