Underdetermined Convolutive Blind Source Separation Research Articles

SA-UCBSS: Sparsity-Based Adaptive Underdetermined Convolutive Blind Source Separation

Blind source separation is the process of separating unknown source signals based only on the received mixing signals when the source signal cannot be accurately known. Traditional methods are mainly based on linear approximate transformation models that often have large systematic errors in high reverberation environments, resulting in poor separation performance. To avoid these limitations, a sparsity-based adaptive underdetermined convolutive blind source separation (SA-UCBSS) algorithm is proposed by unifying a convolutive approximate transformation model and an Lp(0<p≤1)-norm regularisation penalty. A crosstalk canceller is designed for room impulse response pretreatment with p-norm optimisation to eliminate audible echoes, and a sparse optimisation scheme is designed for the parameter initialisation to accelerate the convergence of the iterative recovery process. Subsequently, a convolutive approximate transformation model is built to achieve a more accurate estimation of the mixing system. The SA-UCBSS algorithm is proposed to achieve better source separation by adaptively tuning the value of parameter p. Experimental results including BSS of the synthesised and live-recorded speech convolutive mixtures showed that the SA-UCBSS algorithm had superior separating properties and better robustness than several popular algorithms.

Underdetermined Convolutive Blind Source Separation Based on Phase-Normalized Single Source Points and Adjacently Weighted Alignment

Underdetermined Convolutive Blind Source Separation Based on Phase-Normalized Single Source Points and Adjacently Weighted Alignment

Underdetermined convolutive blind source separation in the time–frequency domain based on single source points and experimental validation

To effectively separate underdetermined convolutive mixtures, an accurate and robust underdetermined convolutive blind source separation (BSS) method in the time–frequency domain based on single source points (SSPs) is proposed. Firstly, convolutive BSS in the time domain is transformed into instantaneous BSS in the time–frequency domain by short-time Fourier transform (STFT). Secondly, hierarchical clustering is carried out after the extraction and identification of SSPs by using sparse coding technology. Thirdly, source separation in the frequency domain is obtained based on Lp norm minimization and then alignments are permutated and scales are compensated. Finally, inverse STFT is adopted to reconstruct the separated signals in the time domain. Furthermore, numerical case studies and experimental case studies on a cylindrical test bed are carried out to validate the effectiveness of the proposed method. Generally, this paper provides an accurate and robust underdetermined convolutive BSS technique for mixing matrix estimation, source identification and contribution evaluation, which can provide significant evidence for vibration and noise monitoring and control.

Underdetermined blind source separation using CapsNet

In this paper, we consider the problem of separating the speech source signal from the underdetermined convolutive mixture signals using capsule network (CapsNet). The objective of this paper is twofold. They are (1) to improve the underdetermined convolutive blind source separation algorithm in terms of signal-to-distortion ratio, signal-to-interference ratio and signal-to-artifact ratio; (2) to minimize the computational burden of the algorithm so that it is useful for applications like speech recognition system. The time–frequency points of the observed mixture signals are input to the first layer of CapsNet. In the first layer, single-source active point (SSP) is calculated using the ratio of mixtures. These SSPs are lower-level capsules in our system. In the second layer, we find a cluster center using a dynamic routing algorithm and these clusters are used to construct a binary mask. Finally, the algorithm solves the permutation problem by determining the correlation between the amplitudes of adjacent frequency bins. We test our algorithm on the live recording mixture signals obtained in the real environment and synthetically convoluted mixture signals. The test result shows the effectiveness of the proposed method when compared with the existing algorithms in terms of computational load, signal-to-distortion ratio and signal-to-interference ratio.

Source Number Estimation and Effective Channel Order Determination Based on Higher-Order Tensors

Source number estimation is an essential task in underdetermined convolutive blind source separation, and effective channel order determination is also a challenging issue. For solving the two problems, the classical methods are based on information theoretic criteria. However, these are prone to the underestimation and overestimation of the number of sources in the underdetermined case. To compensate for this shortcoming, in this paper we propose two algorithms based on higher-order tensors. First, an improved algorithm is presented to estimate the number of sources. By transforming the tensor into a matrix, the eigenvalues of the resultant matrices are used to estimate the number of sources. Additionally, we employ higher-order tensors to detect the effective channel order and confirm the relationship between the number of sources and the effective channel order in the convolutive mixture model. Finally, a series of simulation experiments demonstrate that the proposed algorithms have an advantage over the conventional methods.

Underdetermined Convolutive Blind Source Separation via Frequency Bin-Wise Clustering and Permutation Alignment

This paper presents a blind source separation method for convolutive mixtures of speech/audio sources. The method can even be applied to an underdetermined case where there are fewer microphones than sources. The separation operation is performed in the frequency domain and consists of two stages. In the first stage, frequency-domain mixture samples are clustered into each source by an expectation-maximization (EM) algorithm. Since the clustering is performed in a frequency bin-wise manner, the permutation ambiguities of the bin-wise clustered samples should be aligned. This is solved in the second stage by using the probability on how likely each sample belongs to the assigned class. This two-stage structure makes it possible to attain a good separation even under reverberant conditions. Experimental results for separating four speech signals with three microphones under reverberant conditions show the superiority of the new method over existing methods. We also report separation results for a benchmark data set and live recordings of speech mixtures.

Underdetermined Convolutive Blind Source Separation via Time–Frequency Masking

In this paper, we consider the problem of separation of unknown number of sources from their underdetermined convolutive mixtures via time-frequency (TF) masking. We propose two algorithms, one for the estimation of the masks which are to be applied to the mixture in the TF domain for the separation of signals in the frequency domain, and the other for solving the permutation problem. The algorithm for mask estimation is based on the concept of angles in complex vector space. Unlike the previously reported methods, the algorithm does not require any estimation of the mixing matrix or the source positions for mask estimation. The algorithm clusters the mixture samples in the TF domain based on the Hermitian angle between the sample vector and a reference vector using the well known <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -means or fuzzy <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> -means clustering algorithms. The membership functions so obtained from the clustering algorithms are directly used as the masks. The algorithm for solving the permutation problem clusters the estimated masks by using <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -means clustering of small groups of nearby masks with overlap. The effectiveness of the algorithm in separating the sources, including collinear sources, from their underdetermined convolutive mixtures obtained in a real room environment, is demonstrated.

Under-Determined Reverberant Audio Source Separation Using a Full-Rank Spatial Covariance Model

This paper addresses the modeling of reverberant recording environments in the context of under-determined convolutive blind source separation. We model the contribution of each source to all mixture channels in the time-frequency domain as a zero-mean Gaussian random variable whose covariance encodes the spatial characteristics of the source. We then consider four specific covariance models, including a full-rank unconstrained model. We derive a family of iterative expectation-maximization (EM) algorithms to estimate the parameters of each model and propose suitable procedures adapted from the state-of-the-art to initialize the parameters and to align the order of the estimated sources across all frequency bins. Experimental results over reverberant synthetic mixtures and live recordings of speech data show the effectiveness of the proposed approach.