State-of-the-art soundfield reconstruction methods are computationally expensive and their performance is generally undermined by the presence of strong reverberation and of near-field sources, which are usually modeled using omnidirectional radiation patterns. In this work, we propose a compressive sensing approach for the reconstruction of the soundfield produced by arbitrary directive sources in a reverberant room. Assuming sparsity in the distribution of sources, along with a loose prior knowledge on their position and on the geometry of the environment, we reconstruct both the direct and the reverberant components of the soundfield by modeling early reflections as near-field sources. Moreover, the directivity of sources is explicitly modeled by first expressing the soundfield produced by arbitrarily directive sources as an expansion of multipoles, and then introducing group sparsity constraints. Numerical simulations in two rooms with different reverberation characteristics are conducted to perform the validation of the proposed method.

Differential Microphone Arrays (DMAs) are of great interest in the literature on small-sized microphone arrays, due to their good directivity properties and nearly frequency-invariant spatial responses. Recently developed beamforming techniques combine multiple DMA units to form flexible two-stage spatial filtering systems, where the output of each DMA is fed into a higher-level filter, called virtual filter, for further processing. In this manuscript, we analyze and discuss some properties of a broad class of two-stage beamformers with arbitrary planar geometry. In this context, the DMA units are all assumed to have the same directivity pattern of arbitrary order and can be characterized by a variable number of omnidirectional sensors organized in an arbitrary geometry. For any given choice of the virtual array filter, we introduce a closed-form optimization procedure to design DMA filters that maximize the White Noise Gain (WNG) or the Directivity Factor (DF) of the resulting two-stage beamformer at any frequency. Based on this frequency-dependent design, we propose a frequency-invariant design of the two-stage beamformer and we compare the performance of the two approaches. Finally, we propose two possible computational schemes for the proposed generic two-stage spatial filtering system and discuss their efficiency in performing filtering, steering, and changing beampattern.

The literature is rich with techniques for the design of small-size Differential Microphone Arrays (DMAs), known for their almost frequency-invariant beampatterns and low computational cost. Few works, instead, discuss the properties of beamformers based on multiple DMA units. In this paper, we consider arbitrarily shaped planar arrays of DMA units. In turn, each DMA unit is a first-order continuously-steerable differential microphone characterized by an arbitrary configuration of omnidirectional sensors and a symmetric beampattern. We present a beamforming technique that, assumed all the DMA units to steer identical beams in the same direction, allows us to approach the behavior of a Delay-And-Sum beamformer or Super-Directive beamformer by solely varying a single scalar parameter. Efficient implementations of the proposed beamformers can be developed by taking into account that, for a wide range of frequencies, the values of such a parameter are practically invariant with respect to the geometry of the array.

We present a spatial filtering approach to first-order steerable Differential Microphone Arrays (DMAs) with arbitrary planar geometry. In particular, the design of the spatial filter is based on a recently proposed frequency-domain design methodology that approximates, in a least-square sense, a target beampattern using the Jacobi-Anger expansion involving Bessel functions. Despite the generality of that approach, however, its computational cost turns out to be excessive when working with limited processing resources. The beamforming technique proposed in this manuscript overcomes this issue by exploiting the fact that in DMAs the spacing between sensors is typically smaller than the smallest wavelength of audio signals of interest. This allows us to substitute zero- and first-order Bessel functions with their Taylor series approximation truncated to the first order. Moreover, we show that this approximation allows us to derive an efficient discrete-time-domain implementation of first-order steerable differential beamformers based on arrays with arbitrary geometries.

In this article we present a methodology for source localization in reverberant environments from Generalized Cross Correlations (GCCs) computed between spatially distributed individual microphones. Reverberation tends to negatively affect localization based on Time Differences of Arrival (TDOAs), which become inaccurate due to the presence of spurious peaks in the GCC. We therefore adopt a data-driven approach based on a convolutional neural network, which, using the GCCs as input, estimates the source location in two steps. It first computes the Ray Space Transform (RST) from multiple arrays. The RST is a convenient representation of the acoustic rays impinging on the array in a parametric space, called Ray Space. Rays produced by a source are visualized in the RST as patterns, whose position is uniquely related to the source location. The second step consists of estimating the source location through a nonlinear fitting, which estimates the coordinates that best approximate the RST pattern obtained through the first step. It is worth noting that training can be accomplished on simulated data only, thus relaxing the need of actually deploying microphone arrays in the acoustic scene. The localization accuracy of the proposed techniques is similar to the one of SRP-PHAT, however our method demonstrates an increased robustness regarding different distributed microphones configurations. Moreover, the use of the RST as an intermediate representation makes it possible for the network to generalize to data unseen during training.

