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Four-order tensor joint diagonalization algorithm for joint blind source separation of four data sets

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, failure to fully exploit high-order joint diagonalization structures, and signal time-domain characteristics. use, etc.

Active Publication Date: 2018-07-13
DALIAN UNIV OF TECH
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  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

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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  • Four-order tensor joint diagonalization algorithm for joint blind source separation of four data sets
  • Four-order tensor joint diagonalization algorithm for joint blind source separation of four data sets
  • Four-order tensor joint diagonalization algorithm for joint blind source separation of four data sets

Examples

Experimental program
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Effect test

Embodiment 1

[0211] Example 1, randomly generating superdiagonal tensor D k , and unitary matrix U (1) ,U (2) ,U (3) ,U (4) , and directly construct the tensor according to the formula (4)

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

[0213]

[0214] in, Superscript Represents the Moore-Penrose pseudoinverse. The PIs of the separation results were calculated separately, and then averaged. 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 to Figure 2-4 When K and N take different values, the variation curve of the A-PI value of the JTD algorithm in 10 independent experiments with the number of scans is drawn.

[0216] As a reference, we draw the A-PI curve of the generalized orthogonal ...

Embodiment 2

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

[0219]

[0220] where the mixing matrix A (m) ∈C N×R Randomly generated by the program, the noise term n (m) (t)∈C N×T Gaussian white noise with zero mean and unit variance.

[0221] The source signal is constructed by:

[0222] the s r (t)=Q r s' r (t), (22)

[0223] in s' r (t)∈C 4 It is a random phase signal with segmental amplitude modulation, and its phase and amplitude modulation coefficient are randomly generated by the program. Matrix Q r ∈R 4×4 Randomly generated by the program, used to introduce correlation between sets. It is not difficult to know that the constructed source signals are non-stationary and non-Gaussian signals (assumption A3), and the source signals of different data sets satisfy the inter-group correlation and intra-group independence assumptions (assumptions A1, A2).

[0224] In formula (21),...

Embodiment 3

[0239] Example 3, the experiment aims to extract the FECG signal from the actually collected observation data mixed with maternal ECG (Mother ECG, MECG), fetal ECG (Fetal ECG, FECG), and other interference signals.

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

[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 length is L=500, and the overlap rate is α=0.5. It is not difficult to know that K=10 at...

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Abstract

The invention discloses a four-order tensor joint diagonalization algorithm for joint blind source separation of four data sets. The method comprises the following steps: S1, observation signal: pre-whitening the observation signals of the four data sets respectively; S2, target tensor: after the pre-whitening, constructing a set of mutual four-order cumulant tensors; S3, initializing a factor matrix; and S4, cost function convergence calculation: if the algorithm converges after once scanning, the calculation ends, if the algorithm still does not converge, then, the factor matrix obtained bythe present update is used as an initial value, and the next scanning is performed, a Jacobian rotation matrix is traversed and updated to update the factor matrix until convergence. According to thefour-order tensor joint diagonalization algorithm for joint blind source separation of four data sets, the algorithm is based on orthogonal rotation transformation, thereby an optimal solution in thesense of least squares can be obtained, and the algorithm is a J-BSS method for no more than four dataset signals.

Description

technical field [0001] The invention relates to signal processing fields such as biomedicine, communication, voice, and array, and relates to 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-dataset fusion processing technology, has received a lot of attention in the fields of biomedical, communication, speech, array and other signal processing [1 ]–[14]. [0003] Different from traditional blind source separation (BSS) [14]–[24], J-BSS usually assumes the following multi-dataset signal model: [0004] x (m) (t)=A (m) the s (m) (t),m=1,2,...,M, (1A) [0005] where x(t) (m) ∈C N and s(t) (m) ∈C R Denote the observed signal and the source signal of the mth data set respectively, A (m) ∈C N×R Represents the mixing matrix for the mth dataset. [0006] The parameters M, N, and R represent the n...

Claims

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Application Information

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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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