Self-adaptive noninvasive fetal electrocardiosignal extraction method based on logarithmic hyperbolic secant function

Abstract

The invention discloses a self-adaptive noninvasive fetal electrocardiosignal extraction method based on a logarithmic hyperbolic secant function. The method comprises the following steps: constructing a mother abdomen electrocardiosignal model; based on a self-adaptive filtering framework, inputting a chest electrocardiosignal MECG of the mother as a reference signal and an abdomen signal AECG as an expected signal, and calculating filtering output; defining a target function and updating a weight coefficient; the extracted fetal electrocardiosignals are output through Monte Carlo experiment optimization parameter combination; the invention further lays a foundation for long-term real-time monitoring of puerperae and fetuses through portable equipment.

Description

Technical Field

[0001] The present invention relates to the technical field of biomedical signal processing, and in particular to an adaptive non-invasive fetal electrocardiogram signal extraction method based on a logarithmic hyperbolic secant function. Background Art

[0002] The fetal electrocardiogram (FECG) can directly reflect the health of the fetus and has high diagnostic value. Certain fetal physiological changes, such as arrhythmias, fetal distress, a prolonged PQRS duration, and congenital heart disease, can be reflected in the FECG. It is a sensitive indicator for the early diagnosis of intrauterine fetal distress, with a success rate of over 90% for detecting intrauterine fetal abnormalities. There are two methods for measuring fetal ECG signals: invasive direct scalp measurement and non-invasive (non-invasive) indirect abdominal measurement. Direct scalp measurement, performed only during labor, involves placing electrodes on the fetal scalp. It is an invasive method and cannot be used for long-term monitoring or perinatal monitoring. Only non-invasive indirect abdominal measurement allows for long-term continuous monitoring without causing harm to the fetus. However, abdominal ECG signals, in addition to the fetal ECG, are mixed with various noise sources (such as power line interference, muscle contractions, respiration, skin resistance interference, and instrument noise) and the maternal ECG signal. In real-world scenarios, these noise sources are typically pulsed / non-Gaussian in nature, and the maternal ECG amplitude is much larger than the fetal ECG amplitude. The two spectra are similar and largely overlap. Obtaining a clear and accurate fetal ECG from non-invasive abdominal ECG signals is both a hot topic and a challenge in fetal ECG signal research.

[0003] Adaptive filtering (AF) methods are highly preferred for fetal ECG extraction. Compared to other algorithms, FECG extraction algorithms based on adaptive filtering have low computational complexity and are easy to implement. By continuously adjusting the weights of the adaptive filter according to an optimal criterion, they can simultaneously and rapidly track the non-stationary variations of both the maternal ECG signal in the reference channel and the mixed abdominal ECG signal in the original channel. Adaptive fetal ECG extraction methods primarily suppress the maternal ECG component in the mixed abdominal ECG signal, thereby separating the fetal ECG signal from the mixed abdominal ECG signal to a clearer level. This significantly improves fetal ECG detection accuracy. Among these, the traditional least mean square (LMS) algorithm and its family, including normalized LMS (NLMS) and improved proportional normalized LMS (IPNLMS), are the most widely used. However, the above-mentioned adaptive filtering algorithms derived from LMS are all constructed based on the mean square error (MSE) criterion because of its simple calculation and optimality under the Gaussian assumption. However, the algorithm based on the MSE criterion can only obtain the optimal estimate under the Gaussian noise assumption and its performance deteriorates in non-Gaussian noise environments. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is to provide an adaptive non-invasive fetal ECG signal extraction method based on the logarithmic hyperbolic secant function to solve the problem of fetal ECG signal and maternal signal overlapping and difficulty in distinguishing in non-invasive fetal ECG signal extraction; and the problem of fetal ECG signal being contaminated by pulse signals and poor extraction quality.

[0005] Technical solution: The present invention provides an adaptive non-invasive fetal electrocardiogram signal extraction method based on a logarithmic hyperbolic secant function, comprising the following steps:

[0006] (1) Construct a model of the mother's abdominal ECG signal: AECG = FECG + m(n) + v(n) = FECG + 0.2MECG + noise; where v(n) is an impulse noise that obeys a symmetric α-stable distribution SαS, and its generation parameters are adjusted by the generalized signal-to-noise ratio (GSNR) and signal energy.

