Algorithm for Underdetermined Blind Source Separation Based on Least-Mean-Square Error and Sparse Features

Underdetermined blind source separation is to recover the source signals from the observed signals without prior knowledge of the mixing channel. In signal processing, it is an open problem attracted the attention of more and more researchers. In this paper, we presents a fast and effective time-frequency algorithm to separate speech source signals in the underdetermined mixture case. In the proposed algorithm, the time-domain mixture signals are transformed to the frequency-domain by using short-time Fourier transform (STFT). Then the mixing matrix is estimated using K-means clustering, and frequency-domain sources are separated by solving a low-dimensional linear programming problem based on the estimated mixing matrix. Finally, the time-domain source signals are obtained using inverse STFT. The proposed algorithm has two advantages, one is to save time consumption, the other is to obtain better separation performance. Experimental results based on two mixtures of four speech sources demonstrate the feasibility and superiority of the proposed algorithm.

This paper discusses underdetermined blind source separation (BSS) using a compressed sensing (CS) approach, which contains two stages. In the first stage we exploit a modified K-means method to estimate the unknown mixing matrix. The second stage is to separate the sources from the mixed signals using the estimated mixing matrix from the first stage. In the second stage a two-layer sparsity model is used. The two-layer sparsity model assumes that the low frequency components of speech signals are sparse on K-SVD dictionary and the high frequency components are sparse on discrete cosine transformation (DCT) dictionary. This model, taking advantage of two dictionaries, can produce effective separation performance even if the sources are not sparse in time-frequency (TF) domain.

This paper presents a robust blind separation method of sparse sources named robust sparse blind source separation (r-SBSS). Allowing for the morphological diversity of the source, we first assume that one source can be divide into two parts, namely global component and local component. Furthermore, a novel optimization model is built upon the low-rank matrix recovery and the sparse modeling of both the sources and the outliers with different regularized constraints. We also provide the corresponding optimization algorithm, which allows combining both low-rank double dictionary learning and low-rank representation strategy to realize source separation and mixing matrix estimation respectively. In the proposed method, the dictionary learning strategy guarantees the adaptive representation of sparsity, and the low-rank representation strategy is first introduced to implement the effective estimation of the mixing matrix and outliers. Extensive experimental results on AR dataset and real EMI signals demonstrate the superiority of r-SBSS, compared to the state-of-the-art methods.

Blind separation of non-stationary sources using continuous density hidden Markov models

This paper considers the mixing matrix estimation in the underdetermined blind source separation. An effective estimation algorithm based on local directional density detection (LDDD) and dynamic data field clustering (DDFC) is proposed. First, argument-based time-frequency single source points detection is employed to improve signal sparsity. To overcome the limitation of traditional clustering algorithms, which depend on the preset of initial clustering centers and the number of sources, the LDDD is introduced to choose the single source points with high potential energy as representative objects to form data preliminary classification. Then DDFC algorithm is adopted to move and merge the representative objects until all column vectors of mixing matrix are estimated. Simulation results show that the proposed method can effectively estimate mixing matrix with high accuracy, especially in the real non-cooperative cases where the number of sources is unknown.

Underdetermined mixing matrix estimation by exploiting sparsity of sources

Blind single-channel source separation is a long-standing machine learning and signal processing problem. Traditional blind source separation (BSS) algorithms were proposed to solve this task utilizing multiple signal constraints. Generative adversarial network (GAN) are free from statistical constraints and samples, but the role of adversarial training in the task of BSS has not been fully demonstrated. Therefore, a new separation network model that enables to learn the known separated signal distribution from the stepwise fine estimation of the unknown mixture distribution was presented in this paper, and a self-attention mechanism was introduced to solve the problem of the blurring details of the generated image by the generator which preserves image details in the process of image separation. Compared with the existing single-channel blind source separation algorithm based on generative adversarial network-neural egg separation (NES), the detailed information of this new separation algorithm is more prominent, and the source signal in the mixed image has been separated more effectively, and has better separation performance than the classic blind source separation algorithms.

In this paper, a single source points (SSPs) detection method based on local dominance is devised for mixing matrix estimation in underdetermined blind source separation (UBSS). In the proposed detector, time-frequency (TF) points of mixed signals are firstly divided into different groups, and the local covariance matrix of each group is calculated. Taking advantage of the local dominance property, the groups with rank-one local covariance matrices are then identified as single source groups, i.e., the TF points of mixed signals in single source groups are regarded as SSPs. Finally, the obtained SSPs are clustered by the hierarchical clustering algorithm to achieve mixing matrix estimation. Simulations with real audio sources show that the proposed method yields competitive robustness, efficiency and effectiveness, in comparison with the traditional methods.

Robust techniques for independent component analysis (ICA) with noisy data

This paper considers complex-valued mixing matrix estimation in underdetermined blind source separation. An effective estimation algorithm based on both single-source-point (SSP) detection and modified dynamic data field clustering is proposed. First, array-processing-based time–frequency SSP detection is applied to improve signal sparsity, therein utilizing the real and imaginary components of the observed signals in the time–frequency domain. The algorithm can be applied to the estimation of complex-valued mixing matrix based on L-shaped arrays and uniform circular arrays. Then, to overcome the limitation that the clustering performance of traditional algorithms is affected by noise, data cleansing detection is introduced to reselect the SSPs with high potential energy as representative objects to achieve preliminary data classification. Finally, a dynamic data field clustering algorithm is adopted to move and merge the representative objects until all column vectors of the mixing matrix are estimated. Simulation results show that the proposed method can effectively estimate complex-valued mixing matrices with high accuracy, especially in real-world noncooperative cases without prior knowledge.

