A non-invasive fetal electrocardiogram signal extraction method based on multi-dimensional subspace representation and space-time tensor decomposition

Abstract

The application provides a non-invasive fetal electrocardiosignal extraction method based on multidimensional subspace representation and space-time tensor decomposition. The method firstly removes baseline drift, power line interference and electromyographic interference through various filters, then removes the maternal electrocardiosignal with the most influence through a template matching method, and then extracts the fetal electrocardiosignal through KPCA and a joint blind source separation method based on tensor decomposition, so that the accuracy of calculating the fetal heart rate and average R-R interval under the condition of nonlinearity and non-stationarity is enhanced. The non-invasive fetal electrocardiosignal extraction with high efficiency and high precision is realized.

Description

Technical Field

[0001] This invention relates to the field of fetal electrocardiogram (ECG) signal monitoring technology in biomedical signal processing, and in particular to a non-invasive method for extracting fetal ECG signals based on multidimensional subspace representation and time-space tensor decomposition. Background Technology

[0002] The incidence of birth defects in newborns with congenital heart disease in China is as high as 8.98%. Regular prenatal checkups are crucial to ensure the health of newborns. Currently, the main methods of pregnancy monitoring include non-invasive prenatal DNA screening, Doppler ultrasound, and magnetic resonance imaging (MRI). However, these methods are cumbersome to operate and pose serious safety risks with long-term use. Electrocardiography (ECG) is a technique for recording the electrical activity of the heart. An abdominal electrocardiogram (AECG) is obtained by placing multiple electrodes on the pregnant woman's abdomen, and then a 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 disease, hypoxia, and other problems, allowing for timely intervention and treatment, improving treatment outcomes and fetal survival rates.

[0003] Currently, various methods exist for extracting fetal electrocardiogram (ECG) signals, including Kalman filtering, singular value decomposition, nonnegative matrix factorization, deep learning (DP), wavelet transform, and independent component analysis. However, these methods still face numerous challenges. First, because the FECG signal is relatively weak, it is easily masked by the high-amplitude MECG signal, increasing the difficulty of signal separation and extraction. Second, the FECG signal is susceptible to environmental noise interference, which may lead to the loss of crucial information, thus affecting the accuracy of subsequent clinical diagnosis. Therefore, obtaining an ECG carrying accurate fetal heart rate information is a problem that needs to be solved in non-invasive fetal ECG signal extraction. Summary of the Invention

[0004] The purpose of this invention is to solve the problems in the prior art and propose a non-invasive method for extracting fetal electrocardiogram signals based on multidimensional subspace representation and time-space tensor decomposition.

[0005] This invention is achieved through the following technical solution: This invention proposes a non-invasive fetal electrocardiogram signal extraction method based on multidimensional subspace representation and time-space tensor decomposition, the method comprising the following steps:

[0006] Step 1: Preprocess the various ECG signals obtained from the pregnant woman's abdomen through electrodes, using high-pass filters, notch filters, and low-pass filters to successively eliminate baseline drift, electric field interference, and electromyographic interference, thereby reducing the influence of various interference signals;

[0007] Step 2: Select the template matching method to remove the maternal ECG signal from the preprocessed abdominal ECG signal. Cut the signal according to the average cardiac cycle of 0.8 seconds for adult ECG signals. Take the average of each signal segment to obtain the maternal ECG signal template. Obtain the residual signal by subtracting the abdominal ECG signal from the template maternal ECG signal.

[0008] Step 3: Before unmixing, the nonlinear residual signal is first mapped into a linearly separable signal in the feature space using kernel principal component analysis (KPCA) to deal with various nonlinear mixing situations in the real environment.

