Sparse plane wave decomposition of a low frequency sound field within a cylindrical cavity using spherical microphone arrays

Conventionally plane wave decomposition (PWD) of a low frequency sound field using a spherical microphone array (SMA) would suffer from low spatial resolution. Although compressive sensing (CS) has been employed to estimate a sparse set of plane waves when formulated in the spherical harmonics domain, its performance at the low frequency is still not fully discussed, particularly if the plane waves are densely discretized, the columns of the sensing matrix will become highly correlated. To address these problems, a two-step l₁-norm minimization method for the PWD is developed. First, a sufficient set of sound field coefficients in the spherical harmonics domain is solved using CS, which is equivalent to the sparse spherical harmonics decomposition (SHD), however, with the sparsity constraint imposed on the plane-wave basis instead of the coefficients vector. With the estimated coefficients, a sparse set of plane waves can then be recovered using CS by requiring that the truncated order is sufficiently high. By means of a scan-based measurement with a feasible SMA, and with the sparsity constraint imposed on the plane-wave basis, the proposed method proved effective in improving spatial resolution with less measurements through both simulations and experiments within a cylindrical cavity.