A wavelet denoising method

Abstract

The present invention discloses a wavelet denoising method, comprising: S1 performing wavelet decomposition on a noisy signal to obtain wavelet coefficients and scale coefficients of each layer; S2 calculating the kurtosis of each coefficient in the wavelet coefficients and scale coefficients of each layer respectively; S3 identifying the coefficients with kurtosis less than a preset threshold as noise corresponding coefficients; S4 calculating the thresholds of the noise corresponding coefficients in the wavelet coefficients and scale coefficients of each layer respectively by using the 3σ criterion as the wavelet threshold of this layer; S5 extracting the pulse corresponding coefficients from the wavelet coefficients and scale coefficients of each layer by combining the wavelet threshold and the chi-square energy window method; S6 setting to zero the coefficients in the wavelet coefficients and scale coefficients of each layer except the pulse corresponding coefficients to obtain the processed wavelet coefficients and scale coefficients of each layer; S7 reconstructing the denoised signal by using the processed wavelet coefficients and scale coefficients of each layer. The present invention can achieve high-fidelity of pulse waveforms while quickly and accurately removing white noise.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a wavelet denoising method. Background Art

[0002] Wavelet threshold denoising is an effective Gaussian white noise suppression technology, which is widely used in the field of health status monitoring of people and objects such as human acoustic-electric signal detection and power equipment status monitoring. The threshold calculation rule and the threshold processing function are the key problems faced by wavelet threshold denoising, and have a great impact on the denoising effect.

[0003] For this reason, scholars at home and abroad have proposed many solutions. Common threshold calculation rules include general threshold, unbiased risk threshold, and minimax threshold, etc. However, these thresholds generally have problems affected by the coefficient length, pulse frequency, and amplitude size. Chinese Patent Publication No. CN105701456B, publication date October 25, 2019, the name of the invention is an adaptive denoising method for angular accelerometer signals based on wavelet analysis. This application discloses a wavelet threshold estimation method based on 3σ. Its disadvantage is that the coefficients for estimating the noise standard deviation σ include pulse corresponding coefficients and noise corresponding coefficients. Therefore, the obtained σ will be significantly larger than the actual noise standard deviation, and an excessive threshold will suppress the front and rear edges of some small-amplitude pulses and large-amplitude pulses. Chinese Patent Publication No. CN111723677A, publication date September 29, 2020, the name of the invention is a wavelet denoising method based on an adaptive threshold. This application discloses a method of using the chi-square energy window method to iteratively filter the coefficients to extract pure noise corresponding coefficients for estimating σ to solve the problems existing in Application Case CN105701456B. Its disadvantage is that it is necessary to iteratively use the chi-square energy window method to identify the pulse corresponding coefficients from the coefficients. Therefore, the analysis and calculation time will increase significantly. The threshold processing functions mainly include hard threshold and soft threshold. The hard threshold will cause the denoised signal to be discontinuous, and the soft threshold will cause amplitude attenuation, and the effects are not ideal. Summary of the Invention

[0004] The present invention aims to overcome the disadvantages and deficiencies existing in the existing wavelet threshold calculation rules and threshold processing functions. By using the difference in the amplitude distribution statistical characteristics between pulse signals and white noise, kurtosis is introduced to quickly identify the noise corresponding coefficients from the coefficients to obtain an accurate estimate of the noise standard deviation. Furthermore, combined with the chi-square energy window method, the identification and extraction of the pulse corresponding coefficients are completed, so as to provide a fast and accurate wavelet denoising method, solve the problems of threshold adaptive calculation and fast and accurate processing in the fields such as online monitoring of humans, machines, and objects, and ensure the high fidelity of the pulse waveform after denoising while effectively suppressing white noise.

[0005] The object of the present invention is achieved by the following technical solutions.

