Electrocardiogram noise reduction method and device based on double recursive dense network and storage medium

By applying the ECG noise reduction method of dual recursive dense network in the remote electrocardiogram monitoring system, the problem of noise interference in the ECG signal is solved, and signal quality is improved and diagnostic accuracy is enhanced.

CN119444601APending Publication Date: 2025-02-14HUNAN CITY UNIV +3
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Patent Information

Application Number
CN202411411402.0
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-10-10
Publication Date
2025-02-14

AI Technical Summary

Technical Problem

In the remote electrocardiogram monitoring system, ECG signals are susceptible to noise interference caused by equipment, environment, human body movements and network transmission, resulting in a decrease in signal quality and affecting diagnostic accuracy.

Method used

Using the electrocardiogram noise reduction method based on dual recursive dense network, the DRDnet model and DRLDnet model are constructed, combined with long and short-term memory algorithm (LSTM) and dense network, the noise characteristics are iteratively calculated to extract the clean ECG signal.

Benefits of technology

It effectively removes noise in ECG signals, improves signal quality, enhances diagnostic accuracy and efficiency, and provides a more reliable data analysis basis for remote ECG monitoring systems.

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Abstract

The invention relates to the technical field of image data processing, and provides an electrocardiogram noise reduction method and device based on a double-recursion dense network and a storage medium. The method comprises the following steps: S1, constructing a dense relationship-based extraction network algorithm model DRDnet, and extracting an ECG signal # imgabs0 # denoised for the first time from an original ECG signal R; S2, constructing a double-recursion dense network algorithm model DRLDnet based on a long short-term memory (LSTM) algorithm and the model DRDnet in the step S1, and carrying out iterative calculation to obtain an ECG signal # imgabs1 # denoised for the tth time. According to the method, the ECG signals are subjected to noise reduction from the perspective of image noise reduction, and reference is provided for a processing method of massive ECG signals in a remote monitoring system.
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Description

Technical Field

[0001] The present invention relates to the technical field of image data processing, and in particular to an electrocardiogram denoising method based on a dual recursive dense network, an electronic device and a computer-readable storage medium. Background Art

[0002] The widespread application of remote electrocardiogram (ECG) monitoring systems can effectively and real-timely monitor patients' heart health information remotely and transmit monitoring signals to doctors in hospitals in real time through sensors.

[0003] However, the massive ECG signals generated by remote ECG monitoring systems face the challenges of multiple interference sources and strong noise. Low-quality ECG waveforms will affect doctors' accurate diagnosis of diseases, reduce diagnostic efficiency, and even lead to misdiagnosis, which seriously hinders the development and application of intelligent remote ECG monitoring technology. There are mainly the following aspects: The first is the non-human noise generated by equipment and environment, which can cause glitches in the signal and affect the doctor's clinical diagnosis. Second, there is transient noise caused by human movements, which are usually accompanied by sudden movements, violent breathing, and sudden displacement or even falling off of the data acquisition equipment. Various irregular human movements that occur instantly cause baseline drift and myoelectric interference on the ECG, which may cause misdiagnosis of myocardial infarction, Brugada syndrome, and other ST-segment-related abnormalities. The third is the structural noise caused by network transmission. The structural noise generated by network delay, channel interference, etc. will cause distortion of ECG morphological characteristics.

[0004] Therefore, it is necessary to design an ECG noise reduction method to eliminate various types of noise caused by the remote monitoring system, so as to improve the accuracy of clinical diagnosis and lay a solid theoretical foundation for realizing intelligent analysis and diagnosis of ECG signals, improving the efficiency of remote ECG monitoring, and developing high-precision wearable devices. Summary of the invention

[0005] The object of the present invention is to provide an electrocardiogram denoising method, an electronic device and a computer-readable storage medium based on a dual recursive dense network to solve the above-mentioned technical problems.