[0007] (2) Based on the adaptive filtering framework, the mother's chest ECG signal MECG is input as the reference signal x(n), and the abdomen signal AECG is input as the desired signal d(n). The filtered output is calculated as follows: y(n) = w(n) T x(n); where w(n) T is the adaptive filter weight coefficient;

[0008] (3) Define the objective function and update the weight coefficient; the objective function is: The weight update rule is: in μ is the step size factor;

[0009] e(n)=d(n)-y(n);

[0010] (4) The parameter combination, i.e., the filter order L and the step size μ, is optimized through Monte Carlo experiments, and the extracted fetal ECG signal e(n) is output.

[0011] Furthermore, the impulse noise v(n) of the symmetric α-stable distribution SαS is generated in the following way: the characteristic index α∈(0,2] controls the impulse intensity, and the smaller α is, the stronger the noise impulse is; the generation parameter β=δ=0, where P dn represents the energy of the desired signal d(n), and GSNR is the generalized signal-to-noise ratio.

[0012] Furthermore, the gradient calculation of the objective function includes: the first-order derivative of the instantaneous objective function is:

[0013]

[0014] Where ln(·) is the logarithm with base e, sech(·) is the hyperbolic secant function, and the parameter λ>0.

[0015] Furthermore, the parameter λ is set to λ = 3 to preserve the linear characteristics of the fetal ECG signal. The approximate linear interval of the objective function is determined by the maximum curvature point, and combined with the fetal ECG signal amplitude estimate H, the weight update rule is adjusted as follows: in, Estimation of fetal ECG signal amplitude.

[0016] Furthermore, the performance of the adaptive filter was evaluated by the following indicators: signal-to-noise ratio (SNR), root mean square error (RMSE), percentage root mean square difference (PRD); sensitivity (Se), positive predictive value (PPV), and F1 score of R-peak detection.

[0017] Furthermore, the calculation formula of the indicator is:

[0018]

[0019] Where s(n) is the pure fetal ECG signal provided by the dataset, e(n) is the extracted fetal ECG signal, and L is the filter order.

[0020]

[0021] Among them, TP is the number of fetal R-peaks correctly detected within ±10 milliseconds of the reference annotation; FP is the number of fetal R-peaks detected as R-peaks that are actually not R-peaks; FN is the number of fetal R-peaks that were missed.

[0022] Furthermore, the method is applicable to portable fetal heart monitoring equipment, and can achieve real-time extraction of fetal ECG signals by suppressing maternal ECG components and pulse noise.

[0023] An electronic device described in the present invention includes a memory and a processor, wherein the memory stores a computer program, and the processor implements any of the methods described above when executing the program.

[0024] The computer-readable storage medium of the present invention stores a computer program, and when the program is executed by a processor, any of the methods described above is implemented.

[0025] Beneficial Effects: Compared with existing technologies, this invention offers the following significant advantages: It improves the robustness and stability of adaptive filtering algorithms, avoids the performance degradation of traditional mean square error-based adaptive filtering algorithms under impulse noise, and expands the practical application of hyperbolic functions. Furthermore, this invention demonstrates promising results in noninvasive fetal ECG signal extraction, further paving the way for long-term, real-time monitoring of mothers and fetuses using portable devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is the signal model extracted by the present invention;

[0027] Figure 2 Schematic diagram of the relationship between the gradient and error of the objective function of the present invention as λ changes;

[0028] Figure 3 This is a graph showing the functional behavior of the tanh(λx) function of the present invention for different λ values;

[0029] Figure 4 It is a graphic response of the present invention performing fetal electrocardiogram signal extraction on the object marked as subject-01 in the FECGSYN database under the impulse noise background of α=2.0 and α=1.4.

[0030] Figure 5 This is the graphical response of the present invention to extract fetal ECG signals from objects in the Daisy database under the background of α=1.4 impulse noise.

