Noninvasive fetal electrocardiosignal extraction method based on multidimensional subspace representation and time-space tensor decomposition

Abstract

The invention provides a noninvasive fetal electrocardiosignal extraction method based on multidimensional subspace representation and time-space tensor decomposition. According to the method, baseline drift, power line interference, myoelectricity interference and the like are removed through various filters, maternal electrocardiosignals with the largest influence are removed through a template matching method, and fetal electrocardiosignals are extracted through KPCA and a combined blind source separation method based on tensor decomposition. And the accuracy of calculating the fetal heart rate and the average R-R interval under nonlinear and non-stationary conditions is enhanced. High-efficiency and high-precision non-invasive fetal electrocardiosignal extraction is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of fetal electrocardiogram signal monitoring in biomedical signal processing, and particularly to a non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition. Background Art

[0002] The incidence of congenital heart disease in newborns in China is as high as 8.98%. To ensure the health of newborns, it is particularly important to conduct regular prenatal examinations. Currently, the main pregnancy monitoring methods include non-invasive DNA prenatal screening, Doppler ultrasound, and magnetic resonance imaging. However, these methods are cumbersome to operate and have serious safety problems when used for a long time. Electrocardiogram (ECG) is a technology for recording the electrical activity of the heart. The abdominal electrocardiogram (AECG) is obtained by placing multiple electrodes on the abdomen of a pregnant woman, and then the fetal electrocardiogram (FECG) is extracted using signal separation technology. The fetal physiological information provided by FECG can be used to detect fetal arrhythmias, congenital heart diseases, hypoxia, etc., so as to intervene and treat in time, improve the treatment effect and the survival rate of the fetus.

[0003] Currently, there are various methods for extracting fetal electrocardiogram signals, including algorithms such as Kalman filtering, singular value decomposition, non-negative matrix decomposition, deep learning (DP), wavelet transform, and independent component analysis. However, the above methods still face many challenges. First, since the FECG signal is relatively weak and is easily masked by the high-amplitude MECG signal, it increases the difficulty of signal separation and extraction. Second, the FECG signal is vulnerable to environmental noise interference, which may lead to the loss of key information, thus affecting the accuracy of subsequent clinical diagnosis. Therefore, how to obtain an electrocardiogram carrying accurate fetal heart rate information is a problem that needs to be solved in the current non-invasive fetal electrocardiogram signal extraction. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems in the prior art, and a non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition is proposed.

[0005] The present invention is realized by the following technical solutions. The present invention proposes a non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition. The method includes the following steps:

[0006] Step 1: Preprocess each electrocardiogram signal obtained from the pregnant woman's abdomen through electrodes. Use a high-pass filter, a notch filter, and a low-pass filter to eliminate baseline drift, power line interference, and electromyogram interference in sequence, reducing the influence of various interference signals;

[0007] Step 2: Select the template matching method to remove the maternal electrocardiogram signal from the preprocessed abdominal electrocardiogram signal. Cut it according to the average cardiac cycle of the adult electrocardiogram signal being 0.8 seconds, take the average of each segment of the signal to obtain the maternal electrocardiogram signal template, and obtain the residual signal by subtracting the abdominal electrocardiogram signal from the template maternal electrocardiogram signal;

[0008] Step 3: Before unmixing, first map the non-linear residual signal to a linearly separable signal in the feature space through kernel principal component analysis (KPCA) to cope with various non-linear mixing situations in the actual environment;

[0009] Step 4: Use the joint blind source separation algorithm based on tensor decomposition to extract the fetal electrocardiogram signal, and then detect the position of the fetal QRS wave and calculate the fetal heart rate.

[0010] Furthermore, in Step 1, the high-pass filter is designed based on the Butterworth filter, which is used to remove frequency components below 0.5 Hz and retain frequencies of above 8 Hz; the squared magnitude of its amplitude-frequency characteristic is:

[0011]

[0012] where N is the order of the filter, and Ω c is the cut-off frequency of the high-pass filter; the notch filter is implemented by a second-order IIR filter, which performs deep attenuation near the designed center frequency while keeping the signals of other frequencies unchanged. The squared magnitude of its amplitude-frequency characteristic is:

[0013]

[0014] where f0 represents the frequency component to be filtered out; use the Butterworth low-pass filter to filter out signals above 200 Hz. The squared magnitude of its amplitude-frequency characteristic is:

[0015]

[0016] Furthermore, in Step 3, KPCA maps the non-linear residual signal to a linearly separable signal in the feature space. First, map the residual signal to a signal in the high-dimensional space through the Gaussian kernel, and then perform PCA to reduce the dimension to the feature space.

