Permutation Alignment Research Articles

The effect of source sparsity on independent vector analysis for blind source separation

In this paper, the effect of source sparsity on the performance of the independent vector analysis (IVA) algorithm for blind source separation is investigated. The IVA algorithm was originally developed under the assumption of statistical independence between the sources and has made great advances in recent years. However, its performance under different sparsity conditions is rarely studied. This study begins by mathematically analyzing the performance of IVA in permutation alignment, which is proved to directly correlate with the degree of frame-level W-disjoint orthogonality (F-WDO) of the sources. We further prove that IVA can theoretically achieve the optimal separation in the cases where the sources are F-WDO. Experimental results show a strong positive correlation between a quantitative measure of F-WDO and the IVA algorithm’s performance under various conditions.

Convolutive blind source separation in the frequency domain of mechanical noise for gas turbines based on bounded component analysis

Noise source identification of gas turbines can provide the basis and guidance for vibration and noise reduction of gas turbines. Independent component analysis (ICA) is one of the most popular techniques for blind source separation (BSS) widely used in vibration and noise source separation in mechanical systems. ICA is suitable for independent source signals. However, in order to identify dependent mechanical noise sources in gas turbines, a convolutive BSS in the frequency domain based on bounded component analysis (BCA) is proposed. First, the basic theory of BSS and BCA is introduced in detail. The convolutive mixing in the time domain is transformed into an instantaneous mixing in the frequency domain by short time Fourier transform (STFT), and complex BCA is performed at each frequency bin. Second, a permutation alignment method based on local and global optimization is proposed to solve the problem of the permutation ambiguity. Finally, the accuracy and robustness of the proposed method are comparatively studied through typical numerical and experimental studies on a three-rotor experimental bench. The results show that the proposed method can effectively separate and identify independent and dependent source signals.

Measuring Dependence for Permutation Alignment in Convolutive Blind Source Separation

This brief proposes an effective implementation for addressing permutation ambiguity issue of convolutive blind source separation in frequency domain. Generally, signal envelope and power ratio as common inter-frequency dependence measures are utilized to group bin-wise separated signals for convolutive mixtures, where the new measure of permutation alignment method is represented by the activation matrix of bin-wise spectrum which is based on nonnegative matrix factorization (NMF). Meanwhile, canonical correlation analysis (CCA) rather than the maximum sum of correlation coefficient among different bins, is applied for verifying correlation determinations. In addition, the influence of bin distance and separation quality at each bin are explored to optimize permutation result. Simulation results demonstrate the effectiveness of the proposed technique in real recorded convolutive mixtures.

A Blind Source Separation Framework for Ego-Noise Reduction on Multi-Rotor Drones

Acoustic sensing from a multi-rotor drone is heavily degraded by the strong ego-noise produced by the rotating motors and propellers. To address this problem, we propose a blind source separation (BSS) framework that extracts a target sound from noisy multi-channel signals captured by a microphone array mounted on a drone. The proposed method addresses the challenging problem of permutation alignment, in extremely low signal-to-noise-ratio scenarios (e.g. SNR $ −15 dB), by performing clustering on the time activities of the separated signals across frequencies. Since initialization plays an important role to the success of clustering, we propose a pre-processing algorithm which uses time-frequency spatial filtering (TFS) to generate a reference to pre-align the permutation. The pre-alignment not only improves the performance of clustering and permutation alignment, but also solves the target-channel selection problem for BSS. The proposed method integrates the advantages of both TFS and BSS. Experimental results with real-recorded data show that the proposed method is capable of processing the audio stream continuously in a blockwise manner and also remarkably outperforms the state-of-the-art.

A low-complexity permutation alignment method for frequency-domain blind source separation

Frequency-domain blind source separation is an effective way to separate the signals from convolutive mixtures. The independence component analysis (ICA) is commonly employed to separate signals in each frequency bin, resulting in the well-known permutation problem. To resolve this problem, we present a low-complexity permutation alignment method based on the inter-frequency dependence of signal power ratio. A bin-wise permutation alignment is first carried out across all the frequency bins by measuring the correlation between the current frequency bin and the previous one, but only the permutation with a high confidence is fixed. The permutation with low confidence is then determined by maximizing the correlation between the current frequency bin and a local centroid, which is calculated from a set of determined frequency bins with high confidence. By so doing, the permutation for most frequency bins is aligned without iterations. Finally, a clustering algorithm with centroids is adopted to achieve the fine global optimization in the fullband with only a few iterations. Experiment results show that the proposed method achieves a comparable performance with the state-of-the-art permutation alignment schemes, but the new method achieves a significant computational saving.