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

[0010] Furthermore, in step 1, the high-pass filter is designed based on a Butterworth filter to remove frequency components below 0.5Hz and retain frequencies of 8Hz and above; its amplitude-frequency response modulus squared is:

[0011]

[0012] Where N is the order of the filter, Ω c Here is the cutoff frequency of the high-pass filter; the notch filter is implemented using a second-order IIR filter, which performs deep attenuation near its designed center frequency while keeping other frequencies unchanged. Its amplitude-frequency response modulus squared is:

[0013]

[0014] Where f0 represents the frequency component to be filtered out; using a Butterworth low-pass filter to filter out signals above 200Hz, its amplitude-frequency response modulus squared is:

[0015]

[0016] Furthermore, in step 3, the nonlinear residual signal is mapped to a linearly separable signal in the feature space using KPCA. First, the residual signal is mapped to a signal in a high-dimensional space using a Gaussian kernel, and then PCA is performed to reduce the dimensionality to the feature space.

[0017] Furthermore, the kernel principal component analysis method uses a mapping function φ to map nonlinear 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) implicitly calculates the inner product in F without needing to determine 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 preserves the main features of the original data, selects an orthonormal basis for the d-dimensional subspace, and maps the data to a lower-dimensional subspace; let Φ(x[t]) be the mapping point of the observed data in the feature space, and use Φ x Represented as [Φ(x[1]),...,Φ(x[T])]; since the covariance matrix of the measurement data cannot be directly calculated, the kernel matrix is ​​used. Indirectly obtain the eigenvalues ​​and eigenvectors of the covariance matrix:

[0020]

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

[0022]

[0023] In the formula, Λ d E represents the first d eigenvalues ​​sorted from largest to smallest; d Let d represent the eigenvector matrix composed of the eigenvectors corresponding to d eigenvalues, column by column; multiplying the inverse of the orthonormal basis by the mapping point yields the coordinates of the d-dimensional feature space.

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

[0025] Furthermore, in step 4, the residual signal will generate multi-source signals after passing through the joint blind source separation algorithm based on tensor decomposition. Channel selection is required to extract the fetal electrocardiogram signal, then the fetal QRS wave position is detected and the fetal electrocardiogram signal is smoothed, and then the fetal heart rate and mean RR interval are calculated.

[0026] Furthermore, in step 4, a joint blind source separation algorithm based on tensor decomposition is used to process the mapping point Ψ. x[t] utilizes the statistical properties between multiple datasets to jointly estimate the unmixing matrix, i.e.:

[0027]

[0028] in, A[ represents a matrix consisting of N independent source signals from pregnant women in different datasets; A[] k ]∈R d×n This represents a mixing matrix of different datasets, where d and n correspond to the dimensions of the observed signal and the source signal, respectively. This represents the observed data, corresponding to the feature space data of the k-th dataset; assuming the dataset is... The first step is to convert the dataset Pairing the signal with other datasets yields (K-1) combinations. Utilizing the temporal structure of the signal and the correlation between datasets, and based on different time delays τ... L Construct a dataset with a mean of 0 and The L spatial covariance matrices are:

[0029]

[0030] Stack the L spatial covariance matrices into a tensor X; based on the column vector expression and slice expression of the tensor CP decomposition, we can obtain the factor matrices A and B, which correspond to the mixture matrices of the two datasets, respectively. The row vectors of the factor matrix C correspond to the matrix The diagonal elements are such that the tensor X can be represented in the following form:

[0031]

[0032] In the formula, They are respectively the mixing matrix The nth column; the cost function of the above tensor is:

[0033]

[0034] Applying Alternating Least Squares (ALS) to the above cost function allows us to solve for the mixture matrix of each combination. The second step is to extract (K-1) estimated mixing matrices. The new matrix F is formed by the nth column vectors. The singular value decomposition of the column vectors is then performed on 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] The left singular component with the maximum singular value is selected as the mixing matrix. The estimation of the nth column can be repeated N times to obtain the dataset. The mixing matrix is ​​obtained by repeating the above steps until the mixing matrix of each dataset is obtained. Finally, the unmixing matrix is ​​obtained by inverting each mixing matrix. This unmixing matrix can be applied to the observation dataset to separate the independent source signals.