[0006] A wavelet denoising method, comprising:

[0007] Step S1: Performing wavelet decomposition on the noisy signal to obtain wavelet coefficients and scale coefficients of each layer;

[0008] Step S2: Calculating the kurtosis of each coefficient in the wavelet coefficients and scale coefficients of each layer respectively;

[0009] Step S3: Identifying the coefficients with kurtosis less than the preset threshold as the coefficients corresponding to noise;

[0010] Step S4: Using the 3σ criterion to calculate the thresholds of the coefficients corresponding to noise in the wavelet coefficients and scale coefficients of each layer respectively as the wavelet threshold a_thr = 3σ of this layer, where σ is the standard deviation of the coefficients corresponding to noise in the wavelet coefficients and scale coefficients of each layer;

[0011] Step S5: Extracting the coefficients corresponding to pulses from the wavelet coefficients and scale coefficients of each layer by combining the wavelet threshold and the chi-square energy window method;

[0012] Step S6: Setting the coefficients other than the coefficients corresponding to pulses in the wavelet coefficients and scale coefficients of each layer to zero to obtain the processed wavelet coefficients and scale coefficients of each layer;

[0013] Step S7: Reconstructing the denoised signal by using the processed wavelet coefficients and scale coefficients of each layer.

[0014] Further, the formula for calculating the kurtosis of each coefficient in Step S2 is:

[0015]

[0016] where x i (i = 1, 2, …, N) is the coefficient sequence centered on the coefficient to be calculated for kurtosis, N is the length of the coefficient sequence, the value of N should be less than half the wavelength of the pulse signal, μ is the average value of the coefficient sequence, and σ is the standard deviation of the coefficient sequence.

[0017] Further, the wavelet decomposition is binary wavelet decomposition, and the length N of the coefficient sequence satisfies: the N used for the highest-layer wavelet coefficients is the same as the N used for the highest-layer scale coefficients, the N used for the sub-highest-layer wavelet coefficients is twice the N used for the highest-layer wavelet coefficients, and so on to determine the N used for the wavelet coefficients of each layer.

[0018] Further, the value range of the preset threshold is [2, 5].

[0019] Preferably, the chi-square energy window method can be improved to include:

[0020] Step S51: Setting the energy window width M according to the lower limit of the pulse width;

[0021] Step S52: Compare the absolute value of the coefficient with the wavelet threshold a_thr point by point. The coefficient x(n) whose absolute value is greater than a_thr is the coefficient corresponding to the pulse;

[0022] Step S53: Starting from the identified x(n), slide the energy window with x(n) as the end point point by point forward. When the nominal cumulative energy E of the energy window is less than the energy threshold e_thr, the coefficient corresponding to the end point of the energy window is the starting point of the pulse, where

[0023]

[0024] Step S54: Starting from the identified x(n), slide the energy window with x(n) as the starting point point by point backward. When the nominal cumulative energy E of the energy window is less than the energy threshold e_thr, the coefficient corresponding to the starting point of the energy window is the end point of the pulse. The coefficients between the end point of the pulse and the starting point of the pulse described in Step S53 are all the coefficients corresponding to the pulse, where

[0025]

[0026] Step S55: Starting from the next coefficient that is M points away from the end point of the pulse identified in Step S54, repeat Steps S52 to S55 until the end of the coefficients;

[0027] where x(i) is the coefficient sequence within the energy window, and σ is the standard deviation of the coefficients corresponding to the noise in each layer of wavelet coefficients or scale coefficients.

[0028] The energy threshold e_thr is obtained by querying the chi-square distribution table according to the chi-square energy window width M.

[0029] According to the second aspect of the object of the present invention, the present invention provides a non-transitory computer-readable storage medium, on which a computer program is stored, characterized in that when the computer program is executed by a processor, the wavelet denoising method as described above is implemented.

[0030] According to the third aspect of the object of the present invention, the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that when the processor executes the program, the wavelet denoising method as described above is implemented.