[0017] Furthermore, the kernel principal component analysis method uses a mapping function φ to map the non-linear data points x ∈ X in the input space X to φ(x) in the high-dimensional feature space F, i.e., φ: X → F; the kernel function K(x, y) is used to implicitly calculate the inner product in F without determining the mapping function and the mapped data φ(x), i.e.,

[0018] K(x, y) = φ(x) · φ(y) = φ(x) T φ(y).

[0019] Furthermore, KPCA retains the main features of the original data, selects the orthonormal basis of the d-dimensional subspace and maps the data to the low-dimensional subspace; let the mapped points of the observed data in the feature space be Φ(x[t]), and use Φ x to represent [Φ(x[1]),..., Φ(x[T])]; since the covariance matrix of the measurement data cannot be directly calculated, the covariance matrix's eigenvalues and eigenvectors are obtained indirectly using the kernel matrix :

[0020]

[0021] where the diagonal matrix Λ is composed of the eigenvalues λ1 >,..., λ T along the diagonal; the eigenvector matrix E is composed of the eigenvectors e1,..., e T corresponding to each eigenvalue by columns; therefore, the orthonormal basis of the d-dimensional feature space can be represented by the eigenvector matrix and the diagonal matrix as:

[0022]

[0023] In the formula, Λ d represents the first d eigenvalues sorted from largest to smallest; E d represents the eigenvector matrix composed of the eigenvectors corresponding to the d eigenvalues by columns; multiplying the inverse of the orthonormal basis by the mapped points gives the coordinates of the d-dimensional feature space:

[0024] ψ x [t] = Ξ -1 Φ(x[t]) = Ξ T Φ(x[t]).

[0025] Furthermore, after the residual signal in step 4 passes through the joint blind source separation algorithm based on tensor decomposition, multiple source signals will be generated. Channel selection is required to extract the fetal electrocardiogram signal, then detect the position of the fetal QRS wave and smooth the fetal electrocardiogram signal, and then calculate the fetal heart rate and the average R-R interval.

[0026] Furthermore, in step 4, the mapped points Ψ are processed using the joint blind source separation algorithm based on tensor decomposition x[t], the statistical characteristics between multiple datasets are utilized to jointly estimate the unmixing matrix, i.e.:

[0027]

[0028] where, denotes the matrix composed of N independent source signals of pregnant women in different datasets; A k ∈ R d×n represents the mixing matrix of different datasets, and d and n correspond to the dimensions of the observed signal and the source signal respectively; denotes the observed data, corresponding to the feature space data of the k-th dataset; assuming the dataset is In the first step, the dataset is paired with other datasets in pairs to obtain (K - 1) combinations. Utilizing the characteristics of the signal having a time structure and the correlation between datasets, according to different time delays τ L the dataset with a mean of 0 is constructed and L spatial covariance matrices, i.e.:

[0029]

[0030] The L spatial covariance matrices are stacked in a tensor X; according to the column vector expression and slice expression of the tensor CP decomposition, the factor matrices A and B respectively correspond to the mixing matrices of two datasets The row vectors of the factor matrix C correspond to the diagonal elements of the matrix Therefore, the tensor X can be expressed in the following form:

[0031]

[0032] In the formula, are respectively the n-th column of the mixing matrix The cost function of the above tensor is:

[0033]

[0034] [[ID=%50]]Applying the alternating least squares method ALS to the above cost function can solve the mixing matrix of each combination In the second step, the new matrix F composed of the n-th column vectors of the (K - 1) estimated mixing matrices is taken out, and the column vector singular value decomposition is performed on the matrix F:

[0035] FF T = UΣV T VΣ T U T = UΣΣ T U T

[0036] F T F = VΣ T U T UΣV T = VΣ T ΣV T

[0037] Select the left singular component with the maximum singular value as the mixing matrix Estimate the nth column and repeat N times to obtain the data set of the mixing matrix; repeat the above steps until the mixing matrix of each data set is obtained, and finally obtain the demixing matrix by taking the inverse of each mixing matrix, and apply it to the observed data set to separate the independent source signals of each path.

