Noise reduction method based on CEEMDAN sample entropy analysis and main noise segment positioning

Abstract

The invention discloses a noise reduction method based on CEEMDAN sample entropy analysis and main noise segment positioning, and belongs to the technical field of signal processing. The method comprises the following steps: firstly, decomposing a series of IMF signals by using CEEMDAN, calculating the sample entropy of each IMF, comparing the difference between the sample entropy of each IMF and the average value of the sample entropy, separating a high-frequency IMF from a low-frequency IMF, and then carrying out correlation analysis on the high-frequency IMF signal to find out the position of a noise signal. The IMF where the noise signals are located is equally divided, the energy entropy of each noise signal is calculated, the interval where the maximum energy entropy is located is found to serve as a main noise section, the variance is calculated through the main noise section, a threshold value is calculated through the variance, the threshold value is applied to a soft threshold value for noise suppression, and finally the signals are reconstructed to obtain reconstructed signals. According to the invention, the noise reduction is more targeted, and meanwhile, the loss of useful information of the signal is avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and more specifically to a noise reduction method based on CEEMDAN sample entropy analysis and main noise segment positioning. Background Art

[0002] Complete Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is a processing method for nonlinear and non-stationary signals. It decomposes the original signal into a series of Intrinsic Mode Functions (IMFs) and a residual term. These IMFs are evenly distributed in the time domain and frequency domain, representing different frequency and amplitude components, while the residual term contains the remaining signal part that cannot be represented by the IMF. The CEEMDAN method uses adaptive noise technology to control the decomposition process, and screens important components by calculating the correlation coefficient between the original signal and the IMF, thereby effectively extracting the time-frequency characteristics of the signal. However, the existing methods are not very targeted in noise suppression, the noise reduction effect is poor, and the loss of effective signal information is also large. Summary of the invention

[0003] 1. Technical problem to be solved by the invention

[0004] In order to further improve the denoising performance of CEEMDAN and avoid the loss of effective information in the IMF of high-frequency signals, the present invention provides a denoising method based on CEEMDAN sample entropy analysis and main noise segment positioning. The present invention first performs CEEMDAN decomposition on the processed signal to obtain a series of IMFs; then divides the high-frequency IMF and the low-frequency IMF, finds the position of the noise signal in the high-frequency signal, determines the interval where the main noise is located, and finally calculates the threshold, uses the threshold as a parameter to perform soft threshold filtering on the noisy signal; finally, the signal is reconstructed to obtain a denoised signal. This makes the denoising more targeted and avoids the loss of useful information of the signal.

[0005] 2. Technical solution

[0006] In order to achieve the above object, the technical solution provided by the present invention is:

[0007] A noise reduction method based on CEEMDAN sample entropy analysis and main noise segment positioning of the present invention comprises the following steps:

[0008] Step 1: Decompose the signal to be processed using the CEEMDAN method to obtain the IMF components from high to low frequencies;

[0009] Step 2: Find and divide high-frequency IMF and low-frequency IMF according to sample entropy theory;

[0010] Step 3: Perform correlation analysis on high-frequency IMF to distinguish noise signals from useful signals;

[0011] Step 4: Group the noise signals, and select the main noise interval from the noise signal group in combination with the energy entropy theory; calculate the variance of the main noise interval, and further obtain the threshold of the signal;

[0012] Step 5: Use the threshold as a parameter to perform soft threshold filtering on the noisy signal, and finally reconstruct the signal after soft threshold processing, the low-frequency IMF component obtained in step 2, and the useful signal component obtained in step 3 to obtain a denoised signal.

[0013] 3. Beneficial effects

[0014] Compared with the existing known technologies, the technical solution provided by the present invention has the following significant effects:

[0015] (1) The present invention determines the interval with the most concentrated noise energy in each IMF based on the calculation of energy entropy. By analyzing the energy entropy of each IMF and comparing their deviations from the average energy entropy, the main noise interval with the highest energy entropy is identified. This interval usually contains the most significant noise component in the signal. Therefore, applying threshold and soft threshold functions to suppress noise in these intervals can significantly improve the purity and availability of the signal. This method of locating the main noise interval is not only accurate but also efficient, and is suitable for the actual denoising needs of some noise signal concentrations.

