Spherical harmonic decomposition facilitates decomposing the sound pressure at different microphones into independent functions of frequency, azimuth and elevation of the source and microphone locations. This decomposition facilitates the extraction of two sets of features containing different information about elevation and azimuth of the source for the direction of arrival (DOA) estimation. These features can be given as input to a learning approach for the estimation of azimuth and elevation separately. This approach aims at breaking down the problem of DOA estimation into azimuth and elevation estimation separately. An advantage of this is the reduction in computational complexity when compared with the joint DOA estimation. This facilitates a straightforward extension of this approach to denser DOA search grids. The contribution of this paper is threefold. First, we propose spherical harmonic magnitude and phase features and discuss the information present in these features regarding the azimuth and elevation of the source. Second, we propose the convolutional neural network architectures for DOA estimation. Third, we analyse the training, run-time computational complexities and propose to extend the DOA estimation approach to dense DOA search grid rather than restricting to a sparse DOA search grid. The performance of conventional DOA estimation approaches degrades in case of a noisy and reverberant environment. Several advancements to the existing DOA estimation approaches have been recently proposed. However, to the best of the authors' knowledge, learning approaches to DOA estimation with dense DOA search grids with few frames in the context of spherical arrays have not been proposed. Performance evaluation is carried out using simulated as well as real datasets. The proposed approach is also evaluated on LOCATA dataset in the context of a moving source. The results are motivating enough to consider the application of the proposed method in practical scenarios.

Near-field acoustic source localization and beamforming has hitherto not been investigated extensively in the spherical harmonic domain under reverberant conditions. In this paper, a novel method for the near-field direction of arrival (DOA) and range estimation using signal invariant and direction independent spherical harmonic features is proposed. A spatial pressure interpolation method that effectively captures the acoustic energy on the surface of the sphere is first developed in the spherical harmonic domain. Near-field DOA estimates are then computed using this pressure distribution. Spherical harmonic features that are signal invariant and direction independent are then extracted using the near field DOA estimates. Signal invariant features are obtained by normalizing spherical harmonic coefficients with a component that is proportional to the source signal strength. Direction independent features are obtained using two methods. Rotation of spherical harmonic functions over a sphere is performed using Wigner-D functions in one method, whereas in the other, the effect of DOA is compensated by spherical harmonic normalization. Using the signal invariant and direction independent features, a learning-based framework which utilizes a convolutional neural network and voicing activity detection is also developed to compute the range of the near-field source. Experiments are conducted both on simulated and real speech data for evaluating the performance of the proposed spherical harmonic features in the context of near-field localization as well as beamforming. Root mean square error of both near-field DOA and source range estimates are obtained. Objective evaluation of near-field beamformed acoustic outputs is also performed. Results obtained are motivating enough for the method to be used in practical near-field beamforming applications.

Frequency and location dependent components in the speech signal can be decoupled by signal processing in the spherical harmonic domain. In this paper, a sparsity based method for joint source localization and separation method using online dictionary learning is proposed. Conventional sparsity based methods utilize an overcomplete dictionary to find a sparse linear combination of dictionary atoms. Online dictionary learning discussed herein, addresses the joint localization and separation problem by learning the dictionary atoms based on stochastic approximation. The location dependent terms present in the dictionary atoms at various frequencies are then clustered to find a robust estimate of number of sources and their locations. Using these estimates, the sources are separated from the mixture. Experiments on speech source localization and separation are conducted at various SNR. Performance evaluation scores like RMSE, log spectral distance and perceptual mean opinion scores indicate reasonable improvement over conventional methods for speech source separation.

Signal processing in spherical harmonic domain has the ability to decouple frequency dependent and location dependent components of the signal received. A method for low dimensional spherical harmonic feature extraction is proposed in this work for DOA estimation in noisy and reverberant environments. The features are extracted using frequency smoothing and a transformation which makes them frequency and signal invariant. Additionally an online manifold regularization framework is explored which utilizes the proposed spherical harmonic features to compute real time DOA estimates. This framework minimizes an instantaneous risk function and finds an inverse mapping function that maps spherical harmonic features to the DOA estimate. Performance of the proposed DOA estimation method is then compared with DOA estimates obtained from features such as generalized cross correlation and relative transfer function in a semi-supervised manifold regularization framework. Experimental results on DOA estimation in terms of root mean square error and probability of resolution indicate a reasonable improvement in the localization performance along with significant reduction in feature dimension.