[0038] Furthermore, select the fetal electrocardiogram signal from the source signals of each channel for channel selection; specifically: first use the Pan-Tompkins algorithm to detect the R peak points of each source signal, and detect the interval between adjacent QRS waves to calculate the instantaneous heart rate CH(t), that is:

[0039]

[0040] where RR(t) is the R-R interval at the tth moment; then calculate the single residual channel smoothing index SMI, and SMI is defined as the number of times the absolute value of the change in the instantaneous heart rate CH(t) within each minute segment exceeds 29 times per minute, and select the channel with the lowest SMI as the fetal electrocardiogram signal, and the marked R peak is the position of the fetal QRS wave.

[0041] The present invention also provides an electronic device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, the steps of the non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition are implemented.

[0042] The present invention also provides a computer-readable storage medium for storing computer instructions, and when the computer instructions are executed by a processor, the steps of the non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition are implemented.

[0043] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0044] The present invention provides a non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition. This method first uses various filters to remove baseline drift, power line interference, and electromyogram interference, etc. Then, it removes the maternal electrocardiogram signal with the greatest influence through template matching. Next, it extracts the fetal electrocardiogram signal through KPCA and a joint blind source separation method based on tensor decomposition, enhancing the accuracy of calculating the fetal heart rate and average R-R interval in non-linear and non-stationary situations. The efficient and high-precision non-invasive fetal electrocardiogram signal extraction is realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on the provided drawings.

[0046] Figure 1 It is a flowchart of a non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition according to the present invention.

[0047] Figure 2 It is a structural framework diagram for non-invasive fetal electrocardiogram signal extraction.

[0048] Figure 3 It is a block diagram of a blind source separation method based on tensor decomposition.

[0049] Figure 4 It is a diagram of the fetal electrocardiogram signal and R peak estimation result before smoothing.

[0050] Figure 5 It is a schematic diagram of the fetal electrocardiogram signal before and after smoothing.

[0051] Figure 6 It is a diagram of the difference between the reference annotated RR interval and the estimated annotated RR interval. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0053] In view of the problems in the prior art, the present invention proposes a non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition. To solve the problem that the maternal electrocardiogram signal masks the weak fetal electrocardiogram signal, template matching is used to remove the maternal electrocardiogram signal with the greatest influence, and a residual signal containing the fetal electrocardiogram signal and part of the maternal electrocardiogram signal is obtained. Then, in order to obtain an accurate fetal electrocardiogram signal, before using the joint blind source separation algorithm based on tensor decomposition, the non-linear residual signal in the low-dimensional space is mapped to the high-dimensional space by the kernel method to meet the condition of linear unmixing in blind source separation. At the same time, the mapped signal is evenly divided into multiple data sets according to time, so that each data set maintains the stationarity of the mixing process of FECG and various noise signals in a very short time, thereby solving the problems that the rhythm and signal amplitude of the fetal heartbeat fluctuate due to fetal movement, maternal body position change, etc., and the signal exhibits non-stationary characteristics in a short time.

[0054] Specifically, in combination with Figures 1-6 , the present invention proposes a non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition, and the method includes the following steps:

[0055] Step 1: Preprocess each electrocardiogram signal obtained from the abdomen of a pregnant woman through electrodes, and use a high-pass filter, a notch filter, and a low-pass filter to sequentially eliminate baseline drift, power line interference, and electromyogram interference, reducing the influence of various interference signals;

[0056] The data set used in Step 1 is the non-invasive fetal electrocardiogram: the data set used in the 2013 Cardiology Challenge. A high-pass filter is used to remove baseline drift with a frequency usually less than 0.5 Hz; a notch filter is used to filter out power line interference usually appearing at a frequency of 50 Hz or 60 Hz; a low-pass filter is used to retain the fetal electrocardiogram signal from 0.5 Hz to 200 Hz, thereby reducing the influence of electromyogram signals with a wide frequency range.

[0057] In Step 1, the high-pass filter is designed based on a Butterworth filter and is used to remove frequency components below 0.5 Hz and retain frequencies of 8 Hz and above; the squared magnitude of its amplitude-frequency characteristic is:

[0058]

[0059] where N is the order of the filter, and Ω c is the cut-off frequency of the high-pass filter; the notch filter is implemented by a second-order IIR filter, which performs deep attenuation near the center frequency of its design while keeping the signals at other frequencies unchanged, and the squared magnitude of its amplitude-frequency characteristic is:

[0060]

[0061] Among them, f0 represents the frequency component to be filtered out; a Butterworth low-pass filter is used to filter out signals above 200 Hz, and the square of the magnitude-frequency characteristic modulus of it is:

[0062]