[0016] (2) The entropy-based screening mechanism of the present invention is more sophisticated than the traditional frequency- or amplitude-based screening method, has strong adaptability in different signal environments, and can effectively suppress noise without reducing the main components of the signal. In addition, the present invention can reduce noise interference while avoiding the loss of useful information of the signal, which is more effective for applications that require high-fidelity signal reconstruction.

[0017] (3) The present invention designs a threshold adaptive selection mechanism, which not only has a good suppression effect on primary noise, but also can flexibly cope with various complex signal environments, making the signal time-frequency feature extraction more effective. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a main step diagram of the present invention;

[0019] Figure 2 It is a flow chart of the denoising method based on CEEMDAN sample entropy analysis and main noise segment positioning;

[0020] Figure 3 The IMF waveforms of sample 41.wave after being decomposed by CEEMAN;

[0021] Figure 4 To separate low-frequency and high-frequency IMF graphs in combination with sample entropy theory;

[0022] Figure 5 It is a partial diagram of the waveform of the original signal and the signal after filtering by the present invention. DETAILED DESCRIPTION

[0023] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments.

[0024] Combination Figure 1 , a noise reduction method based on CEEMDAN sample entropy analysis and main noise segment positioning of the present invention, firstly, CEEMDAN decomposition is performed on the processed signal X(t) to obtain a series of IMFs; then, high-frequency IMFs and low-frequency IMFs are found and divided according to the sample entropy theory; then, the position of the noise signal is found from the perspective of correlation analysis; then, the interval where the main noise is located is found from the noise signal through energy entropy analysis, the variance of the interval is calculated, and the threshold is calculated, and the threshold is used as a parameter to perform soft threshold filtering on the noise signal. Finally, the signal is reconstructed to obtain a denoised signal. This method not only finds the main noise position in the IMF of the noise signal, making the noise suppression more targeted and effective, but also after the main noise segment is effectively identified, the remaining signal part can be reconstructed, reducing the loss of effective signal information.

[0025] The following is combined with Figure 2 and further detailed descriptions of specific samples.

[0026] like Figure 2 As shown, the method specifically comprises the following steps:

[0027] Step 1: Decompose the signal X(t) to be processed using the CEEMDAN method to obtain the IMF components from high to low frequencies, as follows:

[0028]

[0029] Where X(t) represents the input signal, C i (t) represents the IMF obtained by the i-th CEEMDAN decomposition, res(t) represents the residual function, and I represents the maximum number of IMF layers of CEEMDAN decomposition. The index of the number of IMFs is established based on the number of CEEMDAN decomposition layers, and the original signal and each IMF signal are assigned a positive integer index starting from 1 based on the time sequence of the signal.

[0030] Step 2: Calculate the sample entropy of each IMF component according to the sample entropy theory, and find the average value of the overall sample entropy. Compare the sample entropy of each IMF component with the average value, and select the one with a larger value than the average value as the high-frequency component for the next step of processing, and retain the low-frequency component with a smaller value than the average value. The specific calculation steps are as follows:

[0031] Step 2-1: For the C of the ith IMF i (t), construct a delay vector Y p . C i (t) time series {c i,1 ,c i,2 ,...,c i,N}, select the embedding dimension m and tolerance r, where m is usually 2, r is between 0.1 and 0.25, i represents the IMF index, and N represents the number of original signal data points. Construct the following delay vector:

[0032] Y p ={C i，p , v i，p+1 , ..., v i，p+m-1}

[0033] Where p = 1, 2, ..., N-m+1.

[0034] Step 2-2, calculate the Euclidean distance d[Y p ,Y q ],as follows:

[0035]

[0036] Where p and q are used to represent the delay vector Y p At different positions in the sequence, |c i,p+k -c i,q+k | represents vector c i,p+k With vector c i,q+k The Euclidean distance between .

[0037] Step 2-3: Calculate the ratio of similar vectors, for each Y p Calculate the number of similar vectors. Similar vectors are defined as pairs of vectors whose distance is less than the tolerance r. The ratio B of the pth similar vector is p :

[0038]

[0039] Step 2-4: Calculate the average similarity ratio for all B p Take the average value B m (r):

[0040]

[0041] Step 2-5: Increase the embedding dimension from m to m+1, repeat steps 2-1 to 2-4, and calculate the average similarity ratio B in m+1 dimension. m+1 (r).