We propose an algorithm that exploits the benefits of sparse filtering and directional clustering when estimating under-determined mixing matrix from mixtures of sufficiently sparse sources. To express the direction of each sample by only a few vectors in which one vector is more dominant than the remaining ones, we propose to minimize the power mean of the magnitude-squared cosine distances between the estimated mixing matrix and the data. For the special case of estimating determined mixing matrix, we derive a stability condition for methods based on the magnitude-squared cosine metric. Our stability condition shows that the proposed approach, K-hyperlines, and sparse filtering can recover the invertible mixing matrix when the sources are i.i.d. super-Gaussian. Simulations using both synthetic data and recorded speech mixtures show that the proposed algorithm outperforms existing algorithms with lower computational complexity.

This paper presents a new low-latency online blind source separation (BSS) algorithm. Although algorithmic delay of a frequency domain online BSS can be reduced simply by shortening the short-time Fourier transform (STFT) frame length, it degrades the source separation performance in the presence of reverberation. This paper proposes a method to solve this problem by integrating BSS with Weighted Prediction Error (WPE) based dereverberation. Although a simple cascade of online BSS after online WPE upgrades the separation performance, the overall optimality is not guaranteed. Instead, this paper extends a recently proposed batch processing algorithm that can jointly optimize dereverberation and separation so that it can perform online processing with low computational cost and little processing delay (< 12 ms). The results of a source separation experiment in a noisy car environment suggest that the proposed online method has better separation performance than the simple cascaded methods.

We consider the scenario of an unknown overdetermined instantaneous mixture of quasi-stationary sources. Blind source separation (BSS) under this scenario has drawn much attention, motivated by applications such as speech and audio separation. The ideas in the existing BSS works often focus on exploiting the time-varying statistics characteristics of quasi-stationary sources, through various kinds of formulations and optimization methods. In this paper, we are interested in further assuming that the sources exhibit some form of local sparsity, which is generally satisfied in speech. By exploiting this additional assumption, we show that there is a simple closed-form solution for the BSS problem. Simulation results based on real speech show that the proposed closed-form algorithm is computationally much lower than some existing BSS algorithms, while delivering a promising mean-square-error performance.

Blind source separation (BSS) and sound activity detection (SAD) from a sound source mixture with minimum prior information are two major requirements for computational auditory scene analysis that recognizes auditory events in many environments. In daily environments, BSS suffers from many problems such as reverberation, a permutation problem in frequency-domain processing, and uncertainty about the number of sources in the observed mixture. While many conventional BSS methods resort to a cascaded combination of subprocesses, e.g., frequency-wise separation and permutation resolution, to overcome these problems, their outcomes may be affected by the worst subprocess. Our aim is to develop a unified framework to cope with these problems. Our method, called permutation-free infinite sparse factor analysis (PF-ISFA), is based on a nonparametric Bayesian framework that enables inference without a pre-determined number of sources. It solves BSS, SAD and the permutation problem at the same time. Our method has two key ideas: unified source activities for all the frequency bins and the activation probabilities of all the frequency bins of all the sources. Experiments were carried out to evaluate the separation performance and the SAD performance under four reverberant conditions. For separation performance in the BSS_EVAL criteria, our method outperformed conventional complex ISFA under all conditions. For SAD performance, our method outperformed the conventional method by 5.9–0.5% in F-measure under the condition RT20 = 30–600 [ms], respectively.

Clustering is one of unsupervised classification method, that is, it classifies a data set into some clusters without any external criterion. Typical clustering methods, e.g. k-means (KM) and fuzzy c-means (FCM) are constructed based on optimization of the given objective function. Many clustering methods as well as KM and FCM are formulated as optimization problems with typical objective functions and constraints. The objective function itself is also an evaluation guideline of results of clustering methods. Considering together with its theoretical extensibility, there is the great advantage to construct clustering methods in the framework of optimization. From the viewpoint of optimization, some of the authors proposed an even-sized clustering method based on optimization (ECBO), which is with strengthened constraints of cluster size, and constructed some variations of ECBO. The constraint considered in ECBO is that each cluster size is K or K + 1. ECBO is based on KM and its algorithm is constructed as iterative optimization. The belongingness of each object to clusters are calculated by the simplex method in each iteration. The numerical experiments show that ECBO has higher classification accuracy than other similar clustering methods. It is considered that ECBO has the advantage in the viewpoint of clustering accuracy, cluster size, and optimization framework than other similar methods. However, the constraint of cluster sizes of ECBO is strict so that it may be inconvenient in case that the partition results, of which each cluster size need not be strictly even, but uneven, is desirable. Moreover, it is expected that new clustering algorithms of which each cluster size can be controlled can deal with more various datasets. In this paper, we first propose two new clustering algorithms based on ECBO. Each cluster size can be controlled in the proposed algorithms. Next, we estimate the new clustering algorithms through some numerical experiments.