[0063] Step 2: Select the template matching method to remove the maternal electrocardiogram signal from the preprocessed abdominal electrocardiogram signal. Cut according to the average cardiac cycle of the adult electrocardiogram signal being 0.8 seconds, take the average of each segment of the signal to obtain the maternal electrocardiogram signal template, and obtain the residual signal by subtracting the abdominal electrocardiogram signal from the template maternal electrocardiogram signal;

[0064] Step 3: Before demixing, first map the non-linear residual signal to a linearly separable signal in the feature space through kernel principal component analysis (KPCA) to deal with various non-linear mixing situations in the actual environment;

[0065] In Step 3, the non-linear residual signal is mapped to a linearly separable signal in the feature space through KPCA. First, the residual signal is mapped to a signal in a high-dimensional space through a Gaussian kernel, and then PCA is performed to reduce the dimension to the feature space, so as to reduce the problem of high subsequent computational complexity caused by too high a dimension.

[0066] The kernel principal component analysis method uses the mapping function φ to map the non-linear data point x ∈ X in the input space X to φ(x) in the high-dimensional feature space F, that is: φ: X → F; uses the kernel function K(x, y) to implicitly calculate the inner product in F without determining the mapping function and the mapped data φ(x), that is:

[0067] K(x, y) = φ(x) · φ(y) = φ(x) T φ(y).

[0068] KPCA retains the main features of the original data, selects the standard orthogonal basis of the d-dimensional subspace and maps the data to the low-dimensional subspace; let the mapped point of the observed data in the feature space be Φ(x[t]), and use Φ x to represent [Φ(x[1]),..., Φ(x[T])]; since the covariance matrix of the measurement data cannot be directly calculated, the kernel matrix is used to indirectly obtain the eigenvalues and eigenvectors of the covariance matrix:

[0069]

[0070] Among them, the diagonal matrix Λ is composed of the eigenvalues λ1 >,..., λ T along the diagonal; the eigenvector matrix E is composed of the eigenvectors e1,..., e corresponding to each eigenvalue T by columns; therefore, the standard orthogonal basis of the d-dimensional feature space can be represented by the eigenvector matrix and the diagonal matrix as:

[0071]

[0072] In the formula, Λ d represents the first d eigenvalues sorted from largest to smallest; E d represents the eigenvector matrix formed by the eigenvectors corresponding to the d eigenvalues column by column; multiplying the inverse of the orthonormal basis by the mapping point can obtain the coordinates in the d-dimensional feature space:

[0073] ψ x [t] = Ξ -1 Φ(x[t]) = Ξ T Φ(x[t]).

[0074] Step 4: Use the joint blind source separation algorithm based on tensor decomposition to extract the fetal electrocardiogram signal, and then detect the position of the fetal QRS wave and calculate the fetal heart rate.

[0075] After passing through the joint blind source separation algorithm based on tensor decomposition, the residual signal in Step 4 will generate multiple source signals. Channel selection is required to extract the fetal electrocardiogram signal, then detect the position of the fetal QRS wave and smooth the fetal electrocardiogram signal, and then calculate the fetal heart rate and the average R-R interval.

[0076] In Step 4, the mapping point Ψ x [t] is processed using the joint blind source separation algorithm based on tensor decomposition, and the statistical characteristics between multiple data sets are used to jointly estimate the demixing matrix, that is:

[0077]

[0078] where represents the matrix composed of N independent source signals of pregnant women in different data sets; A k ∈ R d×n represents the mixing matrix of different data sets, and d and n respectively correspond to the dimensions of the observed signal and the source signal; represents the observed data, corresponding to the feature space data of the k-th data set; assuming the data set is In the first step, the data set is paired with other data sets in pairs to obtain (K - 1) combinations. Utilizing the characteristics of the signal having a time structure and the correlation between data sets, according to different time delays τ L construct the data sets and with a mean of 0 and L spatial covariance matrices, that is:

[0079]

[0080] Stack L spatial covariance matrices in a tensor X; according to the column vector expression and slice expression of tensor CP decomposition, the factor matrices A and B correspond to the mixing matrices of two datasets respectively The row vectors of the factor matrix C correspond to the diagonal elements of the matrix Therefore, the tensor X can be expressed in the following form:

[0081]

[0082] In the formula, are the nth columns of the mixing matrix respectively; the cost function of the above tensor is:

[0083]

[0084] Apply the alternating least squares method ALS to the above cost function to solve the mixing matrices of each combination In the second step, take out the new matrix F composed of the nth column vectors of (K - 1) estimated mixing matrices Perform column vector singular value decomposition on the matrix F:

[0085] FF T = UΣV T VΣ T U T = UΣΣ T U T

[0086] F T F = VΣ T U T UΣV T = VΣ T ΣV T

[0087] Select the left singular component with the maximum singular value as the estimate of the nth column of the mixing matrix Repeat N times to obtain the mixing matrix of the dataset Repeat the above steps until the mixing matrices of each dataset are obtained. Finally, obtain the demixing matrix by taking the inverse of each mixing matrix and apply it to the observed dataset to separate the independent source signals of each path.