Convolutive blind source separation in frequency domain with kurtosis maximization by modified conjugate gradient

Abstract To efficiently and accurately separate sources from the measured signals and align their permutation, a convolutive blind source separation (BSS) in frequency domain with kurtosis maximization (CBSS_FDKM) by the modified conjugate gradient is proposed. Firstly, Short Time Fourier Transform (STFT) is used to convert the convolutive BSS problem in time domain into an instantaneous BSS in frequency domain. Secondly, CBSS_FDKM is adopted to separate complex signals in each frequency bin, and kurtosis maximization is used as the objective function and optimized by a modified conjugate gradient with iterative step sizes optimized by an efficient algebraic method, and thus the accuracy and convergence speeds are significantly enhanced. Thirdly, the power spectra are obtained from the separated signals and the cosine distances based on power spectra are calculated for permutation alignment. Finally, inverse Short Time Fourier Transform (ISTFT) is adopted to reconstruct the separated signals in time domain. Furthermore, the accuracy and robustness of the proposed method are comparatively studied according to typical numerical studies and experimental studies on a cylindrical test bed. Generally, this paper provides a more accurate and robust BSS for source separation and identification, which can provide significant evidences for vibration & noise monitoring and control.

Underdetermined convolutive blind separation of sources integrating tensor factorization and expectation maximization

Underdetermined convolutive blind separation of sources is a challenging topic in speech and audio processing. In plenty of conventional separation algorithms, the source signal estimation is performed in the frequency-domain, thus leading to permutation problems and poor separation results. In this paper, to solve the permutation alignment and obtain better source separation results, we exploit the algebraic structure of tensor factorization model and expectation–maximization (EM) to provide a new time-frequency algorithm. This is because tensor factorization has an advantage to estimate the channel for the underdetermined convolutive mixture case, and EM algorithm is conducive to faster converge to the desired solution and better source separating property. In the proposed algorithm, we first estimate the mixing matrix by using tensor decomposition, while permutation alignment algorithm is used to deal with the permutation problems. Then, the model parameters are updated using EM algorithm for improving source separation performance. At the same time, the spatial images of source signals are obtained using Wiener filters constructed from the estimated parameters. Furthermore, the time-domain source signals can be obtained through inverse short-time Fourier transform. Finally, a series of simulations show that compared with some existing separation algorithms, the proposed algorithm achieves better separation performance.

Pseudo-Determined Blind Source Separation for Ad-hoc Microphone Networks

We propose a pseudo-determined blind source separation framework that exploits the information from a large number of microphones in an ad-hoc network to extract and enhance sound sources in a reverberant scenario. After compensating for the time offsets and sampling rate mismatch between (asynchronous) signals, we interpret as a determined $M\times M$ mixture the over-determined $M\times N$ mixture, where $M>N$ is the number of microphones and $N$ is the number of sources. Next, we propose a pseudodetermined mixture model that can apply an $M\times M$ independent component analysis (ICA) directly to the $M$ -channel recordings. Moreover, we propose a reference-based permutation alignment scheme that aligns the permutation of the ICA outputs and classifies them into target channels, which contain the $N$ sources, and nontarget channels, which contain reverberation residuals. Finally, using the signals from nontarget channels, we estimate in each target channel the power spectral density of the noise component that we suppress with a spectral postfilter. Interestingly, we also obtain late-reverberation suppression as by-product. Experiments show that each processing block improves incrementally source separation and that the performance of the proposed pseudodetermined separation improves as the number of microphones increases.

A permutation algorithm based on dynamic time warping in speech frequency-domain blind source separation

Frequency-Domain Blind Source Separation (FD-BSS) is an efficient way to analyze convolutive mixed speech. To improve the quality of the separated speech, a permutation algorithm based on Dynamic Time Warping (DTW) is proposed in this paper. Because signals in adjacent frequency bins have high similarity, DTW technology is used to compare them and generate adjustment matrices to solve the permutation ambiguity. Our approach is evaluated through simulated and practical experiments. Using Signal to Distortion Ratio (SDR), Signal to Interference Ratio (SIR), Signal to Artifacts Ratio (SAR), and Perceptual Estimation of the Speech Quality (PESQ) for measurements. To examine the quality of the separated speech in a practical acoustic environment, we adopt the accuracy ratio of Automatic Speech Recognition (ASR). In the experiments, we compare our approach with other classical permutation criteria such as K-L divergence distance, envelope correlation and higher-order statistics. The experimental results show that the proposed algorithm performs permutation alignment more accurately and improves the acoustic quality of separation.

