Multiple source localisation in the spherical harmonic domain

The area of sound field synthesis has significantly advanced in the past decade, facilitated by the development of high-quality sound-field capturing and re-synthesis systems. Spherical microphone arrays are among the most recently developed systems for sound field capturing, enabling processing and analysis of three-dimensional sound fields in the spherical harmonics domain. In spite of these developments, a clear relation between sound fields recorded by spherical microphone arrays and their perception with a re-synthesis system has not yet been established, although some relation to scalar measures of spatial perception was recently presented. This paper presents an experimental study of spatial sound perception with the use of a spherical microphone array for sound recording and headphone-based binaural sound synthesis. Sound field analysis and processing is performed in the spherical harmonics domain with the use of head-related transfer functions and simulated enclosed sound fields. The effect of several factors, such as spherical harmonics order, frequency bandwidth, and spatial sampling, are investigated by applying the repertory grid technique to the results of the experiment, forming a clearer relation between sound-field capture with a spherical microphone array and its perception using binaural synthesis regarding space, frequency, and additional artifacts. The experimental study clearly shows that a source will be perceived more spatially sharp and more externalized when represented by a binaural stimuli reconstructed with a higher spherical harmonics order. This effect is apparent from low spherical harmonics orders. Spatial aliasing, as a result of sound field capturing with a finite number of microphones, introduces unpleasant artifacts which increased with the degree of aliasing error.

Source localization has been studied in the spatial domain using differential geometry in earlier work. However, parameters of the sensor array manifold have hitherto not been investigated for source localization in spherical harmonics domain. The objective of this work is to represent and model the manifold surface using differential geometry. The system model for source localization over a spherical harmonic manifold is first formulated. Subsequently, the manifold parameters are modeled in the spherical harmonics domain. Source localization methods using MUSIC and MVDR over the spherical harmonics manifold are developed. Experiments on source localization using a spherical microphone array indicate high resolution in noise.

A gridless sound field decomposition method based on the reciprocity gap functional (RGF) is proposed. An intuitive and powerful way of reconstructing a sound field inside a region including sound sources is to decompose the sound field into Green's functions. Current methods based on sparse representation require discretization of the reconstruction region into grid points to construct the dictionary matrix; however, this procedure causes an off-grid problem and has a high computational cost. We apply the RGF, which was first proposed in the field of inverse problems, to sound field decomposition in the spherical harmonic domain. The proposed method enables a sound field to be decomposed in a gridless manner with a computationally efficient algorithm. Numerical simulation results indicated that the reconstruction accuracy as well as the source localization accuracy can be improved by the proposed method compared with current methods, especially at low frequencies.

A constrained Kalman beamforming (CKB) method in spherical harmonics domain is proposed to localize multiple sources captured by spherical arrays. It scans the Euclidean norm of the weights in three-dimensional space to estimate source directions. It can improve the accuracy of sound source localization when steering vector mismatch exits. Moreover, it has the advantage of rapid convergence and online implementation. Compared with the desired minimum variance distortionless response (MVDR) and diagonal loading (DL) methods, simulation results show that the proposed algorithm has robustness to arbitrary steering vector mismatch and low number of snapshots.

The reliable estimation of fiber orientation distributions from diffusion-sensitized magnetic resonance imaging is an important processing step for revealing structural connectivity in the human brain. Fiber orientation distributions are usually represented in spherical harmonic (SH) domain, but many modern spatial regularization techniques were not yet formulated in SH-domain such that they cannot benefit from the well known advantages. In this article we propose a novel SH-formulation of the contour enhancement propagator (fiber continuity) which enables to implement a variety of processing steps in SH-domain.

Fast direction-of-arrival estimation algorithm for multiple wideband acoustic sources using multiple open spherical arrays

Open-sphere microphone arrays are preferred over rigid-sphere arrays when minimal interaction between array and the measured sound field is required. However, open-sphere arrays suffer from poor robustness at null frequencies of the spherical Bessel function. This letter proposes a maximum likelihood method for direction of arrival estimation in the spherical harmonic domain, which avoids the division of the spherical Bessel function and can be used at arbitrary frequencies. Furthermore, the method can be easily extended to wideband implementation. Simulation and experiment results demonstrate the superiority of the proposed method over the commonly used methods in open-sphere configurations.

Estimation of the direction of arrival (DOA) of reflections in a room using spherical microphone arrays can be performed using several methods such as plane-wave decomposition, and delay-and-sum beamforming, for which the resolution of the estimation process is usually bounded by the array order, or the number of microphones. In this paper a method for DOA estimation of the reflections in a room using room impulse-response data and spherical microphone arrays is presented, in which only a first order microphone array is required. The proposed method uses signal processing in the spherical harmonics domain, utilizing an analytical dependence of the spherical harmonic coefficients on different acoustics parameters. It is shown that the zero order spherical harmonics coefficients is a function of the time delays and amplitudes of the planes waves composing the sound field, while the first order coefficients are a function of the time delays, amplitudes and the elevation and azimuth components of the wave arrival direction. Using this property leads to the development of an estimator based on the least-squares approach, in which each order is used to estimate a single sound-field parameter.

