A convolutional plane wave model for sound field reconstruction.

Spatial sound field interpolation relies on suitable models to conform to available measurements and predict the sound field in the domain of interest. A suitable model can be difficult to determine when the spatial domain of interest is large compared to the wavelength or when spherical and planar wavefronts are present or the sound field is complex, as in the near-field. To span such complex sound fields, the global reconstruction task can be partitioned into local subdomain problems. Previous studies have shown that partitioning approaches rely on sufficient measurements within each domain due to the higher number of model coefficients. This study proposes a joint analysis of all of the local subdomains while enforcing self-similarity between neighbouring partitions. More specifically, the coefficients of local plane wave representations are sought to have spatially smooth magnitudes. A convolutional model of the sound field in terms of plane wave filters is formulated and the inverse reconstruction problem is solved via the alternating direction method of multipliers. The experiments on simulated and measured sound fields suggest that the proposed method retains the flexibility of local models to conform to complex sound fields and also preserves the global structure to reconstruct from fewer measurements.

Sound source localization using multiple ad hoc distributed microphone arrays.

Sound source localization is crucial for communication and sound scene analysis. This study uses direction-of-arrival estimates of multiple ad hoc distributed microphone arrays to localize sound sources in a room. An affine mapping between the independent array estimates and the source coordinates is derived from a set of calibration points. Experiments show that the affine model is sufficient to locate a source and can be calibrated to physical dimensions. A projection of the local array estimates increases localization accuracy, particularly further away from the calibrated region. Localization tests in three dimensions compare the affine approach to a nonlinear neural network.

Spatial reconstruction of sound fields using local and data-driven functions.

Sound field analysis methods make it possible to characterize and reconstruct a sound field from a limited set of observations. Classical approaches rely on the use of analytical basis functions to model the sound field throughout the observed domain. When the complexity of the sound field is high, for example, in a room at mid and high frequencies, propagating wave representations can be suboptimal due to model discrepancy. We examine the use of local representations to alleviate this model discrepancy and explore data-driven approaches to obtain suitable models. Specifically, local representations are used to reconstruct the sound field over a large spatial aperture in a room. The performance of local models is compared against conventional plane wave reconstructions and the use of data-driven local functions is examined. Dictionary learning and principal component analysis are used to obtain functions from extensive spatial measurements in an empty room. The results indicate that local partitioning models conform to fields of high spatial complexity. Dictionary learning generalizes across different rooms and frequencies-conferring potential for modelling complex sound fields based on their local and statistical properties.

Spatial reconstruction of the sound field in a room in the modal frequency range using Bayesian inference.

Spatial characterization of the sound field in a room is a challenging task, as it usually requires a large number of measurement points. This paper presents a probabilistic approach for sound field reconstruction in the modal frequency range for small and medium-sized rooms based on Bayesian inference. A plane wave expansion model is used to decompose the sound field in the examined domain. The posterior distribution for the amplitude of each plane wave is inferred based on a uniform prior distribution with limits based on the maximum sound pressure observed in the measurements. Two different application cases are studied, namely a numerically computed sound field in a non-rectangular two-dimensional (2D) domain and a measured sound field in a horizontal evaluation area of a lightly damped room. The proposed reconstruction method provides an accurate reconstruction for both examined cases. Further, the results of Bayesian inference are compared to the reconstruction with a deterministic compressive sensing framework. The most significant advantage of the Bayesian method over deterministic reconstruction approaches is that it provides a probability distribution of the sound pressure at every reconstruction point, and thus, allows quantifying the uncertainty of the recovered sound field.