Frequency Domain Blind Source Separation Permutation Algorithm Based on Regional Growth Correction

Convolutive blind source separation and adaptive beamforming have similar goals and similar system structure. Both attempt to extract selected source signals from observed sensor mixtures by a filter array. However, time and frequency information are utilized in convolutive blind source separation while spatial information of source signals or sensor array is used in adaptive beamforming. In this paper, we start with a brief introduction of blind source separation and adaptive beamforming. Next, we review approaches combining spatial information used in beamforming with time/frequency processing used in convolutive blind source separation. We also present a new proposed combination approach and simulation results.

Permutation of the outputs at different frequency bins remains as a major problem in convolutive blind source separation (BSS). A coupled hidden Markov model (CHMM) effectively exploits the psychoacoustic characteristics of signals to mitigate such permutations. A joint diagonalization algorithm has been used for convolutive BSS; it incorporates a non-unitary penalty term within the cross-power spectrum-based cost function in the frequency domain. The proposed CHMM system couples a number of conventional HMMs, equivalent to the number of outputs, by making state transitions in each model dependent, not only on its own previous state, but also on some aspects of the state of the other models. Using this method, the permutation effect is substantially reduced; it is demonstrated using a number of simulation studies.

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.

In this study, cross-talk cancellation in convolutive blind source separation (BSS) is investigated using a new post-processing algorithm. In this algorithm, exclusive activity periods (EAPs) are used to model cross-talks in which only one BSS output signal is assumed to be active. Inactive intervals of each EAP are used to estimate the cross-talk leaked from each active signal. Then, the estimated cross-talk is subtracted from BSS outputs. Simulation results show that the proposed algorithm successfully suppresses the crosstalk by improving the signal-to-interference ratio (SIR) and signal-to-distortion ratio (SDR) of BSS outputs about 12 and 5 dB, respectively.

A new independent component analysis (ICA) formulation called independent vector analysis (IVA) was proposed in order to solve the permutation problem in convolutive blind source separation (BSS). Instead of running ICA in each frequency bin separately and correcting the disorder with an additional algorithmic scheme afterwards, IVA exploited the dependency among the frequency components of a source and dealt with them as a multivariate source by modeling it with sparse and spherically, or radially, symmetric joint probability density functions (pdfs). In this paper, we compare the speech separation performances of IVA by using a group of l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> -norm-invariant sparse pdfs where the value of and the sparseness can be controlled. Also, we derive an IVA algorithm from a nonparametric perspective with the constraint of spherical symmetry and high dimensionality. Simulation results confirm the efficiency of assuming sparseness and spherical symmetry for the speech model in the frequency domain.

Convolutive blind source separation by efficient blind deconvolution and minimal filter distortion

Convolutive blind source separation based on joint block Toeplitzation and block-inner diagonalization

In this paper, we investigate the importance of the high frequencies in the problem of convolutive blind source separation (BSS) of speech signals. In particular, we focus on frequency domain blind source separation (FD-BSS), and show that when separation is performed in the low frequency bins only, the recovered signals are similar in quality to those extracted when all frequencies are taken into account. The methods are compared through informal listening tests, as well as using an objective measure.

We present a method of blind source separation (BSS) for speech signals using a complex extension of infinite sparse factor analysis (ISFA) in the frequency domain. Our method is robust against delayed signals that usually occur in real environments, such as reflections, short-time reverberations, and time lags of signals arriving at microphones. ISFA is a conventional non-parametric Bayesian method of BSS, which has only been applied to time domain signals because it can only deal with real signals. Our method uses complex normal distributions to estimate source signals and mixing matrix. Experimental results indicate that our method outperforms the conventional ISFA in the average signal-to-distortion ratio (SDR).

This paper describes a novel modification to the well-known natural gradient or INFOMAX algorithm for blind source separation that largely mitigates its divergence problems. The modified algorithm imposes an a posteriori scalar gradient constraint that adds little computational complexity to the algorithm and exhibits fast convergence and excellent performance for fixed step size values that are largely independent of input signal magnitudes and initial separation matrix estimates. Evaluation of the approach for the separation of instantaneous and convolutive source mixtures using both time- and frequency-domain implementations shows its excellent separation behavior.

We present a general broadband approach to blind source separation (BSS) for convolutive mixtures based on second-order statistics. This avoids several known limitations of the conventional narrowband approximation, such as the internal permutation problem. In contrast to traditional narrowband approaches, the new framework simultaneously exploits the nonwhiteness property and nonstationarity property of the source signals. Using a novel matrix formulation, we rigorously derive the corresponding time-domain and frequency-domain broadband algorithms by generalizing a known cost-function which inherently allows joint optimization for several time-lags of the correlations. Based on the broadband approach time-domain, constraints are obtained which provide a deeper understanding of the internal permutation problem in traditional narrowband frequency-domain BSS. For both the time-domain and the frequency-domain versions, we discuss links to well-known, and also, to novel algorithms that constitute special cases. Moreover, using the so-called generalized coherence, links between the time-domain and the frequency-domain algorithms can be established, showing that our cost function leads to an update equation with an inherent normalization ensuring a robust adaptation behavior. The concept is applicable to offline, online, and block-online algorithms by introducing a general weighting function allowing for tracking of time-varying real acoustic environments.

Fast fixed-point independent vector analysis algorithms for convolutive blind source separation

Separation and identification of structural modes in largely underdetermined scenarios using frequency banding

We present an efficient algorithm for the blind signal separation (BSS) problem with convolutive signal mixtures, as it usually appears in acoustics, e.g., in the cocktail party problem. Since acoustical signals are typically nonstationary and nonwhite, we make use of these two statistical properties in the formulation of the blind cost function. In order to achieve true signal separation, the algorithm aims at finding a single polynomial matrix, the convolutive separation matrix that jointly diagonalizes a set of measured spatiotemporal correlation matrices. Minimizing the cost function turns out to be mathematically equivalent to a convolutive joint approximate diagonalization problem (CJAD). In order to increase the initial convergence rate, an Armijo line search is incorporated into the update. The final algorithm operates primarily in the frequency domain (fast convolution techniques) even though the cost function and gradient are formulated in the time domain. This approach reduces the computational complexity and avoids the so-called permutation problem.

Multi-dimensional variational mode decomposition for bearing-crack detection in wind turbines with large driving-speed variations