Dereverberation and acoustic beamforming are jointly used to capture the speech of a desired speaker in the presence of interfering speakers in a reverberant room using an array of microphones. Traditionally, to perform these two tasks, the desired speech is modelled in the time-frequency domain using a complex Gaussian (CG) prior with time-varying variances. The shape parameter of the prior distribution is fixed at the same value for all time-frequency bins. In this work, we proposed to model the inverse of the variance (i.e. the precision parameter) of the CG prior distribution which controls the shape of the distribution as a Gamma distributed random variable. The hyperparameters of the Gamma distribution were then estimated based on the data captured by the microphones. This data-dependent blind estimation of the shape of the prior distribution helped the proposed algorithm to accurately model the desired speech and adapt to different speakers and acoustic scenarios better than algorithms with a fixed shape parameter. We used maximum likelihood techniques to estimate the multi-channel linear prediction (MCLP) dereverberation coefficients and the beamforming weights using the proposed signal model. The stochastically latent precision parameters were obtained by estimating the hyperparameters using the expectation maximization (EM) method. For the online version of the algorithm, a recursive EM method was also proposed for real-time processing. Extensive simulation results showed improved dereverberation and interference cancellation performance of the proposed method highlighting the importance of not choosing the shape parameter of the prior distribution manually. 

Phase-mode array processing which utilizes the spherical harmonics decomposition offers a useful framework for spherical microphone arrays. In the modal domain, one of the major applications of spherical arrays is acoustic beamforming. Usually, beamforming is performed by minimizing the power of the beamformer output with a distortionless constraint towards the look direction. Also, most beamformers model the spectral coefficients of target speech using a Gaussian distribution. In this work, a beamforming method that minimized the L0-norm of the beamformer output in the spherical harmonics domain with a distortionless constraint was proposed. The proposed method assumed a super-Gaussian prior for the target speech and sparsified the beamformer output which was shown to reduce the residual elements of the interfering speech signals from the beamformer output leading to superior spatial separation. The formulation of the proposed beamformer in the spherical harmonics signal model was developed along with an algorithm to solve it. Simulation results showed the effectiveness of the proposed beamformer in spatially filtering the desired speaker signal from the interfering signals using a number of objective measures. 

Conventional direction-of-arrival (DOA) estimation algorithms like MUSIC only allow localization of fewer number of sources than the number of physical sensors. In this work, underdetermined azimuth localization (localizing more sources than the number of sensors) using arbitrary planar arrays was proposed, using only second-order statistics of the received data. To achieve this, we utilized the difference coarray of the actual array and expressed the elements of the array covariance matrix as the signal received by the virtual sensors of the coarray. We explored the structure and geometry of the difference coarray of an N-element planar array and showed that the coarray can provide an increased degreeof-freedom (DOF) of O(N^2) which enabled underdetermined localization. Then, we extended the manifold separation (MS) technique to the coarray to express the coarray steering matrix in terms of a Vandermonde structured matrix by designing a signal independent coarray characteristic matrix. As the signal model of a coarray is a single snapshot model, the Vandermonde structure enabled us to perform a spatial smoothing type operation to restore the rank of the coarray covariance matrix. This allowed us to propose a novel subspace-based algorithm, which we called the coarrayMS-MUSIC, to perform underdetermined source localization using arbitrary planar arrays. We also introduced the polynomial rooting version of our algorithm called the coarrayMS-rootMUSIC. Finally, we conducted extensive numerical simulations to verify the effectiveness and usefulness of the proposed methods.

The order of a three-dimensional wavefield captured by a spherical array is limited by the number of sampling points i.e. the number of sensors in the array. This restricts the source localization performance of existing techniques for a spherical array. In this work, we introduced the concept of difference coarray to spherical arrays and proposed an algorithm which utilised the increased degreesof-freedom (DOF) provided by the virtual coarray sensors to perform enhanced source localization. We made use of coarray manifold separation in the spherical harmonics domain to generate a Vandermonde structured coarray manifold matrix which allowed us to propose a novel subspace-based algorithm, which we called the coarraySH-MUSIC. We also introduced a polynomial rooting version of our algorithm which does not rely on extensive grid searches. The proposed algorithms were evaluated using various simulated experiments on source localization. 

Reverberation is one of the major causes of speech degradation. The popular weighted prediction error (WPE) technique performs dereverberation by estimating the late room reflections using a multi-channel prediction filter. However, the length of the prediction filter in each short-time-Fourier-transform (STFT) band must be sufficiently long to model the late reverberation component accurately. This leads to inverting a large matrix in every frequency bin, making the WPE method computationally expensive. The WPE method is also vulnerable to additive noise. To tackle these issues, we developed a computationally efficient dereverberation technique in this work. We decomposed the long prediction filter into three smaller sub-filters using third-order tensor decomposition. One sub-filter acted as a spatial filter, while the other two acted as temporal prediction filters. We then developed an iterative algorithm to obtain optimal solutions for all three sub-filters. The spatial filter was optimized as a weighted distortionless beamformer to deal with noise, while the temporal filters were optimized as weighted Wiener filters. Since the lengths of the sub-filters are smaller, the respective covariance matrices were computationally easier to invert, leading to an efficient algorithm. Simulation results showed that the proposed algorithm was robust to noise and outperforms the current WPE based algorithms in terms of dereverberation.