[0006] The present invention provides an electrocardiogram denoising method based on a dual recursive dense network, comprising the steps of: S1, build a dense relationship extraction network algorithm model DRDnet to extract the first denoised ECG signal from the original ECG signal R ; Wherein, the dense relationship extraction network model includes an input layer , dense network layer And the output layer ; The input layer It is used to perform convolution operations, extract feature information in R, and then transfer the feature information to the dense network layer. ; The dense network layer It is used to further reuse features and realize the nonlinear ReLU function; the output layer For dense network layers The output result is vector convolution operation to obtain the output result X0, and the obtained noise characteristics are recorded = R-X0; S2, based on the long short-term memory algorithm LSTM and the model DRDnet in step S1, a dual recursive dense network algorithm model DRLDnet is constructed, and the ECG signal after the tth de-noising is obtained by iterative calculation ; The model DRLDnet includes the input layer , the dense network layer , the output layer And the LSTM layer ; Wherein, the R and As the input layer of the model DRLDnet The initial input signal is then iteratively calculated using the R and the model DRLDnet to obtain the ECG signal after the t-1th de-noising. As the input layer of the model DRLDnet The input signal calculated at the tth iteration of ; The As the LSTM layer The initial input signal is used to iteratively calculate the model DRLDnet to obtain the t-1th noise feature As the LSTM layer The input signal calculated at the tth iteration of the LSTM layer Receiving the input layer The output of the R and The characteristic information of or , and passed to the dense network layer ; The dense network layer Receive the input layer in the current t-th iteration calculation Extract the R and The characteristic information and the noise characteristics transmitted by the LSTM layer Further feature reuse to implement nonlinear ReLU function; The output layer Used to calculate the dense network layer in the current t-th iteration The output result is vector convolution operation to obtain the output result X t , and record the noise characteristics obtained = RX t ; in, , N is the maximum preset number of iterations.

[0007] Preferably, the method further includes step S3, training the model DRLDnet through the objective function to obtain the best noise reduction model, which specifically includes: Get the training set ( , ), i = 1,2, ⋯ , n; where n is the number of training samples, is the noisy ECG signal of the i-th training sample, is the clean ECG signal of the i-th training sample; By mixing functions ) trains the model DRLDnet, wherein: , , =1-ssim(B,H(R)), ;in, represents the pixel average of the clean ECG image, is the pixel average of the predicted ECG image, The covariance of the clean ECG image B and the predicted value of the ECG image, , are the standard deviations of B and H(R), , is a constant, is the set value.

[0008] Preferably, by adjusting the parameters , when the number of iterations or When the value no longer changes, the output result is the clean ECG image.

[0009] Preferably, the input layer 32 filters of size 3×3 are used to filter the received R and Converted to 32 feature maps.

[0010] The present invention also provides an electrocardiogram denoising system based on a dual recursive dense network, comprising: DRDnet module is used to build the DRDnet model based on the dense relationship extraction network algorithm model and extract the first denoised ECG signal from the original ECG signal R ; Wherein, the dense relationship extraction network model includes an input layer , dense network layer And the output layer ; The input layer It is used to perform convolution operations, extract feature information in R, and then transfer the feature information to the dense network layer. ; The dense network layer It is used to further reuse features and realize the nonlinear ReLU function; the output layer For dense network layers The output result is vector convolution operation to obtain the output result X0, and the obtained noise characteristics are recorded = R-X0; The DRLDnet module is used to construct a dual recursive dense network algorithm model DRLDnet based on the long short-term memory algorithm LSTM and the model DRDnet in step S1, and iteratively calculate the ECG signal after the tth de-noising ; The model DRLDnet includes the input layer , the dense network layer , the output layer And the LSTM layer ; Wherein, the R and As the input layer of the model DRLDnet The initial input signal is then iteratively calculated using the R and the model DRLDnet to obtain the ECG signal after the t-1th de-noising. As the input layer of the model DRLDnet The input signal calculated at the tth iteration of ; The As the LSTM layer The initial input signal is used to iteratively calculate the model DRLDnet to obtain the t-1th noise feature As the LSTM layer The input signal calculated at the tth iteration of the LSTM layer Receiving the input layer The output of the R and The characteristic information of or , and passed to the dense network layer ; The dense network layer Receive the input layer in the current t-th iteration calculation Extract the R and The characteristic information and the noise characteristics transmitted by the LSTM layer Further feature reuse to implement nonlinear ReLU function; The output layer Used to calculate the dense network layer in the current t-th iteration The output result is vector convolution operation to obtain the output result X t , and record the noise characteristics obtained = RX t ; in, , N is the maximum preset number of iterations.