In this article we propose a methodology for the reconstruction of sound fields in arbitrary locations based on the signals acquired by a spatial distribution of compact microphone arrays (virtual miking). The proposed method is suitable for operating in reverberant environments, thanks to a two-stage analysis process, the former of which aims at separating the direct and the diffuse components of the sound field. The method that we propose is inherently parametric, as the sources of the acoustic scene are characterized by parameters describing location and directivity (spherical harmonics expansion), which are extracted from the exterior model of the direct component of the sound field. Once the parameters of the sources are extracted, the direct sound field at an arbitrary location is reconstructed. The diffuse component is reconstructed from the joint knowledge of the diffuse component at the locations of the distributed microphone arrays, under the assumption of isotropic behavior. Results show that the proposed technique is able to analyze the sound field and reconstruct the parameters of the sources that are active in the scene. In addition, the synthesis of the signals at the virtual microphone locations turns out to accurately match (in terms of spatial cues) the actual sound field, as measured by a microphone places in the desired location.

Sound reproduction systems may highly benefit from detailed knowledge of the acoustic space to enhance the spatial sound experience. This article presents a room geometry inference method based on identification of reflective boundaries using a high-resolution direction-of-arrival map produced via room impulse responses (RIRs) measured with a linear loudspeaker array and a single microphone. Exploiting the sparse nature of the early part of the RIRs, Elastic Net regularization is applied to obtain a 2D polar-coordinate map, on which the direct path and early reflections appear as distinct peaks, described by their propagation distance and direction of arrival. Assuming a separable room geometry with four side-walls perpendicular to the floor and ceiling, and imposing pre-defined geometrical constraints on the walls, the 2D-map is segmented into six regions, each corresponding to a particular wall. The salient peaks within each region are selected as candidates for the first-order wall reflections, and a set of potential room geometries is formed by considering all possible combinations of the associated peaks. The room geometry is then inferred using a cost function evaluated on the higher-order reflections computed via beam tracing. The proposed method is tested with both simulated and measured data.

This paper addresses the problem of soundfield reconstruction over a large area using a distributed array of higher-order microphones. Given an area enclosed by the array, one can distinguish between two components of the soundfield: the interior soundfield generated by sources outside of the enclosed area and the exterior soundfield generated by sources inside the enclosed area. These components form an indistinguishable mixture and, despite the existence of theoretical solutions to separate them, practical implementation is challenging due to high number of microphones needed for large regions and high frequencies. In this work, we consider a scenario where the interior soundfield is characterized by reverberation and show how a set of RIR measurements can be used to parametrize the interior component as a function of the exterior component, effectively reducing the unknowns of the problem.

We propose a spatial filtering method for linear arrays of First-Order Steerable Differential Microphones (FOSDMs), which operates in two layers. In the former, signals acquired by individual microphones are locally filtered to produce the outputs of the FOSDMs. In the latter, the outputs of the FOSDMs are processed by another filter. We analyse different design methodologies and study the conditions under which the two filtering layers can be decoupled. The proposed two-layer spatial filter can be flexibly controlled with a single scalar parameter, which can be chosen, for example, to maximize the White Noise Gain (like in a Delay-and-Sum beamformer); or to maximize the Directivity Factor (like in a Super-Directive beamformer); without needing any matrix inversion. The effectiveness of the proposed beamforming method is compared with traditional spatial filtering techniques using different metrics.

In this paper we propose a parametric sound field reconstruction approach. In particular, the technique is based on the estimation of three parameters for each acoustic source (source position, radiation pattern and source signal) given the signals acquired by few arbitrarily placed microphone arrays. This allows us to synthesize the signal of a virtual microphone placed in any point of the acoustic scene.