A Compressed Sensing Approach to Blind Separation of Speech Mixture Based on a Two-Layer Sparsity Model

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.

Upgrading Sparse NMF algorithm for blind source separation through Adaptive Parameterized Hybrid Kernel based approach

Aiming at the problem that the existing algorithms can only achieve single-channel blind separation (SCBS) for signals with co-frequency and co-modulated, the gravitational field resampling particle filter (GFR-PF) algorithm was proposed. The GFR-PF can realize SCBS of binary phase shift keying (BPSK) and binary frequency shift keying (2FSK) that overlap in both time and frequency domain and are mixed in a single-channel with environmental noise. The GFR-PF was used to jointly detect symbols and estimate unknown parameters of the BPSK and 2FSK signals. Besides, the blind separation of different frequencies and different modulations signals, which was called the mixed heterogeneous signal blind separation (HSBS). The proposed algorithm not only improved the global search performance and tracking accuracy of the blind separation of the same frequency and same modulation mixed signals but also realized the HSBS of BPSK and 2FSK. Thus, the blind separation of heterogeneous mixed signals containing BPSK and 2FSK with different amplitudes and bit rates were achieved by the proposed algorithm. Based on this heterogeneous mixed signal model, it was proposed by this paper that anti-interception capability was improved through mixed transmission of BPSK and 2FSK signals with different amplitudes.

Compressive sensing (CS) is a new technique that give an approach to reconstruct the signal with few numbers of observations or measurements. The CS is based on L1 -norm minimizations to find the sparse solutions and it is known as basis pursuit. In this investigation, CS scheme with different transforms is proposed. The three utilized transform techniques are: Discrete Fourier Transform(DFT), Discrete Cosine Transform(DCT) and Discrete Wavelet Transform(DWT) with daubechies1(DB1) and coiflets1(coif1) basis. The proposed system is tested by employing the following signals: Blocks, Heavy Sine, ‘Bumps’ and ‘Doppler’ which cover wide range of applications. The four testing signals are represented in sparse domain using different transforms. In order to threshold the coefficients of the signals in sparse domain, the universal threshold is utilized in the case of CS with FFT and DWT whereas, the universal threshold is modified to prune the DCT coefficients. The main aim of this study is to investigate the differences among CS with DFT, CS with DCT and CS with DWT, and consequently a suitable transform domain used with CS to be selected. The comparative study is established by assessing the performance of the proposed system using Root Mean Square Error (RMSE), output SNR, and the time required to reconstruct approximated signals. Simulation results have shown that the CS with DWT outperforms the CS with FFT and DCT. CS with DWT has achieved good RMSE values about (0.0014 to 3.359e-8) even when half of the signal elements are removed. CS with FFT and DCT enhanced the noisy Blocks and Bumps signals by 3dB and 1dB respectively, while it is failed to enhance noisy Heavy Sine and Doppler signals. CS with DWT of two basis and for single decomposition level have improved the noisy Blocks, Bumps, Heavy Sine and Doppler signals by 5dB, 4dB, 3dB, and 3dB respectively.

Underdetermined mixing matrix estimation by exploiting sparsity of sources

In order to overcome the problem of low accuracy and poor stability caused by the one-sided information blind separation analysis of the current communication channel interference suppression research methods, this paper proposes the optical communication network channel interference suppression method based on blind signal separation algorithm. The receiver unit, field programmable gate array (FPGA) unit, memory chip group and other modules are used to construct the channel signal acquisition system, and the collected signals are preprocessed by centralisation and whitening. Based on the signal preprocessing results, the blind separation of instantaneous linear mixed signals, blind separation of convolutional mixed signals and blind separation of sparse sources were comprehensively analysed to obtain the source signals and realise channel interference suppression of optical communication network. Experimental results show that this method has high interference precision, strong stability and good application prospect.

This paper deals with the problem of blind separation of audio signals from noisy mixtures. It proposes the application of a blind separation algorithm on the discrete cosine transform (DCT) or the discrete sine transform (DST) of the mixed signals, instead of performing the separation on the mixtures in the time domain. Wavelet denoising of the noisy mixtures is recommended in this paper as a preprocessing step for noise reduction. Both the DCT and the DST have an energy compaction property, which concentrates most of the signal energy in a few coefficients in the transform domain, leaving most of the transform domain coefficients close to zero. As a result, the separation is performed on a few coefficients in the transform domain. Another advantage of signal separation in transform domains is that the effect of noise on the signals in the transform domains is smaller than that in the time domain due to the averaging effect of the transform equations, especially when the separation algorithm is preceded by a wavelet denoising step. The simulation results confirm the superiority of transform domain separation to time domain separation and the importance of the wavelet denoising step.

