A Fourth-Order Tensor Joint Diagonalization Algorithm for Joint Blind Source Separation of Four Datasets

A technology of joint diagonalization and blind source separation, applied in the field of fourth-order tensor joint diagonalization algorithm, which can solve the problem of insufficient algorithm accuracy, utilization of signal time domain characteristics, and failure to fully exploit high-order joint diagonalization. structural issues

Active Publication Date: 2021-02-12
DALIAN UNIV OF TECH
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Problems solved by technology

The only method based on the fourth-order cross cumulant[8] only considers the low-order joint diagonalization structure of the fourth-order cross-cumulant at the matrix level, and fails to fully exploit its high-order joint diagonalization structure
In addition, this method does not take advantage of the time-domain characteristics of the signal (such as non-stationarity), which leads to insufficient accuracy of the algorithm

Method used

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  • A Fourth-Order Tensor Joint Diagonalization Algorithm for Joint Blind Source Separation of Four Datasets
  • A Fourth-Order Tensor Joint Diagonalization Algorithm for Joint Blind Source Separation of Four Datasets
  • A Fourth-Order Tensor Joint Diagonalization Algorithm for Joint Blind Source Separation of Four Datasets

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Experimental program
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Effect test

Embodiment 1

[0211]Example 1, Randomly generate super diagonal tensor Dk, And the unitary matrix U(1),U(2),U(3),U(4), And directly construct the tensor according to formula (4)

[0212]Algorithm performance is evaluated by the performance index (Performance Index: PI) defined by the following formula:

[0213]

[0214]among them,SuperscriptRepresents the Moore-Penrose pseudo-inverse. Calculate the PI of the separation results and then average them. The average PI (Average PI: A-PI) is used as the evaluation index of algorithm performance.

[0215]By calculating the PI value corresponding to the algorithm at the end of each scan, the convergence of the algorithm can be reflected. Figure 2-1 toFigure 2-4 When K and N take different values, the A-PI value of the JTD algorithm varies with the number of scans in 10 independent experiments.

[0216]For reference, we draw the A-PI curve of the generalized orthogonal matrix diagonalization algorithm (GOJD, [8]) under the same conditions (its data matrix is ​​defined b...

Embodiment 2

[0218]Embodiment 2. In this experiment, four sets of observation signals x are generated according to formula (1A)(m)(t),m=1,2,3,4:

[0219]

[0220]Where the mixed matrix A(m)∈ CN×R Randomly generated by the program, the noise term n(m)(t)∈CN×TGaussian white noise with zero mean unit variance.

[0221]The source signal is constructed by:

[0222]sr(t)=Qrs′r(t), (22)

[0223]among thems′r(t)∈C4It is a random phase signal of segmental amplitude modulation, and its phase and amplitude modulation coefficient are randomly generated by the program. Matrix Qr∈R4×4Randomly generated by the program and used to introduce correlations between sets. It is not difficult to know that the constructed source signal is a non-stationary non-Gaussian signal (assuming A3), and the source signals of different data sets satisfy the assumptions of inter-group correlation and intra-group independence (assuming A1, A2).

[0224]In formula (21), σsAnd σnRepresents signal strength and noise strength respectively. The signal-t...

Embodiment 3

[0239]In Embodiment 3, the experiment aims to extract the FECG signal from the actually collected observation data that mixes the mother ECG (MECG), the fetal ECG (Fetal ECG, FECG), and other interference signals.

[0240]The 8-channel ECG data used is taken from the DAISY database 0 of Leuven University. The signal waveform is asFigure 4 Shown. The sampling frequency is 250Hz, the number of sampling points is 2500, and the sampling time is 10s, such asFigure 4 Shown is the eight-channel ECG data actually collected, which is taken from the DAISY database of Leuven University.

[0241]According to the following formula, the eight observation signals are divided into four data sets, and each data set contains five observation signals:

[0242]

[0243]The observation signals of the four data sets are pre-whitened and segmented. Each segment has a length of L=500 and an overlap rate of α=0.5. It is not difficult to know that K=10 at this time. Calculate the mutual fourth-order cumulant for each s...

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Abstract

The invention discloses a fourth-order tensor joint diagonalization algorithm for joint blind source separation of four data sets, comprising the following steps: S1, observation signals: pre-whitening the observation signals of the four data sets respectively; S2, Target tensor: After pre-whitening, construct a set of mutual fourth-order cumulant tensors; S3, initialize factor matrix; S4, cost function convergence calculation: if the algorithm converges after one scan, the calculation ends, if the algorithm has not yet converged, The factor matrix obtained by this update is used as the initial value, and the next scan is performed, and the Jacobian rotation matrix is ​​traversed to update the factor matrix until convergence. The fourth-order tensor joint diagonalization algorithm for joint blind source separation of four data sets described in the present invention is based on orthogonal rotation transformation, so it can obtain the optimal solution in the sense of least squares, which is a kind of J‑BSS method for no more than four dataset signals.

Description

Technical field[0001]The invention relates to the signal processing fields of biomedicine, communication, speech, array, etc., and a fourth-order tensor joint diagonalization algorithm that can be used for joint blind source separation of four data sets.Background technique[0002]Joint Blind Source Separation (J-BSS), as an emerging, data-driven multi-data set fusion processing technology, has gained a lot of attention in the signal processing fields of biomedicine, communications, voice, and arrays [1 ]–[14].[0003]Different from the traditional blind source separation (BSS) [14]–[24], J-BSS usually assumes the following multi-data set signal model:[0004]x(m)(t)=A(m)s(m)(t),m=1,2,...,M, (1A)[0005]Where x(t)(m)∈ CNAnd s(t)(m)∈ CRRespectively represent the observation signal and source signal of the m-th data set, A(m)∈ CN×R Represents the mixing matrix of the m-th data set.[0006]The parameters M, N, and R respectively represent the number of data sets, the number of observation signal...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H04L25/02H04L25/03G10L21/0272
CPCG10L21/0272H04L25/0242H04L25/03089H04L2025/03636H04L2025/03649
Inventor 龚晓峰毛蕾林秋华
Owner DALIAN UNIV OF TECH
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