Non-orthogonal joint diagonalization algorithm preventable ill conditioned solutions for blind source separation

The paper proposes a new BSS algorithm based on the second-order statistics. By jointly diagonalizing the time delay correlation matrix of the observed signals and using the improved new non-orthogonal joint diagonalization (NOJD) method, a better solution is achieved. The proposed algorithm can successfully separate communication signals under SNR as low as 10dB and the over-determined mode regardless of the signals’ modulation methods. Signal to Interference Noise Ratio (SINR) is used to prove the superiority of the proposed algorithm over the classical Second-Order Blind Identification (SOBI).

Blind source separation for convolutive mixtures based on the joint diagonalization of power spectral density matrices

We present a set of gradient based orthogonal and non-orthogonal matrix joint diagonalization algorithms. Our approach is to use the geometry of matrix Lie groups to develop continuous-time flows for joint diagonalization and derive their discretized versions. We employ the developed methods to construct a class of Independent Component Analysis (ICA) algorithms based on non-orthogonal joint diagonalization. These algorithms pre-whiten or sphere the data but do not restrict the subsequent search for the (reduced) un-mixing matrix to orthogonal matrices, hence they make effective use of both second and higher order statistics.KeywordsIndependent Component AnalysisIndependent Component AnalysisBlind Source SeparationHigh Order StatisticIndependent Component Analysis AlgorithmThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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.

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.

Joint estimation of direction-of-arrival (DOA) and polarization with electromagnetic vector-sensors (EMVS) is considered in the framework of complex-valued non-orthogonal joint diagonalization (CNJD). Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a sequence of simple sub-optimization problems, by using LU or LQ decompositions of the target matrices as well as the Jacobi-type scheme. Furthermore, based on the above CNJD algorithms we present a novel strategy to exploit the multi-dimensional structure present in the second-order statistics of EMVS outputs for simultaneous DOA and polarization estimation. Simulations are provided to compare the proposed strategy with existing tensorial or joint diagonalization based methods.

ERP is commonly obtained by averaging over segmented EEC epochs. In case artifacts are present in the raw EEC measurement, pre-processing is required to prevent the averaged ERP waveform being interfered by artifacts. The simplest pre-processing approach is by rejecting trials in which presence of artifact is detected. Alternatively artifact correction instead of rejection can be performed by blind source separation, so that waste of ERP trials is avoided. In this paper, we propose a second order statistics based blind source separation approach to ERP artifact correction. Comparing with blind separation using independent component analysis, second order statistics based method does not rely on higher order statistics or signal entropy, and therefore leads to more robust separation even if only short epochs are available.

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 comparative study of approximate joint diagonalization algorithms of a set of matrices is presented. Using a weighted least-squares criterion, without the orthogonality constraint, an algorithm is compared with an analogous one for blind source separation (BSS). The criterion of the present algorithm is on the separating matrix while the other is on the mixing matrix. The convergence of the algorithm is proved under some mild assumptions. The performances of the two algorithms are compared with usual standard algorithms using BSS simulations results. We show that the improvement in estimating the separating matrix, resulting from the relaxation of the orthogonality restriction, can be achieved in presence of additive noise when the length of observed sequences is sufficiently large and when the mixing matrix is not close to an orthogonal matrix

Blind Signal Separation II. Linear, Convolutive Combinations: II. Linear, Convolutive Combinations

Matrix Joint Diagonalization (MJD) is a powerful approach for solving the Blind Source Separation (BSS) problem. It relies on the construction of matrices which are diagonalized by the unknown demixing matrix. Their joint diagonalizer serves as a correct estimate of this demixing matrix only if it is uniquely determined. Thus, a critical question is under what conditions is a joint diagonalizer unique. In the present work we fully answer this question about the identifiability of MJD based BSS approaches and provide a general result on uniqueness conditions of matrix joint diagonalization. It unifies all existing results which exploit the concepts of non-circularity, non-stationarity, non-whiteness, and non-Gaussianity. As a corollary, we propose a solution for complex BSS, which can be formulated in closed form in terms of an eigen and a singular value decomposition of two matrices.

The technique of blind source separation (BSS) has been well studied. In this paper, we apply the BSS technique, particularly based on independent component analysis (ICA), to a meeting situation. The goal is to enhance the spoken utterances and to estimate the location of each speaker by means of multiple microphones. The technique may help us to take the minutes of a meeting.

Indoor vehicle pass-by noise applications deal with measuring the exterior noise from a vehicle fixed on a chassis dynamometer in a large hemi-anechoic room. During a standardised acceleration test, the noise is measured with an array of microphones placed in the far-field, and the overall noise level versus vehicle position can be simulated. The indoor facility allows controlled and repeatable measurements independent of weather. For engineering purposes, pass-by contribution analysis can be included in the test leading to information about the pass-by noise contribution from major noise sources. This work presents a novel application of blind source separation to vehicle measurements from an indoor pass-by measurement campaign. In contrast to the classical transfer path approach using point sources for modelling vehicle noise sources and combining an operational measurement with transfer functions, the blind approach does not consider a specific noise source model. It only assumes that the noise is produces by a set of independent noise sources using only a single operational measurement for a given vehicle condition as input. Near-field microphone measurements are blindly separated into independent components and further correlated with the signals measured at the far-field indoor pass-by microphones to get the time-domain contributions. Finally, we apply the indoor simulated pass-by algorithm to produce noise contribution levels as a function of vehicle position. We discuss the specified application of blind source separation to vehicle measurements for different operating conditions from a real indoor pass-by test. Separation of tyre and engine related noise at tyre near-field microphones is verified. Furthermore, the tyre pass-by noise contribution is extracted from the overall vehicle measurement.

Blind signal separation is currently an active research topic, and many techniques for accomplishing it have been discussed in the literature. In his excellent survey article [4], Cardoso describes blind signal separation (BSS) as the recovery of “unobserved signals of ‘sources’ from several observed mixtures”. This paper describes a particular implementation, a recently constructed two-channel processor capable of operating on convolutive mixtures of QAM signals running at symbol rates as fast as 40 MHz. This processor has been applied to several practical problems, including the cancellation of cross-pole interference from a digital radio signal of interest and the diversity combination of signals received from two apertures or antenna feeds.

A Nonorthogonal Approximate Joint Diagonalization Method Excluding Degenerate Solution for Blind Source Separation