[0038] Further, fetal electrocardiogram signals are selected from the source signals of each channel for channel selection; specifically, the Pan-Tompkins algorithm is first used to detect the R peak point of each source signal, and the interval between adjacent QRS waves is detected to calculate the instantaneous heart rate CH(t), i.e.:

[0039]

[0040] Where RR(t) is the RR interval at time t; then the smoothing index SMI of a single residual channel is calculated. SMI is defined as the number of times the absolute value of the instantaneous heart rate CH(t) change exceeds 29 times per minute within a minute segment. The channel with the lowest SMI is selected as the fetal electrocardiogram signal, and the marked R peak is the location of the fetal QRS wave.

[0041] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the non-invasive fetal electrocardiogram signal extraction method based on multidimensional subspace representation and time-space tensor decomposition.

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

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

[0044] This invention provides a non-invasive fetal electrocardiogram (ECG) signal extraction method based on multidimensional subspace representation and time-space tensor decomposition. The method first removes baseline drift, electric field interference, and electromyographic interference using various filters. Then, it removes the most influential maternal ECG signal using template matching. Finally, it extracts the fetal ECG signal using a joint blind source separation method based on KPCA and tensor decomposition, enhancing the accuracy of calculating fetal heart rate and mean RR interval under nonlinear and non-stationary conditions. This achieves efficient and high-precision non-invasive fetal ECG signal extraction. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0046] Figure 1 This is a flowchart of a non-invasive fetal electrocardiogram signal extraction method based on multidimensional subspace representation and time-space tensor decomposition, as described in this invention.

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

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

[0049] Figure 4 The image shows the pre-smoothed fetal electrocardiogram signal and the estimated R peak.

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

[0051] Figure 6 This is a graph showing the difference between the reference annotation RR interval and the estimated annotation RR interval. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] To address the problems in existing technologies, this invention proposes a non-invasive fetal electrocardiogram (FECG) signal extraction method based on multidimensional subspace representation and time-space tensor decomposition. To solve the problem of maternal FECG signals masking weak fetal FECG signals, template matching is used to remove the most influential maternal FECG signals, resulting in a residual signal containing both fetal and partial maternal FECG signals. Then, to obtain accurate fetal FECG signals, before using a joint blind source separation algorithm based on tensor decomposition, a kernel method is used to map the low-dimensional nonlinear residual signal to a high-dimensional space to satisfy the linear unmixing condition for blind source separation. Simultaneously, the mapped signal is divided into multiple datasets according to time, ensuring that each dataset maintains the stability of the FECG and various noise signal mixing process in a very short time. This solves the problem of fluctuations in fetal heartbeat rhythm and signal amplitude caused by fetal movement, maternal position changes, etc., leading to non-stationary characteristics of the signal in a short period.

[0054] Specifically, in combination Figures 1-6 This invention proposes a non-invasive method for extracting fetal electrocardiogram signals based on multidimensional subspace representation and time-space tensor decomposition. The method includes the following steps:

[0055] Step 1: Preprocess the various ECG signals obtained from the pregnant woman's abdomen through electrodes, using high-pass filters, notch filters, and low-pass filters to successively eliminate baseline drift, electric field interference, and electromyographic interference, thereby reducing the influence of various interference signals;

[0056] The dataset used in Step 1 was a non-invasive fetal electrocardiogram (NIECG): the dataset used in the 2013 Cardiology Challenge. A high-pass filter was used to remove baseline drift, which typically occurs at frequencies less than 0.5 Hz; a notch filter was used to filter out power line interference, which usually occurs at frequencies of 50 Hz or 60 Hz; and a low-pass filter was used to preserve fetal ECG signals from 0.5 Hz to 200 Hz, thereby reducing the influence of electromyography (EMG) signals over a wider frequency range.