[0011] Preferably, a training module is also included, which is used to train the model DRLDnet through the objective function to obtain the best noise reduction model, specifically including: Get the training set ( , ), i = 1,2, ⋯ , n; where n is the number of training samples, is the noisy ECG signal of the i-th training sample, is the clean ECG signal of the i-th training sample; By mixing functions ) trains the model DRLDnet, wherein: , , =1-ssim(B,H(R)), ;in, represents the pixel average of the clean ECG image, is the pixel average of the predicted ECG image, The covariance of the clean ECG image B and the predicted value of the ECG image, , are the standard deviations of B and H(R), , is a constant, is the set value.

[0012] Preferably, the training module is also used to adjust the parameters , when the number of iterations or When the value no longer changes, the output result is the clean ECG image.

[0013] Preferably, the input layer 32 filters of size 3×3 are used to filter the received R and Converted to 32 feature maps.

[0014] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the electrocardiogram denoising method based on a dual recursive dense network as described in any one of the above items when executing the computer program.

[0015] The present invention also provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the steps of the electrocardiogram denoising method based on a double recursive dense network as described in any one of the above items are implemented.

[0016] The ECG denoising method based on a dual recursive dense network of the present invention eliminates various types of noise caused by the remote transmission of ECG signals from the perspective of a remote ECG monitoring system scenario. The present invention is simple to implement, and uses a combined loss function that integrates L1, L2 and SSIM loss functions as the goal. By designing a DRDNet model and a DRLDNet model, various types of ECG signal noise caused by remote transmission are removed, and then the denoising effect of the present invention is evaluated by analyzing performance indicators such as PSNR and SSIM, providing a reference for the ECG denoising method in a remote ECG monitoring system. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Schematic diagram of the process of an electrocardiogram denoising method based on a dual recursive dense network in one embodiment of the present invention.

[0018] Figure 2 It is a logical schematic diagram of an electrocardiogram denoising method based on a dual recursive dense network in one embodiment of the present invention.

[0019] Figure 3 The figure is a schematic diagram of the hardware structure of a computer system running an electrocardiogram denoising method based on a dual recursive dense network in one embodiment of the present invention.

[0020] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings in conjunction with the embodiments. DETAILED DESCRIPTION

[0021] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0022] In the subsequent description, the suffixes such as "module", "component" or "unit" used to represent elements are only used to facilitate the description of the present invention, and have no specific meanings. Therefore, "module", "component" or "unit" can be used in a mixed manner.

[0023] The present invention will now be described in further detail with reference to the accompanying drawings.

[0024] Please combine Figure 1 and Figure 2 , is an electrocardiogram denoising method based on a dual recursive dense network in one embodiment of the present invention, comprising the steps of: S1, build a dense relationship extraction network algorithm model DRDnet to extract the first denoised ECG signal from the original ECG signal R ; S2, based on the long short-term memory algorithm LSTM and the model DRDnet in step S1, a dual recursive dense network algorithm model DRLDnet is constructed, and the ECG signal after the tth de-noising is obtained by iterative calculation .

[0025] Wherein, the dense relationship extraction network model includes an input layer , dense network layer And the output layer ; The input layer It is used to perform convolution operations, extract feature information in R, and then transfer the feature information to the dense network layer. ; The dense network layer It is used to further reuse features and realize the nonlinear ReLU function; the output layer For dense network layers The output result is vector convolution operation to obtain the output result X0, and the obtained noise characteristics are recorded = R-X0.