A conventional approach to wideband multi-source (MS) direction-of-arrival (DOA) estimation is to perform single source (SS) DOA estimation in time-frequency (TF) bins for which a SS assumption is valid. Such methods use the W-disjoint orthogonality (WDO) assumption due to the speech sparseness. As the number of sources increases, the chance of violating the WDO assumption increases. As shown in the challenging scenarios with multiple simultaneously active sources over a short period of time masking each other, it is possible for a strongly masked source (due to inconsistency of activity or quietness) to be rarely dominant in a TF bin. SS-based DOA estimators fail in the detection or accurate localization of masked sources in such scenarios. Two analytical approaches are proposed for narrowband DOA estimation based on the MS assumption in a bin in the spherical harmonic domain. In the first approach, eigenvalue decomposition is used to decompose a MS scenario into multiple SS scenarios, and a SS-based analytical DOA estimation is performed on each. The second approach analytically estimates two DOAs per bin assuming the presence of two active sources per bin. The evaluation validates the improvement to double accuracy and robustness to sensor noise compared to the baseline methods.

Reproduction of high quality spatial sound has gained considerable importance with the recent technology developments in the fields of virtual and augmented reality. Recently, the reproduction of binaural signals in the Spherical-Harmonics (SH) domain has been proposed. This is performed by using SH representations of the sound-field and the Head-Related Transfer Function (HRTF). These processes offer the flexibility to control the reproduced binaural signals, by manipulating the sound-field or the HRTFs using algorithms that operate directly in the SH domain. However, in most practical cases, the binaural reproduction is order-limited, which introduces truncation error that has a detrimental effect on the perception of the reproduced signals, mainly due to the truncation of the HRTF. A recent study showed that pre-processing of the HRTF by ear-alignment reduces its effective SH order, which may be beneficial for alleviating the above effect. In this paper, a method to incorporate the pre-processed ear-aligned HRTF into the binaural reproduction process is presented. The method uses Ambisonics representation of the sound-field formulated at the two ears, and is denoted here as Bilateral Ambisonics. The proposed method leads to a significant reduction in errors due to the limited-order reproduction, which yields a substantial improvement in perceived binaural reproduction quality even with SH as low as first order.

A unified framework is proposed for analysis and synthesis of spatial sound fields. In the sound field analysis (SFA) phase, an unbaffled 24-element circular microphone array (CMA) is utilized to “encode” the sound field based on the plane-wave decomposition, whereas in the sound field synthesis (SFS) phase a 32-element rectangular loudspeaker array is employed to “decode” the target sound field using pressure matching technique. Depending on the sparsity of the sound sources, the SFA stage can be implemented in two ways. For the sparse-source scenario, a two-stage algorithm is utilized to estimate the source bearings using the minimum power distortionless response (MPDR) and the associated amplitude coefficients of plane waves using the Tikhonov regularization (TIKR) algorithm. Alternatively, a one-stage algorithm based on compressive sensing (CS) algorithm can be used. For the nonsparse-source scenario, a one-stage TIKR is utilized to solve for the amplitude coefficients for plane-wave components uniformly distributed in the angular domain. The SFA technique for the non-sparse source scenario is also useful in establishing the room response model, as required in the pressure matching step of the SFS phase. The integrated acoustic array system is validated with localization and listening tests.

This paper utilizes a rigid spherical microphone array to reduce wind noise. In the experiments conducted, a loudspeaker is used to reproduce the desired sound signal and an axial fan is employed to generate wind noise in an anechoic chamber. The sound signal and wind noise are measured separately with the spherical microphone array and analyzed in the spherical harmonic domain. The wind noise is found to be irregularly distributed in the spherical harmonic domain, distinct from the sound signal which is concentrated in the first few spherical harmonic modes. This difference is utilized to reduce wind noise without degrading the desired sound pressure level (SPL) by use of a low pass filter method in the spherical harmonic domain. Experimental results with both single-tonal and multi-tonal sound signals demonstrate that the proposed method can reduce wind noise by more than 10 dB in the frequency range below 500 Hz. The SPL of the desired sound signal can be extracted from wind noise with an error within 1.0 dB, even when the sound level is 8 dB lower than wind noise.

Spherical array plays important role in 3D targets localization. In this paper, we develop a novel DOA estimation method for the spherical array with super resolution approach. The proposed method operates in spherical harmonic domain. Based on the atomic norm minimization, we develop a gridless L1-SVD algorithm in spherical harmonic domain and then we adopt the spherical ESPRIT method to two-dimensional DOA estimation. Compared to the previous work, the proposed method acquires better estimation performance. Numerical simulation results verify the performance of the proposed method.

This paper concerns the problem of convolutive sound source separation from mutlichannel recordings made with a spherical microphone array. In particular, we formulate two state-of-the-art separation techniques based on Expectation Maximization (EM) and Nonnegative Tensor Factorization (NTF) in the spherical harmonic domain (SHD). Furthermore, we adjust and incorporate the Gaussian Localization Prior (GLP) to the proposed algorithms, which yields two variants of the derived methods. For the source signal reconstruction, a Minimum Variance Distortionless Response (MVDR) beamformer with a single-channel Wiener post-filter is employed. The performance comparison is based on experimental evaluation using micro-phone signals simulated with the image-source method in several scenarios, including diverse geometrical setup, different number of sources and various types of source signals, namely the recordings of speech utterances and musical instruments. The experimental results for the first-order ambisonic signals show that the proposed methods enable high-quality sound source separation in the spherical harmonic domain. In particular, we show that incorporation of the Gaussian Localization Prior to the proposed algorithms leads to a substantial improvement in separation performance.

This paper proposes a three-dimensional wave-domain acoustic contrast control method to reproduce a multizone sound field using a circular loudspeaker array. In this method, sound field analysis is based on spherical harmonic decomposition, and the loudspeaker weights are obtained by maximizing the acoustic energy contrast between the predefined bright zone and dark zone. Simulation results show that the proposed method provides good multizone separation performance over a large spatial region and requires lower-order spherical harmonics, resulting in a much lower number of microphones required to measure the acoustic transfer functions.