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

[0058]

[0059] Where N is the order of the filter, Ω c Here is the cutoff frequency of the high-pass filter; the notch filter is implemented using a second-order IIR filter, which performs deep attenuation near its designed center frequency while keeping other frequencies unchanged. Its amplitude-frequency response modulus squared is:

[0060]

[0061] Where f0 represents the frequency component to be filtered out; using a Butterworth low-pass filter to filter out signals above 200Hz, its amplitude-frequency response modulus squared is:

[0062]

[0063] Step 2: Select the template matching method to remove the maternal ECG signal from the preprocessed abdominal ECG signal. Cut the signal according to the average cardiac cycle of 0.8 seconds for adult ECG signals. Take the average of each signal segment to obtain the maternal ECG signal template. Obtain the residual signal by subtracting the abdominal ECG signal from the template maternal ECG signal.

[0064] Step 3: Before unmixing, the nonlinear residual signal is first mapped into a linearly separable signal in the feature space using kernel principal component analysis (KPCA) to deal with various nonlinear mixing situations in the real environment.

[0065] Step 3 uses KPCA to map the nonlinear residual signal into a linearly separable signal in the feature space. First, the residual signal is mapped into a signal in a high-dimensional space using a Gaussian kernel, and then PCA is performed to reduce the dimensionality to the feature space, thereby reducing the problem of high computational complexity caused by excessive dimensionality.

[0066] Kernel principal component analysis (KPCA) uses a mapping function φ to map nonlinear 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) implicitly calculates the inner product in F without needing to determine the mapping function or the mapped data φ(x), i.e.:

[0067] K(x,y)=φ(x)·φ(y)=φ(x) T φ(y).

[0068] KPCA preserves the main features of the original data, selects an orthonormal basis for the d-dimensional subspace, and maps the data to a lower-dimensional subspace; let Φ(x[t]) be the mapping point of the observed data in the feature space, and use Φ x Represented as [Φ(x[1]),...,Φ(x[T])]; since the covariance matrix of the measurement data cannot be directly calculated, the kernel matrix is ​​used. Indirectly obtain the eigenvalues ​​and eigenvectors of the covariance matrix:

[0069]

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

[0071]

[0072] In the formula, Λ d E represents the first d eigenvalues ​​sorted from largest to smallest; d Let d represent the eigenvector matrix composed of the eigenvectors corresponding to d eigenvalues, column by column; multiplying the inverse of the orthonormal basis by the mapping point yields the coordinates of the d-dimensional feature space.

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

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

[0075] In step 4, the residual signal will generate multi-source signals after passing through the joint blind source separation algorithm based on tensor decomposition. Channel selection is required to extract the fetal electrocardiogram signal. Then, the fetal QRS wave position is detected and the fetal electrocardiogram signal is smoothed. Finally, the fetal heart rate and mean RR interval are calculated.

[0076] In step 4, a joint blind source separation algorithm based on tensor decomposition is used to process the mapping point Ψ. x [t] utilizes the statistical properties between multiple datasets to jointly estimate the unmixing matrix, i.e.:

[0077]

[0078] in, A[ represents a matrix consisting of N independent source signals from pregnant women in different datasets; A[] k ]∈R d×n This represents a mixing matrix of different datasets, where d and n correspond to the dimensions of the observed signal and the source signal, respectively. This represents the observed data, corresponding to the feature space data of the k-th dataset; assuming the dataset is... The first step is to convert the dataset Pairing the signal with other datasets yields (K-1) combinations. Utilizing the temporal structure of the signal and the correlation between datasets, and based on different time delays τ... L Construct a dataset with a mean of 0 and The L spatial covariance matrices are:

[0079]

[0080] Stack the L spatial covariance matrices into a tensor X; based on the column vector expression and slice expression of the tensor CP decomposition, we can obtain the factor matrices A and B, which correspond to the mixture matrices of the two datasets, respectively. The row vectors of the factor matrix C correspond to the matrix The diagonal elements are such that the tensor X can be represented in the following form:

[0081]

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

[0083]

[0084] Applying Alternating Least Squares (ALS) to the above cost function allows us to solve for the mixture matrix of each combination. The second step is to extract (K-1) estimated mixing matrices. The new matrix F is formed by the nth column vectors. The singular value decomposition of the column vectors is then performed on 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] The left singular component with the maximum singular value is selected as the mixing matrix. The estimation of the nth column can be repeated N times to obtain the dataset. The mixing matrix is ​​obtained by repeating the above steps until the mixing matrix of each dataset is obtained. Finally, the unmixing matrix is ​​obtained by inverting each mixing matrix. This unmixing matrix can be applied to the observation dataset to separate the independent source signals.

[0088] Fetal ECG signals are selected from the source signals of each channel for channel selection; specifically, the Pan-Tompkins algorithm is first used to detect the R peak point of each source signal, and the interval between adjacent QRS waves is detected to calculate the instantaneous heart rate CH(t), i.e.:

[0089]

[0090] Where RR(t) is the RR interval at time t; then the smoothing index SMI of a single residual channel is calculated. SMI is defined as the number of times the absolute value of the instantaneous heart rate CH(t) change exceeds 29 times per minute within a minute segment. The channel with the lowest SMI is selected as the fetal electrocardiogram signal, and the marked R peak is the location of the fetal QRS wave.

[0091] Example

[0092] The purpose of this invention is to address the problem of low accuracy in non-invasive fetal electrocardiogram (FECG) signal extraction. A method combining template matching and blind source separation is used to further improve the accuracy of FECG signal extraction, outputting information such as heart rate and RR interval. To achieve this goal, this invention proposes a non-invasive fetal electrocardiogram (FECG) signal extraction method based on multidimensional subspace representation and time-space tensor decomposition, the method comprising the following steps:

[0093] Step 1: Preprocess the various ECG signals obtained from the pregnant woman's abdomen through electrodes, using high-pass filters, notch filters, and low-pass filters to successively eliminate baseline drift, electric field interference, and electromyographic interference, thereby reducing the influence of various interference signals;

[0094] The dataset used in Step 1 was a non-invasive fetal electrocardiogram (NITCA) dataset: the dataset used in the 2013 Cardiology Challenge, containing 75 one-minute fetal ECG recordings, each recording containing 4 non-invasive abdominal signals, with a sampling rate of 1000 Hz. Each recording has a reference annotation for the location of each QRS complex obtained from fetal scalp electrodes. Seven recordings in the dataset (a33, a38, a47, a52, a54, a71, and a74) had annotation errors; the remaining recordings could be used for detecting the location of the fetal ECG QRS complex.

[0095] Fetal electrocardiogram (ECG) signals are transmitted to the abdominal wall through amniotic fluid, the maternal abdominal cavity, and skin, and are collected by electrodes. These signals contain MECG, FECG, and various noise interferences. High-pass, notch, and low-pass filters are used on the multi-channel AEG to eliminate these noise interferences. The high-pass filter, based on a Butterworth filter design, is used to remove frequency components below 0.5Hz, retaining frequencies of 8Hz and above; its amplitude-frequency response modulus squared is:

[0096]

[0097] Where N is the order of the filter, Ω c Here is the cutoff frequency of the high-pass filter; the notch filter is implemented using a second-order IIR filter, which performs deep attenuation near its designed center frequency while keeping other frequencies unchanged. Its amplitude-frequency response modulus squared is:

[0098]

[0099] Where f0 represents the frequency component to be filtered out; using a Butterworth low-pass filter to filter out signals above 200Hz, its amplitude-frequency response modulus squared is:

[0100]

[0101] Step 2: Select the template matching method to remove the maternal ECG signal from the preprocessed abdominal ECG signal. Cut the signal according to the average cardiac cycle of 0.8 seconds for adult ECG signals. Take the average of each signal segment to obtain the maternal ECG signal template. Obtain the residual signal by subtracting the abdominal ECG signal from the template maternal ECG signal.