[0088] Select the fetal electrocardiogram signal from the source signals of each channel for channel selection; specifically: first, use the Pan-Tompkins algorithm to detect the R peak points of each source signal, and detect the interval between adjacent QRS waves to calculate the instantaneous heart rate CH(t), that is:

[0089]

[0090] Among them, RR(t) is the R-R interval at the t-th moment; then calculate the single residual channel smoothing index SMI, which is defined as the number of times the absolute value of the change in the instantaneous heart rate CH(t) within each minute segment exceeds 29 times per minute. Select the channel with the lowest SMI as the fetal electrocardiogram signal, and the marked R peaks are the positions of the fetal QRS waves.

[0091] Embodiment

[0092] The object of the present invention is to solve the problem of low extraction accuracy of non-invasive fetal electrocardiogram signals. The method combining template matching and blind source separation further improves the extraction accuracy of fetal electrocardiogram signals and outputs information such as the heart rate and RR interval of FECG. To achieve this goal, the present invention proposes a non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition, and the method includes the following steps:

[0093] Step 1: Preprocess each electrocardiogram signal obtained from the abdomen of a pregnant woman through electrodes, and use a high-pass filter, a notch filter, and a low-pass filter to sequentially eliminate baseline drift, power line interference, and electromyogram interference to reduce the influence of various interference signals;

[0094] The dataset used in Step 1 is a non-invasive fetal electrocardiogram: the dataset used in the 2013 cardiology challenge, which contains 75 groups of one-minute fetal electrocardiogram records. Each record contains 4 non-invasive abdominal signals, and the sampling rate is 1000 Hz. Each group of records has reference annotations for the position of each QRS complex obtained from fetal scalp electrodes. There are errors in the annotations of seven groups of records, namely a33, a38, a47, a52, a54, a71, and a74, and the remaining records can be used for the detection of the QRS wave positions of fetal electrocardiogram signals.

[0095] The fetal electrocardiogram signal is transmitted through tissues such as amniotic fluid, the abdominal cavity of the mother, and the skin to the abdominal wall and collected by electrodes, which includes MECG, FECG, and various noise interferences. Use a high-pass filter, a notch filter, and a low-pass filter for multi-channel AECG to eliminate various noise interferences. The high-pass filter is designed based on a Butterworth filter and is used to remove frequency components below 0.5 Hz and retain frequencies of 8 Hz and above; the squared magnitude of its amplitude-frequency characteristic is:

[0096]

[0097] Among them, N is the order of the filter, and Ω c is the cut-off frequency of the high-pass filter; the notch filter is implemented by a second-order IIR filter, which performs deep attenuation near its designed center frequency while keeping the signals at other frequencies unchanged. The squared magnitude of its amplitude-frequency characteristic is:

[0098]

[0099] Among them, f0 represents the frequency component to be filtered out; a Butterworth low-pass filter is used to filter out signals above 200 Hz, and the square of the magnitude-frequency characteristic modulus of it is:

[0100]

[0101] Step 2: Select the template matching method to remove the maternal electrocardiogram signal from the preprocessed abdominal electrocardiogram signal. Cut according to the average cardiac cycle of the adult electrocardiogram signal being 0.8 seconds, take the average of each segment of the signal to obtain the maternal electrocardiogram signal template, and obtain the residual signal by subtracting the abdominal electrocardiogram signal from the template maternal electrocardiogram signal;

[0102] Step 3: Before unmixing, first map the non-linear residual signal to a linearly separable signal in the feature space through kernel principal component analysis (KPCA) to cope with various non-linear mixing situations in the actual environment;

[0103] In Step 3, the non-linear residual signal is mapped to a linearly separable signal in the feature space through KPCA. First, the residual signal is mapped to a signal in a high-dimensional space through a Gaussian kernel, and then PCA is performed to reduce the dimension to the feature space, so as to reduce the problem of high subsequent calculation complexity caused by too high dimensions.