[0031] Figure 6 It is a graphic response of the present invention performing fetal electrocardiogram signal extraction on the object marked as ecgca274 in the NIFECG database under the background of α=1.4 impulse noise. DETAILED DESCRIPTION

[0032] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0033] like Figure 1 As shown, an embodiment of the present invention provides an adaptive non-invasive fetal electrocardiogram signal extraction method based on a logarithmic hyperbolic secant function, comprising the following steps:

[0034] A.According to Figure 1 The abdominal electrocardiogram (AECG) of a pregnant woman consists of several components: the FECG signal, the maternal ECG component m(n), and noise v(n). Studies have shown that the amplitude of the maternal ECG component m(n) is correlated with the MECG, typically 0.2 times the amplitude of the maternal thorax electrocardiogram (MECG). Therefore, based on the MECG signal, the AECG can be calculated as:

[0035] AECG=FECG+m(n)+v(n)=FECG+0.2MECG+noise.

[0036] B. In order to separate the pure fetal ECG signal, it is often chosen to adaptively remove the maternal ECG component m(n) and noise v(n) from the AECG signal through a filter. Adaptive filtering extracts the details of the FECG signal, such as Figure 1 As shown, the reference input signal x(n) is the mother's chest signal, and the abdominal signal AECG is the desired signal d(n). Based on the input signal x(n) and the filter coefficient w(n), the filtered output signal y(n) is calculated:

[0037] y(n)=w(n) T x(n),

[0038] where x(n) = [x(n), x(n-1), ..., x(n-L+1)] T ,w(n)=[w1(n),w2(n),...,w L (n)] T , L is the filter order.

[0039] C. According to the expression in μ is the step size factor. The filter adaptively updates the filter weight coefficient and minimizes the objective function J(e(n)). At this time, the error signal e(n) = d(n) - y(n) generated by the filtered output y(n) and the desired signal d(n) is the required fetal ECG signal.

[0040] The additive noise v(n) in step A is simulated by an α-stable distribution with a heavy-tailed probability density function. The specific steps are as follows:

[0041] A1. According to the expression φ(t) = exp{jδt-γ α |t| α [1+jβsgn(t)ε(t,α)]} generates impulse noise S α (β, γ, δ), where

[0042]

[0043] α∈(0,2] represents the characteristic exponent that controls the thickness of the tail of the probability density function. The smaller the value of α, the greater the pulse intensity. β∈[-1,1] is the symmetry parameter, which can describe the slope of the distribution. γ∈(0,+∞) is the dispersion parameter of the variance similar to the Gaussian distribution. δ∈(-∞,+∞) is the location parameter. When α∈(0,1) or α∈[1,2], δ represents the median or mean, respectively. When β=0, the α-stable distribution is symmetric about δ and is called the symmetric α-stable distribution (SαS) distribution. For the SαS distribution, when α=2, the SαS distribution is equivalent to the Gaussian distribution.

[0044] A2. The additive noise v(n) is modeled using the SαS distribution. Since v(n) does not have a second-order statistic, we use the generalized power β=δ=0. In place of the traditional power, P dn α represents the energy of the desired signal d(n), and GSNR is the generalized signal-to-noise ratio. The energy of the fetal ECG signal and the maternal ECG component m(n) are fixed. By varying the values ​​of α and GSNR, the energy of the noise v(n) is varied. Noise of varying pulse intensities is generated to adjust the signal-to-noise ratio between the pure fetal ECG signal and the noise v(n). For each noise combination, 100 sequences are generated as additive noise sources v(n) and saved for future use.

[0045] In the present invention, a novel objective function is proposed as J(e(n)) in step C, and a corresponding adaptive filtering algorithm is derived for non-invasive fetal ECG signal extraction. Step C specifically includes the following steps:

[0046] C1. According to the objective function Calculate the first derivative of the objective function.

[0047]

[0048] Where ln(·) is the logarithm with base e, sech(·) is the hyperbolic secant function, and the parameter λ>0. Figure 2, the objective function is oddly symmetric at the origin and has a certain peak value. When e(n) is large, the amplitude of the gradient approaches 0, indicating strong robustness to outliers. In addition, the gradient change caused by changes in e(n) is very small, and regardless of the value of λ, the gradient peak is always less than 0.3. In other words, although the presence of impulse noise outliers may cause large errors, the impact of such outliers is minimal due to the limiting effect of the objective function, which is exactly what a robust algorithm expects.