[0102] Step 3: Before unmixing, the nonlinear residual signal is first mapped into a linearly separable signal in the feature space using kernel principal component analysis (KPCA) to deal with various nonlinear mixing situations in the real environment.

[0103] Step 3 uses KPCA to map the nonlinear residual signal into a linearly separable signal in the feature space. First, the residual signal is mapped into a signal in a high-dimensional space using a Gaussian kernel, and then PCA is performed to reduce the dimensionality to the feature space, thereby reducing the problem of high computational complexity caused by excessive dimensionality.

[0104] Kernel principal component analysis (KPCA) uses a mapping function φ to map nonlinear 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) implicitly calculates the inner product in F without needing to determine the mapping function or the mapped data φ(x), i.e.:

[0105] K(x,y)=φ(x)·φ(y)=φ(x) T φ(y).

[0106] Some kernel functions map input data to high-dimensional or even infinite-dimensional spaces. This high-dimensional space increases the computational complexity of subsequent blind source separation algorithms. Therefore, it is necessary to preserve the main features of the original data using KPCA, select an orthonormal basis for the d-dimensional subspace, and map the data to a low-dimensional subspace. Let Φ(x[t]) be the mapping point of the observed data in the feature space, and use Φ... x Represented as [Φ(x[1]),...,Φ(x[T])]; since the covariance matrix of the measurement data cannot be directly calculated, the kernel matrix is ​​used. Indirectly obtain the eigenvalues ​​and eigenvectors of the covariance matrix:

[0107]

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

[0109]

[0110] In the formula, Λ d E represents the first d eigenvalues ​​sorted from largest to smallest; d Let d represent the eigenvector matrix composed of the eigenvectors corresponding to d eigenvalues, column by column; multiplying the inverse of the orthonormal basis by the mapping point yields 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 a joint blind source separation algorithm based on tensor decomposition to extract fetal electrocardiogram signals, then detect the location of the fetal QRS wave and calculate the fetal heart rate.

[0113] In step 4, the residual signal will generate multi-source signals after passing through the joint blind source separation algorithm based on tensor decomposition. Channel selection is required to extract the fetal electrocardiogram signal. Then, the fetal QRS wave position is detected and the fetal electrocardiogram signal is smoothed. Finally, the fetal heart rate and mean RR interval are calculated.

[0114] In step 4, a joint blind source separation algorithm based on tensor decomposition is used to process the mapping point Ψ. x [t] utilizes the statistical properties between multiple datasets to jointly estimate the unmixing matrix, i.e.:

[0115]

[0116] in, A[ represents a matrix composed of N independent source signals, including mECG, fECG, artifacts, and noise, from different datasets of pregnant women; k ]∈R d×n This represents a mixing matrix of different datasets, where d and n correspond to the dimensions of the observed signal and the source signal, respectively. This represents the observed data, corresponding to the feature space data of the k-th dataset; assuming the dataset is... The first step is to convert the dataset Pairing the signal with other datasets yields (K-1) combinations. Utilizing the temporal structure of the signal and the correlation between datasets, and based on different time delays τ... L Construct a dataset with a mean of 0 and The L spatial covariance matrices are:

[0117]

[0118] Stack the L spatial covariance matrices into a tensor X; based on the column vector expression and slice expression of the tensor CP decomposition, we can obtain the factor matrices A and B, which correspond to the mixture matrices of the two datasets, respectively. The row vectors of the factor matrix C correspond to the matrix The diagonal elements are such that the tensor X can be represented in the following form:

[0119]

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

[0121]

[0122] Applying Alternating Least Squares (ALS) to the above cost function allows us to solve for the mixture matrix of each combination. The second step is to extract (K-1) estimated mixing matrices. The new matrix F is formed by the nth column vectors. The singular value decomposition of the column vectors is then performed on 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] The left singular component with the maximum singular value is selected as the mixing matrix. The estimation of the nth column can be repeated N times to obtain the dataset. The mixing matrix is ​​obtained by repeating the above steps until the mixing matrix of each dataset is obtained. Finally, the unmixing matrix is ​​obtained by inverting each mixing matrix. This unmixing matrix can be applied to the observation dataset to separate the independent source signals.