[0104] The kernel principal component analysis method uses the mapping function φ to map the non-linear data point x ∈ X in the input space X to φ(x) in the high-dimensional feature space F, that is: φ: X → F; use the kernel function K(x, y) to implicitly calculate the inner product in F, without determining the mapping function and the mapped data φ(x), that is:

[0105] K(x, y) = φ(x) · φ(y) = φ(x) T φ(y).

[0106] Some kernel functions will map the input data in a high-dimensional or even infinite-dimensional space. This high-dimensional space will increase the calculation complexity of the subsequent blind source separation algorithm. Therefore, it is necessary to retain the main features of the original data through KPCA, select the standard orthogonal basis of the d-dimensional subspace and map the data to the low-dimensional subspace; let the mapped point of the observed data in the feature space be Φ(x[t]), and use Φ x to represent [Φ(x[1]),..., Φ(x[T])]; since the covariance matrix of the measurement data cannot be directly calculated, the kernel matrix is used to indirectly obtain the eigenvalues and eigenvectors of the covariance matrix:

[0107]

[0108] Among them, the diagonal matrix Λ consists of eigenvalues λ1>,..., λ TComposed along the diagonal; the eigenvector matrix E consists of the eigenvectors e1,..., e corresponding to each eigenvalue T Composed by columns; thus, the orthonormal basis of the d-dimensional feature space can be represented by the eigenvector matrix and the diagonal matrix as:

[0109]

[0110] In the formula, Λ d Represents the first d eigenvalues sorted from largest to smallest; E d Represents the eigenvector matrix composed of the eigenvectors corresponding to the d eigenvalues by columns; multiplying the inverse of the orthonormal basis by the mapped point can obtain the coordinates of the d-dimensional feature space:

[0111] ψ x [t] = Ξ -1 Φ(x[t]) = Ξ T Φ(x[t]).

[0112] Step 4: Use the joint blind source separation algorithm based on tensor decomposition to extract the fetal electrocardiogram signal, and then detect the position of the fetal QRS wave and calculate the fetal heart rate.

[0113] After passing through the joint blind source separation algorithm based on tensor decomposition, the residual signal in Step 4 will generate multiple source signals. Channel selection is required to extract the fetal electrocardiogram signal, then detect the position of the fetal QRS wave and smooth the fetal electrocardiogram signal, and then calculate the fetal heart rate and the average R-R interval.

[0114] In Step 4, the mapped point Ψ x [t] is processed using the joint blind source separation algorithm based on tensor decomposition, and the statistical characteristics between multiple data sets are used to jointly estimate the demixing matrix, that is:

[0115]

[0116] Among them, Represents the matrix composed of N independent source signals such as the pregnant woman's mECG, fECG, artifacts, and noise in different data sets; A k ∈ R d×n Represents the mixing matrix of different data sets, and d and n correspond to the dimensions of the observed signal and the source signal respectively; Represents the observed data, corresponding to the feature space data of the kth data set; assuming the data set is In the first step, the data set Is paired with other data sets pairwise to obtain (K - 1) combinations. Utilizing the characteristics of the signal having a time structure and the correlation between data sets, according to different time delays τ L Construct a data set with a mean of 0 And L spatial covariance matrices, namely:

[0117]

[0118] Stack the L spatial covariance matrices in a tensor X; according to the column vector expression and slice expression of tensor CP decomposition, the factor matrices A and B correspond to the mixing matrices of two data sets respectively The row vectors of the factor matrix C correspond to the diagonal elements of the matrix Therefore, the tensor X can be expressed in the following form:

[0119]

[0120] In the formula, are the nth columns of the mixing matrix respectively; the cost function of the above tensor is:

[0121]

[0122] Applying the alternating least squares method ALS to the above cost function can solve the mixing matrices of each combination In the second step, take out the new matrix F composed of the nth column vectors of (K - 1) estimated mixing matrices Perform column vector singular value decomposition on the matrix F:

[0123] FF T = UΣV T VΣ T U T = UΣΣ T U T

[0124] F T F = VΣ T U T UΣV T = VΣ T ΣV T

[0125] Select the left singular component with the maximum singular value as the estimate of the nth column of the mixing matrix Repeat N times to obtain the mixing matrix of the data set Repeat the above steps until the mixing matrices of each data set are obtained. Finally, obtain the demixing matrix by taking the inverse of each mixing matrix and apply it to the observed data set to separate the independent source signals of each path.