[0049] C2: Take the instantaneous form of the objective function Calculate the first-order derivative of the instantaneous objective function with respect to the weight coefficient w(n).

[0050]

[0051] C3: Based on the stochastic gradient descent method, the weight coefficient update rule of the hyperbolic secant adaptive filtering algorithm (LHSAF) composed of the objective function is derived.

[0052]

[0053] Since the fetal ECG signal has a small amplitude, an unknown amplitude, and the components of the maternal abdominal signal AECG are complex, it is difficult to capture. In traditional adaptive algorithms, Gaussian noise can be suppressed by second-order statistics. For more complex noise that obeys an α-stable distribution, the algorithm proposed in the present invention starts with retaining the signal of interest (SOI) and flexibly adjusts the amplitude of the SOI and noise, rather than removing the noise as in traditional methods. In order to retain the information of the original fetal ECG signal as much as possible and reduce the influence of impulse noise, the present invention introduces a factor similar to the hyperbolic tangent transform in the weight coefficient update formula in step C3. The specific steps are as follows:

[0054] C3-1: Define the hyperbolic tangent transformation based on the corresponding point of the maximum curvature of the tanh(λx) function. Figure 3, tanh(λx) is approximately linear near x = 0. As |e(n)| increases, tanh(λx) gradually increases and tends to saturation. Therefore, the function can be divided into two parts: the approximately linear interval (ALI) near 0 and the saturation interval (SI) far from 0. When the function curvature reaches its maximum, the corresponding x0 is the endpoint of the ALI. As the value of λ changes, the linear interval is extended or compressed. The hyperbolic tangent transform is defined based on the corresponding point x0 of the maximum curvature, that is:

[0055]

[0056] Among them, H is the scale parameter, It is called the hyperbolic tangent transformation factor.

[0057] C3-2: Solve the approximate linear interval of J'(e(n)) in C1 according to the definition of hyperbolic tangent transformation. Figure 2 , the objective function curve used in the present invention is similar to the curve of tanh(λx), that is, they are both approximately linear near the 0 point. The difference is that J′(e(n)) shows an attenuation characteristic away from the 0 point, which is called the attenuation interval (AI). Therefore, when solving the linear interval of J′(e(n)), the point with the maximum curvature may be located in the inhibition interval, so the linear interval cannot be obtained by solving the maximum curvature method. It is worth noting that J′(e(n)) is monotonically bounded in the approximate linear interval, so the range of the approximate linear interval can be determined by solving the point where the function obtains the maximum value in ALI. Therefore, let Solving this equation gives the approximate linear interval of the J′(e(n)) function.

[0058] C3-3: According to the hyperbolic tangent transformation, in the approximate linear interval, the function can be approximated as a straight line with a slope of k at the zero point, and the closer k is to 1, the more complete the SOI information is retained. According to numerical calculations, when λ=3, the slope is closest to 1, so this invention takes λ=3 as an example to solve

[0059]

[0060] We get e0(n) = 0, e1(n) ≈ -0.35, and e2(n) ≈ 0.35. Therefore, the approximate linear interval of the J′(e(n)) function is approximately [-0.35, 0.35], and this interval changes with λ.

[0061] C3-4: Substitute the solution in C3-3 into C3-1 to obtain the definition of the hyperbolic tangent transformation, which is:

[0062]

[0063] Among them, H is the scale parameter.

[0064] C3-5: According to Figure 1 In the signal model, SOI is the FECG part of the mother's abdominal signal AECG, but its amplitude range cannot be determined. The mother's signal is about 5 to 10 times that of the fetus. Therefore, the amplitude range of FECG can be estimated by the known mother's chest ECG signal MECG. In this method, the amplitude of FECG is estimated as Set the range of H as follows:

[0065]

[0066] C3-6: Substitute the results of C3-4 and C3-5 into C3, and adjust the weight coefficient update formula of the logarithmic hyperbolic secant adaptive extraction algorithm proposed in the present invention to:

[0067]

[0068] in, The step size factor μ∈(0,1). The algorithm after introducing the hyperbolic tangent transform is called the improved logarithmic hyperbolicsecant adaptive filtering (ILHSAF).

[0069] Figure 4 (a) is the chest signal and abdominal ECG signal of the mother labeled as subject-01 in the FECGSYN database.