Source separation employing beamforming and SRP-PHAT localization in three-speaker room environments

This paper presents a new blind speech separation algorithm using beamforming technique that is capable of extracting each individual speech signal from a mixture of three speech sources in a room. The speech separation algorithm utilizes the steered response power phase transform for obtaining a localization estimate for each individual speech source in the frequency domain. Based on those estimates each desired speech signal is extracted from the speech mixture using an optimal beamforming technique. To solve the permutation problem, a permutation alignment algorithm based on the mutual output correlation is employed to group the output signals into the correct sources from each frequency bin. Evaluations using real speech recordings in a room environment show that the proposed blind speech separation algorithm offers high interference suppression level whilst maintaining low distortion level for each desired signal.

Underdetermined Convolutive BSS: Bayes Risk Minimization Based on a Mixture of Super-Gaussian Posterior Approximation

This paper considers the underdetermined blind source separation (BSS) of convolutively mixed super-Gaussian signals that include speech, audio, and various other sparse signals. Here, the separation is performed in three steps. In the first and second steps, the mixing matrix and the sources at each time-frequency location are estimated by minimizing the Bayes risk (or the posterior risk) with squared loss. In the final third step, the permutation alignment is conducted by considering the correlation between adjacent spectral bins as in many conventional algorithms. To overcome any computationally intractable integrations involving a complex-valued super-Gaussian source prior, the posterior distribution of the sources is approximated as a mixture of super-Gaussians. The posterior means of the mixing matrix and the sources are obtained with Metropolis-Hastings within Gibbs sampling and the weighted sum of individual super-Gaussians, respectively. Overall, this approximation leads to a separation that is computationally lighter than and as accurate as the algorithm without the approximation. The simulation results of the synthetically generated data in a virtual room with reverberation show that the estimates of the mixing matrix in the first step and the sources in the second step are more accurate than the estimates from the state-of-the-art algorithms in terms of the mixing error ratio (MER) and the signal-to-distortion ratio (SDR). The experiment was also conducted with recorded data in a real room environment using a public benchmark dataset. Results show that the proposed algorithm gives a better performance compared to the state-of-the-art algorithms in terms of the SDR.

English

This paper presents BSS for additive mixing where every recordings consist of differently weighted signal. Therefore, by using ICA for both time-domain and frequency- domain, we are going to separate source signals from mixed signal. The main aim of our analysis is to perform undetermined convolutive BSS via frequency bin-wise clustering and permutation alignment where convolutive mixture are most delayed and weighted. So, ICA in time- domain is fails to separate signals. Hence, instead of this we use ICA in frequency-domain which playing vital role in separation of audio signals by using MATLAB which is our future work. Keywords— Compressive Sensing; Sparsity; GPSR; K- means; L1-magic. I.

Multi-band multi-centroid clustering based permutation alignment for frequency-domain blind speech separation

This paper investigates the permutation ambiguity problem in frequency-domain blind source separation and proposes a robust permutation alignment algorithm based on inter-frequency dependency, which is measured by the correlation coefficient between the time activity sequences of separated signals. To calculate a global reference for permutation alignment, a multi-band multi-centroid clustering algorithm is proposed where at first the permutation inside each subband is aligned with multi-centroid clustering and then the permutation among subbands is aligned sequentially. The multi-band scheme can reduce the dynamic range of the activity sequence and improve the efficiency of clustering, while the multi-centroid clustering scheme can improve the precision of the reference and reduce the risk of wrong permutation among subbands. The combination of two techniques enables to capture the variation of the time–frequency activity of a speech signal precisely, promising robust permutation alignment performance. Extensive experiments are carried out in different testing scenarios (up to reverberation time of 700 ms and 4×4 mixtures) to investigate the influence of two parameters, the number of subbands and the number of clustering-centroids, on the performance of the proposed algorithm. Comparison with existing permutation alignment algorithms proves that the proposed algorithm can improve the robustness in challenging scenarios and can reduce block permutation errors effectively.

A case study of heterogeneous fleet vehicle routing problem: Touristic distribution application in Alanya

In this study, Fleet Size and Mix Vehicle Routing Problem is considered in order to optimize the distribution of the tourists who have traveled between the airport and the hotels in the shortest distance by using the minimum cost. The initial solution space for the related methods are formed as a combination of Savings algorithm, Sweep algorithm and random permutation alignment. Then, two well-known solution methods named as Standard Genetic Algorithms and random search algorithms are used for changing the initial solutions. Computational power of the machine and heuristic algorithms are used instead of human experience and human intuition in order to solve the distribution problem of tourists coming to hotels in Alanya region from Antalya airport. For this case study, daily data of tourist distributions performed by an agency operating in Alanya region are considered. These distributions are then modeled as Vehicle Routing Problem to calculate the solutions for various applications. From the comparisons with the decision of a human expert, it is seen that the proposed methods produce better solutions with respect to human experience and insight. Random search method produces a solution more favorable in terms of time. As a conclusion, it is seen that, owing to the distribution plans offered by the obtained solutions, the agencies may reduce the costs by achieving savings up to 35%.