[0126] Select the fetal electrocardiogram signal from the source signals of each channel for channel selection. Specifically: First, use the Pan-Tompkins algorithm to detect the R peak points of each source signal, and detect the interval between adjacent QRS waves to calculate the instantaneous heart rate CH(t), that is:

[0127]

[0128] where RR(t) is the R-R interval at the t-th moment; then calculate the single residual channel smoothing index SMI, which is defined as the number of times the absolute value of the change in the instantaneous heart rate CH(t) within each minute segment exceeds 29 times per minute. Select the channel with the lowest SMI as the fetal electrocardiogram signal, and the marked R peak is the position of the fetal QRS wave.

[0129] The present invention also provides an electronic device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps of the non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition are implemented.

[0130] The present invention also provides a computer-readable storage medium for storing computer instructions, and when the computer instructions are executed by a processor, the steps of the non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition are implemented.

[0131] The memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read only memory (ROM), a programmable ROM (PROM), an erasable PROM (EPROM), an electrically erasable PROM (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example but not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchlink DRAM (SLDRAM), and direct rambus RAM (DRRAM). It should be noted that the memory of the method described in the present invention is intended to include but not limited to these and any other suitable types of memories.

[0132] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, the processes or functions described in the embodiments of the present application are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wire (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. that contains one or more integrated available media. The available media can be magnetic media (such as floppy disks, hard disks, magnetic tapes), optical media (such as high-density digital video discs (DVDs)), or semiconductor media (such as solid state discs (SSDs)), etc.

[0133] In the implementation process, the steps of the above method can be completed by the integrated logic circuit of the hardware in the processor or the instructions in the form of software. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as being executed by the hardware processor, or executed by a combination of the hardware and software modules in the processor. The software module can be located in a mature storage medium in the art such as random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method. To avoid repetition, it will not be described in detail here.

[0134] It should be noted that the processor in the embodiments of the present application may be an integrated circuit chip with signal processing capabilities. In the implementation process, the steps of the above method embodiments can be completed by the integrated logic circuit in the hardware of the processor or instructions in the form of software. The above processor may be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of the present application. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as being executed and completed by a hardware decoding processor, or executed and completed by a combination of hardware and software modules in the decoding processor. The software module may be located in a mature storage medium in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method.

[0135] The above has introduced in detail a non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition proposed by the present invention. Specific examples are used in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and time-space tensor decomposition, characterized in that The method includes the following steps: Step 1: Preprocess each electrocardiogram signal obtained from the pregnant woman's abdomen through electrodes, and use a high-pass filter, a notch filter, and a low-pass filter to eliminate baseline drift, power line interference, and electromyogram interference in sequence, reducing the influence of various interference signals; Step 2: Select the template matching method to remove the maternal electrocardiogram signal from the preprocessed abdominal electrocardiogram signal. Cut according to the average cardiac cycle of the adult electrocardiogram signal being 0.8 seconds, take the average of each segment of the signal to obtain the maternal electrocardiogram signal template, and obtain the residual signal by subtracting the abdominal electrocardiogram signal from the template maternal electrocardiogram signal; Step 3: Before unmixing, first map the non-linear residual signal into a linearly separable signal in the feature space through kernel principal component analysis (KPCA) to cope with various non-linear mixing situations in the actual environment; Step 4: Use the joint blind source separation algorithm based on tensor decomposition to extract the fetal electrocardiogram signal, and then detect the position of the fetal QRS wave and calculate the fetal heart rate.

2. The method according to claim 1, characterized in that, In Step 1, the high-pass filter is designed based on the Butterworth filter, which is used to remove frequency components below 0.5 Hz and retain frequencies of 8 Hz and above; the squared magnitude of its amplitude-frequency characteristic is: where N is the order of the filter, and Ω c is the cut-off frequency of the high-pass filter; the notch filter is implemented by a second-order IIR filter, which performs deep attenuation near its designed center frequency while keeping the signals at other frequencies unchanged. The squared magnitude of its amplitude-frequency characteristic is as follows: where f0 represents the frequency component to be filtered out; use the Butterworth low-pass filter to filter out signals above 200 Hz, and the squared magnitude of its amplitude-frequency characteristic is:

3. The method according to claim 1, wherein In Step 3, KPCA maps the non-linear residual signal into a linearly separable signal in the feature space. First, map the residual signal into a signal in a high-dimensional space through the Gaussian kernel, and then perform PCA to reduce the dimension to the feature space.

4. The method according to claim 3, wherein The kernel principal component analysis method uses the mapping function φ to map the non-linear data point x ∈ X in the input space X to φ(x) in the high-dimensional feature space F, that is: φ: X → F; use the kernel function K(x, y) to implicitly calculate the inner product in F without determining the mapping function and the mapped data φ(x), that is: K(x,y) = φ(x)·φ(y) = φ(x) T φ(y).

