A method for reconstructing ECG signals based on improved approximate message passing

Abstract

A method for reconstructing an electrocardiogram signal based on improved approximate message passing includes the following steps: 1) constructing an m*n dimensional sparse observation matrix Φ; 2) using the observation matrix to perform compression measurement on a signal x to obtain an observation vector y of length m; 3) using the prior information of the signal x and likelihood estimation to perform minimum mean square error estimation on the electrocardiogram signal and obtain an estimated value, and then performing denoising processing on the estimated value through a denoiser to obtain a reconstructed electrocardiogram signal, and repeating iterations until convergence. The present invention is based on a vector approximate message passing algorithm, fully utilizes the prior information of the signal, and by using an NLM denoiser, replaces the noise region with a similar structure region in a noisy region, achieving a better denoising effect without losing too much detail, effectively correcting the noise deviation in the electrocardiogram signal in each iteration, improving the convergence speed and reconstruction performance of the algorithm, and significantly superior to the traditional electrocardiogram signal reconstruction method in terms of reconstruction accuracy while ensuring the reconstruction speed.

Description

Technical Field

[0001] The present invention belongs to the field of signal processing, and particularly relates to a high-precision compressive sensing reconstruction method for electrocardiogram signals based on an improved approximate message passing algorithm. Background Art

[0002] There are problems with the reconstruction accuracy of traditional compressive sensing algorithms for reconstructing electrocardiogram signals. Especially when reducing the number of measurements, it is difficult to accurately recover the electrocardiogram signals obtained by reconstruction. The inability to accurately reconstruct electrocardiogram signals will have a huge impact on diagnosis. Therefore, it is particularly important to ensure the quality of the reconstructed electrocardiogram signals. Summary of the Invention

[0003] The object of the present invention is to propose a high-quality reconstruction method for electrocardiogram signals based on an improved approximate message passing, aiming at the problems existing in the prior art. In the first stage of the improved vector approximate message passing (D-VAMP) algorithm, the minimum mean square error estimation of the electrocardiogram signal x is performed using the prior information and likelihood estimation of the signal. In this stage, an estimated value with a precision of is generated , and then ( , ) is converted to ( , ), where is regarded as an additive white Gaussian noise corrupted version of the true signal x with noise precision ; in the iterative second stage, the NLM denoiser is used to denoise to obtain an estimated value, and then it is converted to ( , ), and the iteration ends. The iteration is repeated until converges.

[0004] The present invention is realized through the following technical solutions.

[0005] A method for reconstructing an electrocardiogram signal based on an improved approximate message passing according to the present invention includes the following steps:

[0006] (1) Construct an -dimensional sparse observation matrix Φ, where m < n and n is the length of the original signal x;

[0007] (2) Use the observation matrix to perform compressive measurement on the signal x to obtain an observation vector y with a length of m;

[0008] (3) Use the prior information and likelihood estimation of the signal x to perform minimum mean square error estimation on the electrocardiogram signal, and obtain an estimated value. Then, denoise the estimated value through a denoiser to obtain the reconstructed electrocardiogram signal. The iteration is repeated until convergence. Specifically as follows:

[0009]

[0010] Where w is the additive noise.

[0011] (3.1) Initialization and Assuming that w is Gaussian white noise, it can be estimated by the likelihood of the original signal x and prior information Get the estimated signal The expression is:

[0012] ;

[0013] (3.2) Calculation of relevant parameters :

[0014] ;

[0015] (3.3) Utilization Calculate an estimate Accuracy : ;

[0016] (3.4) and then convert it into the additive Gaussian white noise version of the estimated value : ;

[0017] (3.5) and Noise accuracy It can be solved by the following formula: ;

[0018] (3.6) Using NLM denoiser Perform denoising and find its accuracy:

[0019] ;

[0020] (3.7) Convert it back to an estimated value : ;

[0021] (3.8) Then calculate its accuracy : .

[0022] When the 2-norm of the two most recent reconstructed signal estimates is less than the preset threshold, the iteration is stopped and step (3.1) is calculated again to obtain the estimated value of the original signal. .

[0023] The present invention is based on the vector approximate message passing algorithm, makes full use of the prior information of the signal, and replaces the threshold function with the NLM denoiser. In the noisy area, the similar structure area replaces the noisy area, thereby achieving a better denoising effect without losing too much detail, effectively correcting the noise deviation in the ECG signal in each iteration, and improving the convergence speed and reconstruction performance of the algorithm. Compared with the traditional ECG signal reconstruction algorithm, the present invention can achieve higher reconstruction accuracy while ensuring the reconstruction speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 ECG signal reconstructed by BSBL-BO algorithm.

[0025] Figure 2 ECG signal reconstructed by AMP algorithm.

[0026] Figure 3 ECG signal reconstructed by the D-AMP algorithm.

[0027] Figure 4 ECG signal reconstructed by D-VAMP algorithm.

[0028] Among them, Original is the original signal. DETAILED DESCRIPTION

[0029] The present invention will be further described below with reference to the embodiments.

[0030] In this embodiment, the data comes from the MIT-BIH arrhythmia database. The first 1024 sampling points of the 103rd record are selected as the original signal x.

[0031] (1) Using Bernoulli measurement matrix and wavelet basis construction dimensional observation matrix Φ, where , . Use the measurement matrix Φ to compress and measure the original ECG signal to obtain the measurement vector y of length m. Then take the measurement matrix and the measurement vector as input and give and The initial value of .

[0032] (2) Calculation :

[0033] (3) Obtain the estimated value Noise accuracy :

[0034] (4) Then convert it into the precision of : ,

[0035] (5) Yes Perform denoising and calculate the accuracy after denoising:

[0036]

[0037] (6) Then convert it into : , and calculate Accuracy :

[0038] (7) Obtain the estimated value of the original signal :

[0039] (8) Calculate whether the two most recent estimated values ​​of the reconstructed signal are greater than the threshold. If so, continue to step 3. Otherwise, output the estimated value. .

[0040] from Figure 4 It can be seen that the ECG signal reconstructed based on the D-VAMP algorithm is significantly better than other algorithms when the compression rate is 80%.

Claims

1. A method for reconstructing electrocardiogram signals based on improved approximate message passing, characterized in that The following steps are involved: (1) Structure An m×n sparse observation matrix Φ, where m < n and n is the length of the original signal x; (2) Use the measurement matrix to compress and measure the signal x to obtain an observation vector y with a length of m; (3) Use the prior information and likelihood estimation of the signal x to perform minimum mean square error estimation on the ECG signal and obtain an estimated value. Then, use the denoiser to denoise the estimated value to obtain the reconstructed ECG signal. Repeat the iteration until convergence: Where w is additive noise; (3.1) Initialization and : Assuming w is Gaussian white noise, it can be estimated by the likelihood of the original signal x and prior information Get the estimated signal The expression is: ； (3.2) Calculation of relevant parameters : ； (3.3) Utilization Calculate an estimate Accuracy : ; (3.4) Then the accuracy Transformed additive white Gaussian noise version of the estimate : ; (3.5) and Noise accuracy It can be solved by the following formula: ; (3.6) Using NLM denoiser Perform denoising and find its accuracy: ； (3.7) Convert it back to an estimated value : ; (3.8) Then calculate its accuracy : ; When the 2-norm of the two most recent reconstructed signal estimates is less than the preset threshold, the iteration is stopped and step (3.1) is calculated again to obtain the estimated value of the original signal. .

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