A time–frequency blind signal separation method applicable to underdetermined mixtures of dependent sources

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Blind identification is a crucial subtask in signal processing problems such as blind signal separation (BSS) and direction-of-arrival (DOA) estimation. This paper presents a procedure for <emphasis emphasistype="boldital">multiple-input multiple-output instantaneous blind identification</emphasis> based on second-order temporal properties of the signals, such as coloredness and nonstationarity. The procedure consists of two stages. First, based on assumptions on the second-order temporal structure (SOTS) of the source and noise signals, and using subspace techniques, the problem is reformulated in a particular way such that each column of the unknown mixing matrix satisfies a system of multivariate homogeneous polynomial equations. Then, this nonlinear system of equations is solved by means of a so-called homotopy method, which provides a general tool for solving (possibly nonexact) systems of nonlinear equations by smoothly deforming the known solutions of a simple start system into the desired solutions of the target system. Our blind identification procedure allows to estimate the mixing matrix for scenarios with more sources than sensors without resorting to sparsity assumptions, something that is often believed to be impossible when using only second-order statistics. In addition, since our algorithm does not require <emphasis emphasistype="boldital">any</emphasis> assumption on the mixing matrix, also mixing matrices that are rank-deficient or even have identical columns can be identified. Finally, we give examples and performance results for speech source signals. </para>

Blind signal separation method is the method that the source signals are obtained by separating only the mixed signals. Generally, separation precision is lower when the basic method of blind signal separation is used for the sound signals. It is the cause that the power of the sound signals is concentrated in the low-frequency band. For the problem, we already considered that the method of the blind signal separation using QMF. Specifically, the mixed signals are divided into two frequency bands, and we perform suitable separation for each two bands. As the result, the conventional method has higher separation precision than the basic method. However, in the low-frequency band, power spectrum is not constant for frequency. Therefore, it is expected that the separation precision is higher than the conventional method by performing the suitable separation for each of signals based on the division to several narrow frequency bands on the low-frequency band. Then, in this paper, we propose the method that has higher separation precision and we evaluate the proposed method by computer simulation.

Blind source separation (BSS) in time-frequency (TF) domain is a versatile framework to recover sources from the recorded mixture signals in a reverberant environment. In general, a two-stage strategy is one of the popular BSS frameworks for the underdetermined BSS case (the number of mixtures is less than the number of sources), which is a tough problem due to the mixing matrix is not invertible. In this paper, we propose a new two-stage scheme combining density-based clustering and sparse reconstruction to estimate mixing matrix and sources, respectively. At the first stage, we transform the mixing matrix estimation as an eigenvector clustering problem based on a particular local dominant assumption. The eigenvectors are first exploited from the rank-one structure of local covariance matrices of mixture TF vectors. These eigenvectors are then clustered and adjusted to give estimated mixing matrix by cooperating density-based clustering and weight clustering. At the second stage, we transform the source reconstruction as a ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> norm (0 <; p ≤ 1) minimization by an iterative Lagrange multiplier method. With a proper initialization, the obtained solution is a global minimum for any p in (0, 1] with convergence guarantee. The proposed approach is demonstrated to be superior to the state-of-the-art baseline methods in various underdetermined experiments.

Human eyes have different sensitivity to different frequency components of image signals, typically, low frequency components are relatively more crucial to the perceptual quality of images than high frequency components. Based on this observation, we propose a novel sampling scheme for compressive sensing framework by designing a weighting scheme for the sampling matrix. By adjusting the weighting coefficients, we can tune the structure of the sampling matrix to favor the frequency components that are important to human perception, so that those components could be more precisely recovered in the reconstruction procedure. Experimental results reveal that our proposed scheme can greatly enhance the performance of compressive sensing framework in both PSNR and visual quality without increasing the complexity of the framework structure or computational procedure.

In order to overcome the problem of low accuracy and poor stability caused by the one-sided information blind separation analysis of the current communication channel interference suppression research methods, this paper proposes the optical communication network channel interference suppression method based on blind signal separation algorithm. The receiver unit, field programmable gate array (FPGA) unit, memory chip group and other modules are used to construct the channel signal acquisition system, and the collected signals are preprocessed by centralisation and whitening. Based on the signal preprocessing results, the blind separation of instantaneous linear mixed signals, blind separation of convolutional mixed signals and blind separation of sparse sources were comprehensively analysed to obtain the source signals and realise channel interference suppression of optical communication network. Experimental results show that this method has high interference precision, strong stability and good application prospect.

A blind separation algorithm for underdetermined convolutional mixed communication signals based on time–frequency soft mask

An algorithm based on least-mean-square error and sparse features is presented for underdetermined blind source separation (BSS), i.e., situation when the number of observed signals' is less than that of sources. In this paper, using the sparsity of sources, first, we estimate the mixing matrix using a new potential function based on clustering method. Then use the estimated mixing matrix and the selfcorrelation of sources, by searching the accurate values at the source clustering directions, we can obtain the optimal sub-matrix for separation through least-mean-square error criterion, which overcomes the disadvantages of traditional algorithms in searching the optimal sub-matrix. Simulation results show the separated signals have higher SNR, and compared with the other similar method, the proposed approach has better separation performance.