5. The method according to claim 4, wherein KPCA preserves the main features of the original data, selects the orthonormal basis of the d-dimensional subspace, and maps the data to the low-dimensional subspace. Let the mapped points of the observed data in the feature space be Φ(x[t]), and use Φ x to represent [Φ(x[1]),..., Φ(x[T])]. Since the covariance matrix of the measurement data cannot be directly calculated, the kernel matrix is used to indirectly obtain the eigenvalues and eigenvectors of the covariance matrix: Among them, the diagonal matrix Λ is composed of eigenvalues λ1>,...,λ T along the diagonal; the eigenvector matrix E is composed of eigenvectors e1,...,e corresponding to each eigenvalue T by columns; therefore, the orthonormal basis of the d-dimensional eigenspace can be expressed by the eigenvector matrix and the diagonal matrix as: where Λ d denotes the top d eigenvalues sorted from largest to smallest; E d denotes the eigenvector matrix formed by the eigenvectors corresponding to the d eigenvalues column by column; multiplying the inverse of the orthonormal basis by the mapped point gives the coordinates in the d-dimensional feature space: ψ x [t] = Ξ -1 Φ(x[t]) = Ξ T Φ(x[t]).

6. The method according to claim 1, characterized in that, In Step 4, after the residual signal passes through the joint blind source separation algorithm based on tensor decomposition, multiple source signals will be generated. Channel selection is required to extract the fetal electrocardiogram signal, then detect the position of the fetal QRS wave and smooth the fetal electrocardiogram signal, and then calculate the fetal heart rate and the average R-R interval.

7. The method according to claim 6, characterized in that, In step 4, the joint blind source separation algorithm based on tensor decomposition is used to process the mapping point Ψ x [t], and the statistical characteristics between multiple data sets are used to jointly estimate the demixing matrix, that is: Among them, represents a matrix composed of N mutually independent source signals of pregnant women in different datasets; A k ∈ R d×n represents the mixing matrix of different datasets, where d and n correspond to the dimensions of the observed signal and the source signal respectively; represents the observed data, corresponding to the feature space data of the k-th dataset; Assuming the dataset is In the first step, pair the dataset with other datasets pairwise to obtain (K - 1) combinations. Utilize the characteristics that the signal has a time structure and the correlation between datasets, and according to different time delays τ L construct L spatial covariance matrices of the datasets and with a mean of 0, that is: Stack L spatial covariance matrices in a tensor X; according to the column vector expression and slice expression of tensor CP decomposition, the factor matrices A and B correspond to the mixing matrices of two data sets respectively The row vectors of the factor matrix C correspond to the diagonal elements of the matrix Therefore, the tensor X can be expressed in the following form: In the formula, are respectively the n-th column of the mixing matrix; The cost function of the above tensor is: Applying the Alternating Least Squares (ALS) method to the above cost function can solve the mixing matrix for each combination. In the second step, take out the new matrix F composed of the n-th column vectors of (K - 1) estimated mixing matrices. Perform a column vector singular value decomposition on matrix F: FF T = UΣV T VΣ T U T = UΣΣ T U T F T F = VΣ T U T UΣV T = VΣ T ΣV T Select the left singular component corresponding to the maximum singular value as the mixing matrix Estimate the n-th column and repeat N times to obtain the data set of the mixing matrix; repeat the above steps until the mixing matrix of each data set is obtained. Finally, the demixing matrix is obtained by taking the inverse of each mixing matrix and applied to the observed data set to separate the independent source signals of each path.

8. The method according to claim 7, characterized in that, Select the fetal electrocardiogram signal from the source signals of each channel for channel selection; specifically: first use the Pan-Tompkins algorithm to detect the R peak points of each source signal, and detect the interval between adjacent QRS waves to calculate the instantaneous heart rate CH(t), that is: where RR(t) is the R-R interval at the t-th moment; then calculate the single residual channel smoothing index SMI. SMI is defined as the number of times the absolute value of the change in the instantaneous heart rate CH(t) within each minute segment exceeds 29 times per minute. Select the channel with the lowest SMI as the fetal electrocardiogram signal, and the marked R peak is the position of the fetal QRS wave.

9. An electronic device, comprising a memory and a processor, the memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method described in any one of claims 1-8.

10. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, it implements the steps of the method described in any one of claims 1-8.

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