A modified natural gradient algorithm for blind source separation using generalized constant modulus

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.

Most of the existing algorithms for blind sources separation have a limitation that sources are statistically independent. However, in many practical applications, the source signals are nonnegative and mutual statistically dependent signals. When the observations are nonnegative linear combinations of nonnegative sources, the correlation coefficients of the observations are larger than these of source signals. In this letter, a novel Nonnegative Matrix Factorization (NMF) algorithm with least correlated component constraints to blind separation of convolutive mixed sources is proposed. The algorithm relaxes the source independence assumption and has low-complexity algebraic computations. Simulation results on blind source separation including real face image data indicate that the sources can be successfully recovered with the algorithm.

An efficient algorithm for blind separation of binary symmetrical signals is proposed, which don’t depend on the statistical characteristics of source signals. The mixture matrix is estimated accurately by using the relations of sensor signals in case of no noise and it is also proved in this paper, and the estimated mixture matrix is a primary column transformation of the original mixture matrix by the algorithm, through which the source signals are recovered by permutations and sign changes of their rows. In practice, they can be corrected by introducing headers in the bit-streams and differently encoding them. The algorithm is shown simple and efficient in last simulations.

In correlation‐based signal separation algorithms, the received mixed signals are fed to a de‐coupling system designed to minimize the output cross‐correlation functions. If minimizaion is perfect, each of the system's outputs carries only one signal independent of the others. In these algorithms, the computation burden of the output cross‐correlation functions normally slows down the separation algorithm. This paper, describes a computationally efficient method for off‐line pre‐computation of the needed cross‐correlation functions. Explicit formulas have been derived for the output cross‐correlation functions in terms of the received input signals and the de‐coupling system parameters. Then, it is shown that signal separation amounts to the least‐squares solution of a system of linear equations describing these output cross‐correlation functions, evaluated over a batch of lags. Next, a fast RLS‐type adaptive algorithm is devised for on‐line signal separation. In this respect, an algorithm is derived for updating the de‐coupling parameters as data comes in. This update is achieved recursively, along the negative of the steepest descent directions of an objective cost function describing the output cross‐correlation functions over a batch of lags, subject to equal output power constraints. Illustrative examples are given to demonstrate the effectiveness of the proposed algorithms. Copyright © 2002 John Wiley & Sons, Ltd.

Choosing a proper Region of Interest (ROI) for Remote Photoplethysmography (rPPG) is essential and a challenging first step, and it has a direct effect on the accuracy and reliability of the overall heart rate (HR) algorithm. Non-skin areas have no contribution to the HR information; however, few works have tackled the issue of non-skin pixels included in the ROI. First, this paper considers improving the quality of the rPPG signal by filtering out non-skin pixels included within the ROI. The feasibility of employing skin segmentation for ROI definition is demonstrated. Then, this technique is compared with our previous real-time rPPG-based method. Moreover, we explore the effect of extracting the HR from three ROIs using signal fusion. Second, we give a comprehensive account of the examined methods in our algorithm for face detection, face tracking, skin detection, and blind signal separation. Finally, we compare our rPPG measurements with ground truth values obtained from a commercial pulse oximeter. Based on the simulation results, the proposed algorrithm significantly improves the quality of the rPPG technique.

There are a large variety of applications that require considering sources that usually behave light or strong dependence and this is not the case that common blind signal separation (BSS) algorithms can do. The purpose of this paper is to develop non-parametric BSS algorithm for linear dependent source signals, which is proposed under the framework of contrast method. The contrast function is derived from the Schweizer-Wolff measure of pairwise dependence between the variables. Simulation results show that the proposed algorithm is able to separate the dependent signals and yield ideal performance.

A cyclostationary-based blind signal separation (BSS) algorithm is proposed in this paper. The proposed separation algorithm is used for simultaneously received multiple spectrum overlapped BPSK signals in single channel electromagnetic surveillance system. The mixed signal is separated by means of blind adaptive frequency shift (BA-FRESH) filter based on the independent signals’ cyclostationary. This BA-FRESH filtering technique does not require training signals. It can separate the independent signals only by knowing some of their cycle frequencies, which is gained by the second order cycle cumulants in this work. Numerical simulation results proved the effectiveness of this separation method.