[0026] Specifically, the model DRLDnet includes the input layer , the dense network layer , the output layer And the LSTM layer ; Wherein, the R and As the input layer of the model DRLDnet The initial input signal is then iteratively calculated using the R and the model DRLDnet to obtain the ECG signal after the t-1th de-noising. As the input layer of the model DRLDnet The input signal calculated at the tth iteration of ; The As the LSTM layer The initial input signal is used to iteratively calculate the model DRLDnet to obtain the t-1th noise feature As the LSTM layer The input signal calculated at the tth iteration of the LSTM layer Receiving the input layer The output of the R and The characteristic information of or , and passed to the dense network layer ; The dense network layer Receive the input layer in the current t-th iteration calculation Extract the R and The characteristic information and the noise characteristics transmitted by the LSTM layer Further feature reuse to implement nonlinear ReLU function; The output layer Used to calculate the dense network layer in the current t-th iteration The output result is vector convolution operation to obtain the output result X t , and record the noise characteristics obtained = RX t ; in, , N is the maximum preset number of iterations.

[0027] Preferably, the method further includes step S3, training the model DRLDnet through the objective function to obtain the best noise reduction model, which specifically includes: Get the training set ( , ), i = 1,2, ⋯ , n; where n is the number of training samples, is the noisy ECG signal of the i-th training sample, is the clean ECG signal of the i-th training sample; By mixing functions ) trains the model DRLDnet, wherein: , , =1-ssim(B,H(R)), ;in, represents the pixel average of the clean ECG image, is the pixel average of the predicted ECG image, The covariance of the clean ECG image B and the predicted value of the ECG image, , are the standard deviations of B and H(R), , is a constant, is the set value.

[0028] Preferably, by adjusting the parameters , when the number of iterations or When the value no longer changes, the output result is the clean ECG image.

[0029] Preferably, the input layer 32 filters of size 3×3 are used to filter the received R and Converted to 32 feature maps.

[0030] Preferably, the dense network layer It contains 5 layers, each with 32 filters.

[0031] The present invention also provides an electrocardiogram denoising system based on a dual recursive dense network, comprising: DRDnet module is used to build the DRDnet model based on the dense relationship extraction network algorithm model and extract the first denoised ECG signal from the original ECG signal R ; Wherein, the dense relationship extraction network model includes an input layer , dense network layer And the output layer ; The input layer It is used to perform convolution operations, extract feature information in R, and then transfer the feature information to the dense network layer. ; The dense network layer It is used to further reuse features and realize the nonlinear ReLU function; the output layer For dense network layers The output result is vector convolution operation to obtain the output result X0, and the obtained noise characteristics are recorded = R-X0; The DRLDnet module is used to construct a dual recursive dense network algorithm model DRLDnet based on the long short-term memory algorithm LSTM and the model DRDnet in step S1, and iteratively calculate the ECG signal after the tth de-noising ; The model DRLDnet includes the input layer , the dense network layer , the output layer And the LSTM layer ; Wherein, the R and As the input layer of the model DRLDnet The initial input signal is then iteratively calculated using the R and the model DRLDnet to obtain the ECG signal after the t-1th de-noising. As the input layer of the model DRLDnet The input signal calculated at the tth iteration of ; The As the LSTM layer The initial input signal is used to iteratively calculate the model DRLDnet to obtain the t-1th noise feature As the LSTM layer The input signal calculated at the tth iteration of the LSTM layer Receiving the input layer The output of the R and The characteristic information of or , and passed to the dense network layer ; The dense network layer Receive the input layer in the current t-th iteration calculation Extract the R and The characteristic information and the noise characteristics transmitted by the LSTM layer Further feature reuse to implement nonlinear ReLU function; The output layer Used to calculate the dense network layer in the current t-th iteration The output result is vector convolution operation to obtain the output result X t , and record the noise characteristics obtained = RX t ; in, , N is the maximum preset number of iterations.

