Sparse Plane Wave Approximation of Acoustic Modes to Address Basis Mismatch

Low-frequency sound field reconstruction in an enclosed space has many applications where the plane wave approximation of acoustic modes plays a crucial role. However, the basis mismatch of the plane wave directions degrades the approximation accuracy. In this study, a two-stage method combining ℓ₁-norm relaxation and parametric sparse Bayesian learning is proposed to address this problem. This method involves selecting sparse dominant plane wave directions from pre-discretized directions and constructing a parameterized dictionary of low dimensionality. This dictionary is used to re-estimate the plane wave complex amplitudes and directions based on the sparse Bayesian framework using the variational Bayesian expectation and maximization method. Numerical simulations show that the proposed method can efficiently optimize the plane wave directions to reduce the basis mismatch and improve acoustic mode approximation accuracy. The proposed method involves slightly increased computational cost but obtains a higher reconstruction accuracy at extrapolated field points and is more robust under low signal-to-noise ratios compared with conventional methods.