[0042] Step 2-6: Calculate the i-th IMF sample entropy SampEn i , the sample entropy of the i-th IMF is defined as follows:

[0043]

[0044] Step 2-7: Calculate the sample entropy SampEn of different IMFs according to steps 2-1 to 2-6, and calculate the average sample entropy Average SampEn.

[0045]

[0046] Step 2-8: Compare the size of each IMF sample entropy and the sample entropy mean, and take the IMF where the sample entropy of each IMF is greater than the sample entropy mean as the high-frequency component, and the IMF where the sample entropy of each IMF is less than the sample entropy mean as the low-frequency component.

[0047] Step 3: Perform correlation analysis on the high-frequency IMF obtained in step 2 to distinguish noise signals from useful signals. Specifically:

[0048] The correlation coefficient R between the high-frequency components of each IMF after decomposition and the original signal and its normalized correlation coefficient NR are calculated using the following formulas (1) and (2). The IMF where the normalized correlation coefficient NR is greater than the correlation coefficient R of each high-frequency component is regarded as a useful signal, and the IMF where the normalized correlation coefficient NR is less than is a noise signal.

[0049] The calculation formula of the correlation coefficient between the signal with sequence index V in the i-th IMF component and the data of the original signal is as follows:

[0050]

[0051] In the formula, R i (V) is the correlation coefficient between the signal with sequence index V in the i-th IMF component and the original signal, c i (n) is the discretization representation of the i-th IMF component, and x(v+n) is the discretization representation of the original audio signal that is greater than n parts. At the same time, v+n cannot exceed the upper limit N of the number of signal sampling points.

[0052] R i (V) Normalized correlation coefficient NR i (V) is calculated as follows:

[0053]

[0054] Step 4: further divide the noise signal group, and screen out the main noise interval from the noise signal group in combination with the energy entropy theory; calculate the variance of the main noise interval, and further calculate the threshold of the signal. The specific implementation steps are as follows;

[0055] Process the noise position data of the previous step, assume that the kth IMF contains the noise position, divide the IMF signal into l equal parts, and calculate the energy entropy of each equal part according to the following formula:

[0056] The energy E of the kth IMF component containing the noise signal position k for:

[0057]

[0058] where k = 1, 2, ..., K, C k (n) represents the IMF sequence of the noise signal whose sequence is k and is the signal of part n.

[0059] The kth IMF component of the noise signal group is divided into l intervals, and the energy E of the i-th interval in the kth IMF component interval is ki It is expressed as follows:

[0060]

[0061] The energy E of the i-th interval in the k-th IMF of the noise signal group ki The total energy E of this modal component k The probability P ki as follows:

[0062]

[0063] The energy entropy S of the i-th interval in the k-th IMF of the noise signal group ki as follows:

[0064] S ki =-o ki lnp ki (6)

[0065] Similar steps are used to calculate the energy entropy of the kth IMF component and combine it into the kth IMF energy entropy sequence S in the noise signal group according to the following formula: k :

[0066] S k ={S k1 , …, S kl} (7)

[0067] Select S k The energy entropy parameter is assumed to be the kth IMF energy entropy sequence Sk Medium S km Maximum, S km The IMF signal segment corresponding to the mth group of subintervals after the kth IMF component is evenly divided into l groups is taken as the main noise segment C of the IMF signal. km :

[0068] S km =max{S k1 , …, S kl} (8)

[0069] According to formula 9, calculate the mean value σ of the signal corresponding to the interval k , and σ k The noise variance of the kth IMF component of the noise signal is calculated as follows: km The mean value σ k as follows:

[0070]

[0071] Calculate the threshold: Calculate the threshold T of the kth IMF component of the noise signal group according to formula (10): k ;

[0072]

[0073] Step 5: Use the calculated threshold T k , used as the threshold of the soft threshold function, as follows:

[0074] C′ k =sign(c k )·f(0,|c k |-T k ) (11)

[0075] Among them C k represents the signal of the original k-th IMF, C′ k represents the kth IMF signal after soft threshold denoising, sign(C k ) represents the symbolic function, f(0, |C k |-T k ) means if |C k |Greater than T k , the output is C k , otherwise the output is 0.

[0076] The other high-frequency IMF components containing noise signals are processed using the methods of steps 4 and 5. Finally, the signal after soft threshold processing is reconstructed with the low-frequency IMF component of step 2 and the useful signal component signal of step 3 to obtain the denoised signal.

