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

This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method.

The most standard blind source separation (BSS) methods address the situation when a set of signals are available, e.g. from measurements, and all of them are linear memoryless combinations, with unknown coefficient values, of the same limited set of unknown source signals. BSS methods aim at estimating these unknown source signals and/or coefficients. This generic problem is e.g. faced in the field of Earth observation (where it is also called “unsupervised unmixing”), when considering the commonly used (over)simplified model of hyperspectral images. Each pixel of such an image has an associated reflectance spectrum derived from measurements, which is defined by the fraction of sunlight power reflected by the corresponding Earth surface at each wavelength. Each source signal is then the single reflectance spectrum associated with one of the classes of pure materials which are present in the region of Earth corresponding to the overall considered hyperspectral image. Besides, the associated coefficients define the surfaces on Earth covered with each of these pure materials in each sub-region corresponding to one pixel of the considered image. However, real hyperspectral data e.g. obtained in urban areas have a much more complex structure than the above basic model: each class of pure materials (e.g. roof tiles, trees or asphalt) has so-called spectral or intra-class variability, i.e. it yields a somewhat different spectral component in each pixel of the image. In this complex framework, this chapter shows that Principal Component Analysis (PCA) and its proposed extension are of high interest at three stages of our investigation. First, PCA allows us to analyze the above-mentioned spectral variability of real high-dimensional hyperspectral data and to propose an extended data model which is suited to these complex data. We then develop a versatile extension of BSS methods based on Nonnegative Matrix Factorization, which adds the capability to handle arbitrary forms of intra-class variability by transposing PCA concepts to this original version of the BSS tramework. Finally, PCA again proves to be very well suited to analyzing the high-dimensional data obtained as the result of the proposed BSS method.

In the recent past, blind source separation (BSS) algorithms using multivariate statistical data analysis technique have been successfully used for source identification and separation in the field of biomedical and statistical signal processing. Recently numbers of different BSS techniques have been developed. With BSS methods being the feasible method for source separation and decomposition of biosignals, it is important to compare the different techniques and determine the most suitable method for the applications. This paper presents the performance of five BSS algorithms (SOBI, TDSEP, FastICA, JADE and Infomax) for decomposition of sEMG to identify subtle finger movements. It is observed that BSS algorithms based on second-order statistics (SOBI and TDSEP) gives better performance compared to algorithms based on higher-order statistics (FastICA, JADE and infomax).

Drive system is one of most important key equipment to guarantee safe and stable operation in locomotive. With time variation, unpredictability and nonstationary, fault source of drive system is not obtained by traditional fault diagnosis method. Blind source separation is a kind of method on source signals separation under transmission channel unknown instance. The method of Blind source separation based on variable metric empirical mode decomposition is proposed. Intrinsic mode function is built, redundancy factors are reduced, and recurrent neural network is used to adaptive blind separation. The method is verified by data analysis of on-line measuring. The results show that separation efficiency is improved and unaffected with iteration time in the process of fault information separation, which will be better for further fundamental research and provide technique support for the locomotive.

Blind source separation and feature extraction in concurrent control charts pattern recognition: Novel analyses and a comparison of different methods

The methods that can be done for the estimation of the number of source signals and separation of source signals using time‐frequency information are proposed as a method of blind source separation. In these methods, some independent conditions are assumed in a time‐frequency domain, and observed signals are expanded to time‐frequency domain using wavelet analysis. However, these methods are not considered phase differences (difference of distance) between source signals and observed signals. A new method is proposed. The method can be done not only for the source separation but also the specification of the locations of source signals considering phase differences. In this method, it is necessary to assume a rather stronger independent condition than former methods. But, on account of this assumption, a function that becomes a real value only when phase differences are coincidence in time‐frequency domain is determined. Using this function, first of all, the number of source signals is calculated, then the locations of source signals and source signals are calculated. The effectiveness of the method is shown using actual synthetic signals.

During the operation of rotating machinery, the vibration signals measured by sensors are the aliasing signals of various vibration sources, and they contain strong noises. Conventional signal processing methods have difficulty separating the aliasing signals, which causes great difficulties in the condition monitoring and fault diagnosis of the equipment. The principle and method of blind source separation are introduced, and it is pointed out that the blind source separation algorithm is invalid in strong pulse noise environments. In these environments, the vibration signals are first de-noised with the median filter (MF) method and the de-noised signals are separated with an improved joint approximate diagonalization of eigenmatrices (JADE) algorithm. The simulation results found here verify the effectiveness of the proposed method. Finally, the vibration signal of the hybrid rotor is effectively separated by the proposed method. A new separation approach is thus provided for vibration signals in strong pulse noise environments.

In this study, a new method of blind audio source separation (BASS) of monaural musical harmonic notes is presented. The input (mixed notes) signal is processed using a flexible analysis and synthesis algorithm (complex wavelet additive synthesis, CWAS), which is based on the complex continuous wavelet transform. When the harmonics from two or more sources overlap in a certain frequency band (or group of bands), a new technique based on amplitude similarity criteria is used to obtain an approximation to the original partial information. The aim is to show that the CWAS algorithm can be a powerful tool in BASS. Compared with other existing techniques, the main advantages of the proposed algorithm are its accuracy in the instantaneous phase estimation, its synthesis capability and that the only input information needed is the mixed signal itself. A set of synthetically mixed monaural isolated notes have been analyzed using this method, in eight different experiments: the same instrument playing two notes within the same octave and two harmonically related notes (5th and 12th intervals), two different musical instruments playing 5th and 12th intervals, two different instruments playing non-harmonic notes, major and minor chords played by the same musical instrument, three different instruments playing non-harmonically related notes and finally the mixture of a inharmonic instrument (piano) and one harmonic instrument. The results obtained show the strength of the technique.

Most reported blind source separation (BSS) methods are based on independent component analysis (ICA), which esp. requires the sources to be stationary (and non-Gaussian). Time-frequency (TF) BSS methods avoid these restrictions and are therefore e.g. attractive for speech signals. We first introduce extensions of three types of TF-BSS methods that we recently proposed, and we analyze the relationships between these methods. We then provide a detailed benchmarking of these methods, based on a large number of tests performed with linear instantaneous mixtures of speech signals. This demonstrates the good performance of these methods (SNR typically above 60 dB) and their low sensitivity to the values of their TF parameters.

Spiny Lobster Sound Identification Based on Blind Source Separation (BSS) for Passive Acoustic Monitoring (PAM)

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.

We propose a new method for blind source separation of cyclostationary sources, whose cyclic frequencies are unknown and may share one or more common cyclic frequencies. The suggested method exploits the cyclic correlation function of observation signals to compose a set of matrices which has a particular algebraic structure. The aforesaid matrices are automatically selected by proposing two new criteria. Then, they are jointly diagonalized so as to estimate the mixing matrix and retrieve the source signals as a consequence. The nonunitary joint diagonalization (NU‐JD) is ensured by Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) method which is the most commonly used update strategy for implementing a quasi‐Newton technique. The efficiency of the method is illustrated by numerical simulations in digital communications context, which show good performances comparing to other state‐of‐the‐art methods.

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

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.

Robust approach for blind separation of noisy mixtures of independent and dependent sources