[0070] The circles in the mother's abdominal ECG signal diagram mark, from left to right, the complete overlap, no overlap, and partial overlap of the maternal ECG component and the fetal ECG signal in the abdominal signal.

[0071] Figure 4 (b) is the impulse noise S α＝2.0 The graphical responses of the FECG extracted by each algorithm using subject-01 under the (0, γ, 0) background. The black dotted circle indicates the presence of residual maternal ECG components in the extracted fetal ECG signal.

[0072] Figure 4 (c) is the impulse noise S α＝1.4 The graphical responses of the FECG extracted by each algorithm using subject-01 under the (0, γ, 0) background. The black dotted circle indicates the presence of residual maternal ECG components in the extracted fetal ECG signal.

[0073] Figure 5 (a) shows a four-channel abdominal ECG recording of a subject from the Daisy database. The black circles marked in channel 1 represent, from left to right, the cases where the maternal ECG component and the fetal ECG signal overlap completely, partially, or not at all in that abdominal ECG recording.

[0074] Figure 5 (b) is the performance of each algorithm in the impulse noise S α＝1.4 Graphical response of the fetal ECG signal extracted from channel 1 of a Daisy database subject in a (0, γ, 0) background. The black dotted circle indicates the presence of residual maternal ECG components in the extracted fetal ECG signal.

[0075] Figure 6 is the performance of each algorithm in impulse noise S α＝1.4 The graphical response of the fetal electrocardiogram signal is extracted using the object labeled ecgca274 in the NIFECG database under the background of (0, γ, 0). The present invention can extract fetal electrocardiogram signal information to the greatest extent, and the QRS waveform of the fetal electrocardiogram signal is the most complete.

[0076] The operating steps for actual fetal ECG signal extraction on the MATLAB 2022b platform are as follows:

[0077] a. Download experimental data such as maternal chest ECG signals and clean fetal ECG signals from the FECGSYN, Daisy, and NIFECG databases using the WFDB toolbox in MATLAB. Use the maternal chest ECG signals as the reference input x(n) of the signal model.

[0078] b. According to steps A1 and A2, additive noise v(n) of different pulse intensities is obtained, and according to the expression in step A and the input signal x(n) in step a, the mother's abdominal ECG signal AECG is generated as the reference input signal d(n).

[0079] c. Use the different x(n) and d(n) obtained in steps a and b as the inputs of the LHSAF and ILHSAF algorithms, and use Monte Carlo experiments to find the parameter combination that achieves the optimal extraction of the fetal ECG signal e(n). The parameter range is set to the filter order L∈(0,150) and the step size factor μ∈(0,1).

[0080] d. For the synthetic database, the performance of the algorithm in fetal ECG signal extraction was evaluated based on the statistical data of signal-to-noise ratio (SNR), root mean square error (RMSE), and percentage of the quadratic mean difference (PRD), using known pure fetal ECG signals as a reference. For the real database, the recognition results of the ECG R peak were used to evaluate the performance of the extracted fetal ECG signals.

[0081] e. Based on the graphical response results and statistical data or R-peak identification results, determine whether the fetal ECG signal is successfully extracted from the maternal ECG signal and impulse noise.

[0082] The statistical data expression in step d is as follows:

[0083]

[0084]

[0085] Where s(n) is the pure fetal ECG signal provided by the dataset, e(n) is the extracted fetal ECG signal, and L is the filter order.

[0086] The R peak identification results in step d are given by the following indicators:

[0087]

[0088] Where TP is the number of correctly detected fetal R-peaks within ±10 milliseconds of the reference annotation; FP is the number of locations detected as R-peaks that were not actually R-peaks; and FN is the number of missed fetal R-peaks. The presence of FP and FN indicates an error.

[0089] Table 1 provides Figure 4 (b) Figure 4 (c) The statistical data results of the corresponding examples are provided in Table 2. Figure 5 (b) R-peak recognition results of the corresponding instance.

[0090] Table 1 shows the best response evaluation results of each algorithm for fetal ECG signal extraction in the FECGSYN database.

[0091]

[0092] Among them, the smaller α is, the greater the impulse noise intensity is. Among these algorithms, the LHSAF and ILHSAF algorithms involved in the present invention have higher overall accuracy in extracting fetal ECG signals than the other algorithms, which is reflected in smaller RMSE, PRD and higher SNR.

