Speaker
Description
Plane-wave-based sound field estimation commonly relies on discretising the plane-wave domain into a finite set of propagation directions, which can lead to high-dimensional models and unfavourable conditioning in sparse inverse problems. In this work, we investigate continuous directional latent models by parameterising the plane-wave distribution on the unit sphere with compact mixtures. We consider two component families within the same framework: von Mises–Fisher (vMF) components, which provide an intrinsic isotropic model on the sphere, and tangent-space Gaussian (TG) components, which provide explicit covariance control and analytically convenient local approximations. Inserting these models into the Herglotz plane-wave representation yields compact sound-field models whose atoms are tied to continuous directional distributions rather than to a fixed propagation grid. The unknown amplitudes and directional parameters are estimated from sparse pressure measurements using a variable-projection style procedure: amplitudes are refit by ridge least squares for fixed directional parameters, while directions and spreads or covariances are optimised iteratively. The comparison is motivated by the trade-off between intrinsic spherical fidelity for vMF mixtures and local anisotropic flexibility for TG. Numerical experiments in simulated room-acoustic fields compare reconstruction accuracy and parameter efficiency against ridge and sparse fixed-grid plane-wave estimation. The results show improved reconstruction at matched intrinsic parameter counts in several settings for both methods, with vMF mixtures giving the most consistent high-frequency gains, at the cost of iterative nonlinear fitting.