[0077] We use the DeepShip sample named 41.wave data available online and process the data in MATLAB according to the above steps. The final result is as follows: Figures 3 to 5 shown.

[0078] Depend on Figure 3 and Figure 4 It can be seen that the present invention distinguishes the parts with IMF numbers less than 6 as high-frequency IMFs based on CEEMDAN decomposition. Figure 5 It can be seen that the method of the present invention reduces the signal overlap and peak phenomenon of the signal after being processed by the method of the present invention on the basis of retaining the effective information of the original signal.

[0079] The present invention and its embodiments are described schematically above, and the description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. Therefore, if a person skilled in the art is inspired by it and designs a structural method and an embodiment similar to the technical solution without creativity without departing from the purpose of the invention, they shall all fall within the protection scope of the present invention.

Claims

1. A noise reduction method based on CEEMDAN sample entropy analysis and main noise segment positioning, characterized in that: The steps are: Step 1: Decompose the signal to be processed using the CEEMDAN method to obtain the IMF components from high to low frequencies; Step 2: Find and divide high-frequency IMF and low-frequency IMF according to sample entropy theory; Step 3: Perform correlation analysis on high-frequency IMF to distinguish noise signals from useful signals; Step 4: Group the noise signals and filter out the main noise interval from the noise signal group in combination with the energy entropy theory; Calculate the variance of the main noise interval and further obtain the threshold of the signal; Step 5: Use the threshold as a parameter to perform soft threshold filtering on the noisy signal, and finally reconstruct the signal after soft threshold processing and the unprocessed signal to obtain a denoised signal.

2. The denoising method based on CEEMDAN sample entropy analysis and main noise segment positioning according to claim 1, characterized in that: Step 2: Calculate the sample entropy of each IMF component according to the sample entropy theory, and find the average value of the overall sample entropy. Compare the sample entropy of each IMF component with the average value, and select the one with a larger value than the average value as the high-frequency IMF component for the next step of processing, and retain the low-frequency IMF component with a smaller value than the average value.

3. The denoising method based on CEEMDAN sample entropy analysis and main noise segment positioning according to claim 2, characterized in that: Step 3 calculates the correlation coefficient R and the normalized correlation coefficient NR between each IMF high-frequency component and the original signal after decomposition. The IMF component whose normalized correlation coefficient NR is greater than the correlation coefficient R of each high-frequency component is regarded as a useful signal, and the one whose normalized correlation coefficient NR is less than the correlation coefficient R is a noise signal.

4. A denoising method based on CEEMDAN sample entropy analysis and main noise segment positioning according to any one of claims 1 to 3, characterized in that: Step 4 The process of screening the main noise interval is as follows: Process the noise signal position data in step 3. If the kth IMF contains a noise position, divide the IMF signal into l equal parts and calculate the energy entropy of each equal part; combine them into the kth IMF energy entropy sequence S in the noise signal group. k ; Select the kth IMF energy entropy sequence S k Maximum value S km , S km After the kth IMF component is divided into l groups, the IMF signal segment corresponding to the mth group of sub-intervals is used as the main noise interval segment C of the IMF signal. km .

5. The denoising method based on CEEMDAN sample entropy analysis and main noise segment positioning according to claim 4, characterized in that: Step 4: Calculate the mean value σ of the signal corresponding to the main noise interval k , and σ k The noise variance of the kth IMF component of the noise signal.

6. The denoising method based on CEEMDAN sample entropy analysis and main noise segment positioning according to claim 5, characterized in that: Step 4: Calculate the threshold T of the kth IMF component of the noise signal group according to the following formula: k : Where N represents the number of current signal data points.

7. The denoising method based on CEEMDAN sample entropy analysis and main noise segment positioning according to claim 6, characterized in that: The formula for soft threshold filtering in step 5 is as follows: C′ k =sign(c k )·f(0,|c k |-T k ) Among them, Ck represents the signal of the original k-th IMF, C′ k represents the kth IMF signal after soft threshold denoising, sign(C k ) represents the symbolic function, f(0, |C k |-T k ) means if |C k |Greater than T k , the output is C k , otherwise the output is 0.

8. The noise reduction method based on CEEMDAN sample entropy analysis and main noise segment positioning according to claim 7, characterized in that: In step 5, the signal after soft threshold processing is reconstructed with the low-frequency IMF obtained in step 2 and the useful signal obtained in step 3 to obtain a denoised signal.

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