Design of oversampled generalised discrete Fourier transform filter banks for application to subband‐based blind source separation

A novel design of oversampled generalised discrete Fourier transform filter banks is proposed, with application to subband-based convolutive blind source separation (BSS), where either instantaneous BSS algorithms or joint BSS algorithms can be applied. Conventional filter banks design is usually focused on elimination of the overall aliasing error and the perfect reconstruction (PR) condition, which are required by traditional subband adaptive filtering applications. However, because of the unknown scaling factor, the traditional PR condition is not necessary in the context of subband BSS and can be relaxed in the design. Owing to the increased degrees of design freedom, the authors can introduce an additional cost function to enhance the mutual information between adjacent subband signals. Together with a reduced subband aliasing level, it leads to an improved subband permutation alignment result for instantaneous BSS and an overall better performance for the joint BSS.

Reducing permutation error in subband-based convolutive blind separation

Subband-based blind source separation has great potential in solving the complicated convolutive mixing problem. However, its performance is largely affected by the permutation ambiguity problem during the synthesis stage. Researchers have suggested methods to correct the permutation by exploiting the correlation information between adjacent frequencies/subbands. An improved solution to this permutation problem is proposed based on a novel filter banks design method, which is based on a model that includes inter-subband correlation as part of the optimisation criterion. Simulation results show that a better subband permutation alignment result has been achieved, leading to improved separation performance.

A Region-Growing Permutation Alignment Approach in Frequency-Domain Blind Source Separation of Speech Mixtures

The convolutive blind source separation (BSS) problem can be solved efficiently in the frequency domain, where instantaneous BSS is performed separately in each frequency bin. However, the permutation ambiguity in each frequency bin should be resolved so that the separated frequency components from the same source are grouped together. To solve the permutation problem, this paper presents a new alignment method based on an inter-frequency dependence measure: the powers of separated signals. Bin-wise permutation alignment is applied first across all frequency bins, using the correlation of separated signal powers; then the full frequency band is partitioned into small regions based on the bin-wise permutation alignment result. Finally, region-wise permutation alignment is performed in a region-growing manner. The region-wise permutation correction scheme minimizes the spreading of the misalignment at isolated frequency bins to others, hence to improve permutation alignment. Experiment results in simulated and real environments verify the effectiveness of the proposed method. Analysis demonstrates that the proposed frequency-domain BSS method is computationally efficient.

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.

Combining Superdirective Beamforming and Frequency-Domain Blind Source Separation for Highly Reverberant Signals

Frequency-domain blind source separation (BSS) performs poorly in high reverberation because the independence assumption collapses at each frequency bins when the number of bins increases. To improve the separation result, this paper proposes a method which combines two techniques by using beamforming as a preprocessor of blind source separation. With the sound source locations supposed to be known, the mixed signals are dereverberated and enhanced by beamforming; then the beamformed signals are further separated by blind source separation. To implement the proposed method, a superdirective fixed beamformer is designed for beamforming, and an interfrequency dependence-based permutation alignment scheme is presented for frequency-domain blind source separation. With beamforming shortening mixing filters and reducing noise before blind source separation, the combined method works better in reverberation. The performance of the proposed method is investigated by separating up to 4 sources in different environments with reverberation time from 100 ms to 700 ms. Simulation results verify the outperformance of the proposed method over using beamforming or blind source separation alone. Analysis demonstrates that the proposed method is computationally efficient and appropriate for real-time processing.

Permutation inconsistency in blind speech separation: investigation and solutions

Acoustic reverberation severely limits the performance of multiple microphone blind speech separation (BSS) methods. We show that the limited performance is due to random permutations of the unmixing filters over frequency. This problem, which we refer to as permutation inconsistency, becomes worse as the length of the room impulse response increases. We explore interesting connections between BSS and ideal beamforming, which leads us to propose a permutation alignment scheme based on microphone array directivity patterns. Given that the permutations are properly aligned, we show that the blind speech separation method outperforms the nonblind beamformer in a highly reverberant environment. Furthermore, we discover the tradeoff where permutations can be aligned by affording a loss in spectral resolution of the unmixing filters. We then propose a multistage algorithm, which aligns the unmixing filter permutations without sacrificing the spectral resolution. For our study, we perform experiments in both real and simulated environments and compare the results to the ideal performance benchmarks that we derive using prior knowledge of the mixing filters.