[0093] Table 2 shows the R-peak recognition results of the fetal ECG signal extracted by the ILHSAF algorithm using the Daisy database.

[0094]

[0095] Among them, all indicators reached 100%, indicating that all peaks, including overlapping and partially overlapping signals, were detected in the extracted fetal ECG signals, which shows the high performance of the algorithm.

Claims

1. An adaptive non-invasive fetal electrocardiogram signal extraction method based on logarithmic hyperbolic secant function, characterized in that: The following steps are involved: (1) Constructing a model of the mother's abdominal ECG signal: AECG = FECG + m(n) + v(n) = FECG + 0.2MECG + noise; where v(n) is an impulse noise that follows a symmetric α-stable distribution SαS, and its generation parameters are adjusted by the generalized signal-to-noise ratio (GSNR) and the signal energy. (2) Based on the adaptive filtering framework, the mother's chest ECG signal MECG is input as the reference signal x(n), and the abdomen signal AECG is input as the desired signal d(n). The filtered output is calculated as follows: y(n) = w(n) T x(n); where w(n) T is the adaptive filter weight coefficient; (3) Define the objective function and update the weight coefficient; the objective function is: The weight update rule is: in μ is the step size factor; e(n) = d(n) - y(n); (4) The parameter combination, i.e., the filter order L and the step size μ, is optimized through Monte Carlo experiments, and the extracted fetal electrocardiogram signal e(n) is output.

2. The method for extracting fetal electrocardiogram signals based on a logarithmic hyperbolic secant function according to claim 1, wherein: The impulse noise v(n) of the symmetric α-stable distribution SαS is generated in the following way: the characteristic index α∈(0,2] controls the impulse intensity, the smaller α is, the stronger the noise impulse is; the generation parameter β=δ=0., where P dn represents the energy of the desired signal d(n), and GSNR is the generalized signal-to-noise ratio.

3. The adaptive non-invasive fetal electrocardiogram signal extraction method based on logarithmic hyperbolic secant function according to claim 1, characterized in that: The gradient calculation of the objective function includes: the first-order derivative of the instantaneous objective function is: Where ln(·) is the logarithm with base e, sech(·) is the hyperbolic secant function, and the parameter λ>0.

4. The adaptive non-invasive fetal electrocardiogram signal extraction method based on logarithmic hyperbolic secant function according to claim 3, characterized in that: The parameter λ is set to λ = 3 to preserve the linear characteristics of the fetal ECG signal. The approximate linear interval of the objective function is determined by the maximum curvature point, and combined with the fetal ECG signal amplitude estimate H, the weight update rule is adjusted as follows: in, Estimation of fetal ECG signal amplitude.

5. The adaptive non-invasive fetal electrocardiogram signal extraction method based on logarithmic hyperbolic secant function according to claim 1, characterized in that: The performance of the adaptive filter was evaluated by the following indicators: signal-to-noise ratio (SNR), root mean square error (RMSE), percentage root mean square difference (PRD); sensitivity (Se), positive predictive value (PPV), and F1 score for R-peak detection.

6. The adaptive non-invasive fetal electrocardiogram signal extraction method based on logarithmic hyperbolic secant function according to claim 5, characterized in that: The indicator is calculated as follows: Where s(n) is the pure fetal ECG signal provided by the dataset, e(n) is the extracted fetal ECG signal, and L is the filter order. Among them, TP is the number of fetal R-peaks correctly detected within ±10 milliseconds of the reference annotation; FP is the number of fetal R-peaks detected as R-peaks that are actually not R-peaks; FN is the number of fetal R-peaks that were missed.

7. The adaptive non-invasive fetal electrocardiogram signal extraction method based on logarithmic hyperbolic secant function according to claim 1, characterized in that: The method is applicable to portable fetal heart monitoring equipment and can achieve real-time extraction of fetal ECG signals by suppressing maternal ECG components and pulse noise.

8. An electronic device, characterized in that: The method comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the method according to any one of claims 1 to 7 when executing the program.

9. A computer-readable storage medium, characterized in that A computer program is stored, and when the program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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