When the channel wave propagates in the coal seam and encounters an abnormal structure, the frequency, amplitude and other parameters will change. Receiving the channel wave signal clearly and extracting the time-frequency characteristics accurately are the keys to predict the abnormal structure ahead. In this paper, the phased source and new feature extraction method were employed for channel wave seismic exploration. The controllable phased source is used to generate channel wave. The CEEMDAN algorithm based on the EMD algorithm and the Fast ICA algorithm for blind source signal separation are combined new Fast ICA-CEEMDAN method for decomposing the channel wave signal. The homogeneous medium and the equivalent medium model of the mined-out coal measure stratum are established by the COMSOL multiphysics, the received channel wave signal is decomposed by Fast ICA-CEEMDAN method. The Hilbert marginal spectrum, time spectrum, instantaneous frequency spectrum and instantaneous frequency spectrum of channel wave signal were extracted. There are five characteristic parameters of phase spectrum and instantaneous amplitude spectrum. The results show that the method can accurately reflect the local characteristics of the channel wave signal, and has high time-frequency resolution, which provides favorable reference for coal mining.

This paper investigates the performance of blind signal separation (BSS) algorithms that exploit the temporal predictability of speech. Specifically, the investigation considers how the separation performance of two BSS algorithms will be affected when the length of the AR process (used in the algorithms to model speech) is varied. The investigation concludes that the length of the AR process (prediction order) has a significant impact on separation performance. In particular, the separation performance of both algorithms is degraded, if the AR model’s prediction order, over fits, or under fits, the temporal structure of the speech. It is revealed that a prediction order of 3050 provides maximum separation performance for natural speech, however a prediction order of 10 is more applicable if computational cost is a consideration.

Aiming at a kind of specific situation encountered in practice, the paper proposes a weak-signal separation algorithm based on extended alternating projection neural networks by combining the time-domain features of the signal with the frequency-domain features of the signal and taking advantage of conclusions on EAPNN. Simulation results demonstrate that the algorithm is effective and that the EAPNN-based signal separation algorithm is better than the RLS-based signal separation algorithm. Although the EAPNN-based algorithm is designed for the specific situation, it is also applicable to the other situations and a basic frame of the EAPNN-based signal separation is presented. Owing to adopting neural network structure, the EAPNN-based algorithm is prone to parallel computation and VLSI design, consequently can satisfy real-time processing needs.

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.

The problem of blind separation of signals in a post-nonlinear mixture is addressed in this paper. A post-nonlinear mixture is formed by a component-wise nonlinear distortion of a linear mixture. Hence, a nonlinear adjusting part, placed in front of the linear separation structure, is needed to compensate for the distortion in separating such signals. The learning rules for the post-nonlinear separation structure are derived by a maximum likelihood approach. An algorithm for the blind separation of post-nonlinearly mixed suband super-Gaussian signals is proposed, based on some previous works. Multilayer perceptrons are used in this algorithm to model the nonlinear part of the separation structure. The algorithm switches between sub- and super-Gaussian probability models during learning according to a stability condition, and it operates in a block-adaptive manner. The effectiveness of the algorithm is verified by experiments on artificial and natural signals.

A new algorithm for blind signal separation that does not require pre-whitening is proposed in this paper. The algorithm is based on an iterative inversion of the mixing matrix. The algorithm is capable of working on-line and provides improved convergence speed and steady state error compared to the popular natural gradient algorithm, with a low additional computational cost.

Non-parametric data representation can be done by means of a potential function. This paper introduces a methodology for finding modes of the potential function. Two different methods are considered for the potential function representation: by using summations of Gaussian kernels, and by employing quantum clustering. In the second case each data sample is associated with a quantum physics particle that has a radial energy field around its location. Both methods use a scaling parameter (bandwidth) to model the strength of the influence around each data sample. We estimate the scaling parameter as the mean of the Gamma distribution that models the variances of K-nearest data samples to any given data. The local Hessian is used afterwards to find the modes of the resulting potential function. Each mode is associated with a cluster. We apply the proposed algorithm for blind signal separation and for the topographic segmentation of radar images of terrain.

The algorithm for separation of signals from two different wireless standards (Bluetooth and IEEE 802.11b standard), operating within the same frequency band is proposed in this paper. The components separation is performed using the time-frequency representation and the concept of Compressive Sensing. Knowing the signals nature, it is possible to select just a small set of time-frequency points that entirely belongs to the IEEE 802.11b signal. These points are extracted from the original time-frequency representation and are used to recover the full signal by using Compressive Sensing method. Once when the components of IEEE 802.11b signal are known, it is possible to reconstruct the remaining components in the band, belonging to the Bluetooth signal. Unlike the conventional separation methods, such as windowing or filtering, this approach works well even in the case of overlapping signals as well. The theory is proved with experimental results.