[0126] Fetal ECG signals are selected from the source signals of each channel for channel selection; specifically, the Pan-Tompkins algorithm is first used to detect the R peak point of each source signal, and the interval between adjacent QRS waves is detected to calculate the instantaneous heart rate CH(t), i.e.:

[0127]

[0128] Where RR(t) is the RR interval at time t; then the smoothing index SMI of a single residual channel is calculated. SMI is defined as the number of times the absolute value of the instantaneous heart rate CH(t) change exceeds 29 times per minute within a minute segment. The channel with the lowest SMI is selected as the fetal electrocardiogram signal, and the marked R peak is the location of the fetal QRS wave.

[0129] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the non-invasive fetal electrocardiogram signal extraction method based on multidimensional subspace representation and time-space tensor decomposition.

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

[0131] The memory in this application embodiment can be volatile memory or non-volatile memory, or it can include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be 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 random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DRRAM). It should be noted that the memory used in the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0132] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as 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, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state disks (SSDs)).

[0133] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0134] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The processor can 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, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0135] The above provides a detailed description of a non-invasive fetal electrocardiogram signal extraction method based on multidimensional subspace representation and time-space tensor decomposition proposed in this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A non-invasive method for extracting fetal electrocardiogram signals based on multidimensional subspace representation and time-space tensor decomposition, characterized in that, The method includes the following steps: Step 1: Preprocess the various ECG signals obtained from the pregnant woman's abdomen through electrodes, using high-pass filters, notch filters, and low-pass filters to successively eliminate baseline drift, electric field interference, and electromyographic interference, thereby reducing the influence of various interference signals; Step 2: Select the template matching method to remove the maternal ECG signal from the preprocessed abdominal ECG signal. Cut the signal according to the average cardiac cycle of 0.8 seconds for adult ECG signals. Take the average of each signal segment to obtain the maternal ECG signal template. Obtain the residual signal by subtracting the abdominal ECG signal from the template maternal ECG signal. Step 3: Before unmixing, the nonlinear residual signal is first mapped into a linearly separable signal in the feature space using kernel principal component analysis (KPCA) to deal with various nonlinear mixing situations in the real environment. Step 4: Use a joint blind source separation algorithm based on tensor decomposition to extract fetal electrocardiogram signals, then detect the location of the fetal QRS wave and calculate the fetal heart rate; In step 4, the residual signal will generate multi-source signals after passing through the joint blind source separation algorithm based on tensor decomposition. Channel selection is required to extract the fetal electrocardiogram signal. Then, the fetal QRS wave position is detected and the fetal electrocardiogram signal is smoothed. Finally, the fetal heart rate and mean RR interval are calculated. In step 4, a joint blind source separation algorithm based on tensor decomposition is used to process the mapping points. The unmixing matrix is ​​jointly estimated by utilizing the statistical properties of multiple datasets, i.e.: in, This represents a matrix composed of N independent source signals from pregnant women in different datasets; This represents a mixing matrix of different datasets, where d and n correspond to the dimensions of the observed signal and the source signal, respectively. This represents the observed data, corresponding to the first... Feature space data for each dataset; assuming the dataset is... The first step is to convert the dataset Pairing with other datasets yields This combination utilizes the temporal architecture of signals and the correlation between datasets, based on different time delays. Construct a dataset with a mean of 0 and The L spatial covariance matrices are: … Will The spatial covariance matrices are stacked on a tensor. In the middle; based on the column vector expression and slice expression of tensor CP decomposition, the factor matrices A and B can be obtained as the mixture matrices corresponding to the two datasets, respectively. , The row vectors of the factor matrix C correspond to the matrix The diagonal elements, therefore the tensor It can be expressed in the following forms: In the formula, , They are respectively the mixing matrix , The The cost function of the above tensor is: Applying Alternating Least Squares (ALS) to the above cost function allows us to solve for the mixture matrix of each combination. The second step is to remove it. A number of estimated mixing matrices The A new matrix composed of column vectors For the matrix Perform singular value decomposition on column vectors: The left singular component with the maximum singular value is selected as the mixing matrix. The estimation of the nth column can be repeated N times to obtain the dataset. The mixing matrix is ​​obtained by repeating the above steps until the mixing matrix of each dataset is obtained. Finally, the unmixing matrix is ​​obtained by inverting each mixing matrix. This unmixing matrix can be applied to the observation dataset to separate the independent source signals.