[0032] Preferably, a training module is also included, which is used to train the model DRLDnet through the objective function to obtain the best noise reduction model, specifically including: Get the training set ( , ), i = 1,2, ⋯ , n; where n is the number of training samples, is the noisy ECG signal of the i-th training sample, is the clean ECG signal of the i-th training sample; By mixing functions ) trains the model DRLDnet, wherein: , , =1-ssim(B,H(R)), ;in, represents the pixel average of the clean ECG image, is the pixel average of the predicted ECG image, The covariance of the clean ECG image B and the predicted value of the ECG image, , are the standard deviations of B and H(R), , is a constant, is the set value.

[0033] Preferably, the training module is also used to adjust the parameters , when the number of iterations or When the value no longer changes, the output result is the clean ECG image.

[0034] Preferably, the input layer 32 filters of size 3×3 are used to filter the received R and Converted to 32 feature maps.

[0035] The ECG denoising method based on a dual recursive dense network of the present invention eliminates various types of noise caused by the remote transmission of ECG signals from the perspective of a remote ECG monitoring system scenario. The present invention is simple to implement, and uses a combined loss function that integrates L1, L2 and SSIM loss functions as the goal. By designing a DRDNet model and a DRLDNet model, various types of ECG signal noise caused by remote transmission are removed, and then the denoising effect of the present invention is evaluated by analyzing performance indicators such as PSNR and SSIM, providing a reference for the ECG denoising method in a remote ECG monitoring system.

[0036] Please refer to Figure 3 In one embodiment of the present invention, the embodiment of the present invention further provides an electronic device / computer system 10, including a memory 51, a processor 52, and a computer program 53 stored in the memory 51 and executable on the processor 52, and when the processor 52 executes the computer program, the steps of the electrocardiogram denoising method based on a dual recursive dense network as described in any one of the above items are implemented.

[0037] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the electrocardiogram denoising method based on a dual recursive dense network as described in any one of the above items.

[0038] Exemplarily, the computer program of the computer-readable storage medium includes computer program code, which may be in source code form, object code form, executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium, etc.

[0039] In the description of this specification, the description with reference to the terms "an embodiment", "another embodiment", "other embodiments", or "first embodiment to Xth embodiment" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, method steps or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0040] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0041] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. An electrocardiogram denoising method based on a dual recursive dense network, characterized in that: Includes steps: S1, build a dense relationship extraction network algorithm model DRDnet to extract the first denoised ECG signal from the original ECG signal R ; Wherein, the dense relationship extraction network model includes an input layer , dense network layer And the output layer ; The input layer It is used to perform convolution operations, extract feature information in R, and then transfer the feature information to the dense network layer. ; The dense network layer It is used to further reuse features and realize the nonlinear ReLU function; the output layer For dense network layers The output result is vector convolution operation to obtain the output result X0, and the obtained noise characteristics are recorded = R-X0; S2, based on the long short-term memory algorithm LSTM and the model DRDnet in step S1, a dual recursive dense network algorithm model DRLDnet is constructed, and the ECG signal after the tth de-noising is obtained by iterative calculation ; The model DRLDnet includes the input layer , the dense network layer , the output layer And the LSTM layer ; Wherein, the R and As the input layer of the model DRLDnet The initial input signal is then iteratively calculated using the R and the model DRLDnet to obtain the ECG signal after the t-1th de-noising. As the input layer of the model DRLDnet The input signal calculated at the tth iteration of ; The As the LSTM layer The initial input signal is used to iteratively calculate the model DRLDnet to obtain the t-1th noise feature As the LSTM layer The input signal calculated at the tth iteration of the LSTM layer Receiving the input layer The output of the R and The characteristic information of or , and passed to the dense network layer ; The dense network layer Receive the input layer in the current t-th iteration calculation Extract the R and The characteristic information and the noise characteristics transmitted by the LSTM layer Further feature reuse to implement nonlinear ReLU function; The output layer Used to calculate the dense network layer in the current t-th iteration The output result is vector convolution operation to obtain the output result X t , and record the noise characteristics obtained = RX t ; in, , N is the maximum preset number of iterations.