2. The method according to claim 1, characterized in that, In step 1, the high-pass filter is designed based on a Butterworth filter to remove frequency components below 0.5Hz and retain frequencies of 8Hz and above; its amplitude-frequency response modulus squared is: in, Let the order be the filter order. Here is the cutoff frequency of the high-pass filter; the notch filter is implemented using a second-order IIR filter, which performs deep attenuation near its designed center frequency while keeping other frequencies unchanged. Its amplitude-frequency response modulus squared is: in, This represents the frequency components to be filtered out; using a Butterworth low-pass filter to filter out signals above 200Hz, its amplitude-frequency response modulus squared is: 。 3. The method according to claim 1, characterized in that, Step 3 uses KPCA to map the nonlinear residual signal into a linearly separable signal in the feature space. First, the residual signal is mapped into a signal in a high-dimensional space using a Gaussian kernel, and then PCA is performed to reduce the dimensionality to the feature space.

4. The method according to claim 3, characterized in that, Kernel principal component analysis uses mapping functions. Input space Nonlinear data points Mapping to a high-dimensional feature space In ,Right now: Use kernel functions Implicit computation The inner product in the matrix does not require determining the mapping function or the mapped data. ,Right now: 。 5. The method according to claim 4, characterized in that, KPCA preserves the main features of the original data, selects an orthonormal basis for the d-dimensional subspace, and maps the data to a lower-dimensional subspace; let the mapping point of the observed data in the feature space be... ,use express Since the covariance matrix of the measurement data cannot be directly calculated, a kernel matrix is ​​used. Indirectly obtain the eigenvalues ​​and eigenvectors of the covariance matrix: Among them, diagonal array From eigenvalues Composed along the diagonal; eigenvector matrix Eigenvectors corresponding to each eigenvalue Composed of columns; therefore, the orthonormal basis of the d-dimensional feature space can be represented by the eigenvector matrix and the diagonal matrix as follows: In the formula, This indicates the first few features sorted from largest to smallest. One eigenvalue; express The eigenvector matrix is ​​formed by the column-wise eigenvectors corresponding to each eigenvalue; multiplying the inverse of the orthonormal basis by the mapping point yields the coordinates of the d-dimensional feature space. 。 6. The method according to claim 1, characterized in that, Fetal ECG signals are selected from the source signals of each channel for channel selection. Specifically, the Pan-Tompkins algorithm is first used to detect the R peak point of each source signal, and the interval between adjacent QRS waves is detected to calculate the instantaneous heart rate. ,Right now: in, It is the first The RR interval at each time point; then the smoothing index SMI of a single residual channel is calculated, where SMI is defined as the instantaneous heart rate within each minute segment. If the absolute value of the change exceeds 29 times per minute, the channel with the lowest SMI is selected as the fetal ECG signal, and the marked R peak is the location of the fetal QRS wave.

7. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-6.

8. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-6.

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