2. The method according to claim 1, characterized in that: The step S3 is also included, in which the model DRLDnet is trained through the objective function to obtain the best noise reduction model, which specifically includes: Get the training set ( , ), i = 1,2, ⋯ , n; where n is the number of training samples, is the noisy ECG signal of the i-th training sample, is the clean ECG signal of the i-th training sample; By mixing functions ) trains the model DRLDnet, wherein: , , =1-ssim(B,H(R)), ;in, represents the pixel average of the clean ECG image, is the pixel average of the predicted ECG image, The covariance of the clean ECG image B and the predicted value of the ECG image, , are the standard deviations of B and H(R), , is a constant, is the set value.

3. The method according to claim 2, characterized in that By adjusting the parameters , when the number of iterations or When the value no longer changes, the output result is the clean ECG image.

4. The method according to claim 1, characterized in that: The input layer 32 filters of size 3×3 are used to filter the received R and Converted to 32 feature maps.

5. An electrocardiogram denoising system based on a dual recursive dense network, characterized in that: include: DRDnet module is used to build the DRDnet model based on the dense relationship extraction network algorithm model and extract the first denoised ECG signal from the original ECG signal R ; Wherein, the dense relationship extraction network model includes an input layer , dense network layer And the output layer ; The input layer It is used to perform convolution operations, extract feature information in R, and then transfer the feature information to the dense network layer. ; The dense network layer It is used to further reuse features and realize the nonlinear ReLU function; the output layer For dense network layers The output result is vector convolution operation to obtain the output result X0, and the obtained noise characteristics are recorded = R-X0; The DRLDnet module is used to construct a dual recursive dense network algorithm model DRLDnet based on the long short-term memory algorithm LSTM and the model DRDnet in step S1, and iteratively calculate the ECG signal after the tth de-noising ; The model DRLDnet includes the input layer , the dense network layer , the output layer And the LSTM layer ; Wherein, the R and As the input layer of the model DRLDnet The initial input signal is then iteratively calculated using the R and the model DRLDnet to obtain the ECG signal after the t-1th de-noising. As the input layer of the model DRLDnet The input signal calculated at the tth iteration of ; The As the LSTM layer The initial input signal is used to iteratively calculate the model DRLDnet to obtain the t-1th noise feature As the LSTM layer The input signal calculated at the tth iteration of the LSTM layer Receiving the input layer The output of the R and The characteristic information of or , and passed to the dense network layer ; The dense network layer Receive the input layer in the current t-th iteration calculation Extract the R and The characteristic information and the noise characteristics transmitted by the LSTM layer Further feature reuse to implement nonlinear ReLU function; The output layer Used to calculate the dense network layer in the current t-th iteration The output result is vector convolution operation to obtain the output result X t , and record the noise characteristics obtained = RX t ; in, , N is the maximum preset number of iterations.

6. The system according to claim 1, characterized in that It also includes a training module for training the model DRLDnet through the objective function to obtain the best denoising model, including: Get the training set ( , ), i = 1,2, ⋯ , n; where n is the number of training samples, is the noisy ECG signal of the i-th training sample, is the clean ECG signal of the i-th training sample; By mixing functions ) trains the model DRLDnet, wherein: , , =1-ssim(B,H(R)), ;in, represents the pixel average of the clean ECG image, is the pixel average of the predicted ECG image, The covariance of the clean ECG image B and the predicted value of the ECG image, , are the standard deviations of B and H(R), , is a constant, is the set value.

7. The system according to claim 6, characterized in that The training module is also used to adjust the parameters , when the number of iterations or When the value no longer changes, the output result is the clean ECG image.

8. The system according to claim 5, characterized in that The input layer 32 filters of size 3×3 are used to filter the received R and Converted to 32 feature maps.

9. An electronic device, characterized in that: The method comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the electrocardiogram denoising method based on a dual recursive dense network as described in any one of claims 1 to 4 when executing the computer program.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the electrocardiogram denoising method based on a dual recursive dense network as described in any one of claims 1 to 4 are implemented.