[0031] Compared with the existing wavelet threshold denoising method, the present invention introduces kurtosis to quickly and accurately extract the corresponding noise coefficients from each layer of wavelet coefficients and scale coefficients, and then uses the improved chi-square energy window method to accurately identify the pulse edges. The coefficients in each layer of wavelet coefficients and scale coefficients except the coefficients corresponding to the pulses are set to zero to obtain the wavelet coefficients after threshold processing, and finally the denoised signal is reconstructed. It realizes the fast and automatic calculation of the wavelet denoising threshold, and at the same time avoids the problems such as pulse discontinuity and amplitude attenuation existing in the current hard threshold and soft threshold. While accurately removing white noise, the pulse waveform obtains high fidelity, which can effectively promote the popularization and application of wavelet denoising technology in the fields of electrocardiogram detection, on-line monitoring of power equipment, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic diagram of the implementation process of a wavelet denoising method of the present invention;

[0033] Figure 2 It is a waveform diagram of the stator winding insulation monitoring signal of a large generator motor of the present invention;

[0034] Figure 3 For the Figure 2 denoising result waveform diagram of the signal by a wavelet denoising method of the present invention;

[0035] Figure 4 It is a comparison diagram of the denoising results of the present invention and the existing methods;

[0036] Figure 5 It is a schematic diagram of the process of the chi-square energy window method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0037] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0038] For a white noise sequence n(i) that follows a normal distribution, its amplitude distribution satisfies kurtosis K = 3; while the amplitude distribution of the pulse signal significantly deviates from the normal distribution, and the larger the pulse amplitude, the larger the kurtosis. In addition, kurtosis is calculated based on the statistical characteristics of the amplitude distribution. The size of the pulse amplitude only affects the difference between the corresponding kurtosis and 3, but does not affect its essence of being greater than 3. Therefore, the identification of small-amplitude pulses can also be completed. Therefore, using kurtosis as the preset threshold can initially realize the identification of the corresponding noise coefficients, and the purpose of identifying the corresponding noise coefficients is to accurately estimate the noise standard deviation. It is not required to accurately identify all the corresponding noise coefficients. Therefore, in this application, kurtosis K is introduced as a screening condition to extract some pure corresponding noise coefficients from each layer of wavelet coefficients and scale coefficients mixed with the corresponding noise coefficients and pulse coefficients for quickly and accurately estimating the noise standard deviation.

[0039] For the white noise sequence n(i) that follows a normal distribution, it also satisfies P{-3σ < n(i) < 3σ} = 0.9974, where σ is the standard deviation of n(i). That is, the event that the value of n(i) appears outside the interval (-3σ, 3σ) is a small-probability event. Therefore, the 3σ criterion can be used to calculate the wavelet threshold, and then the wavelet threshold is used to identify the coefficients corresponding to the impulses in the coefficients, thereby completing the preliminary identification of the pulse region. However, it is still necessary to further clarify the range of the pulse, that is, to clarify the front and rear edges of the pulse.

[0040] Considering that n(i) / σ is independently and identically distributed according to the standard normal distribution N(0,1), for the nominal cumulative energy E of the energy window with length M

[0041]

[0042] It follows a chi-square distribution with degree of freedom M, and E also satisfies the statistical law of the chi-square distribution. For example, when the energy window length M = 20, it satisfies P(E≥40) = 0.005. That is, the event that the nominal cumulative energy of the white noise sequence n(i) with length 20 is greater than or equal to 40 is a small-probability event. It can be reasonably considered that when E≥40, the sequence contains the coefficients corresponding to the impulses. Therefore, the edges of the pulse can be found through this condition to complete the final determination of the pulse range.

[0043] For this reason, an embodiment is described in combination with the signal processing of the stator winding insulation monitoring of large generator-motors. The stator winding insulation monitoring of large generator-motors is carried out by installing a coupling capacitor at the neutral point for signal sensing. The sampling frequency of the monitoring system is 40 MHz, and the continuous acquisition time is 100 ms. In this embodiment, 20 ms of data is used as the processing object, and Figure 1 a wavelet denoising method of the present invention as shown is proposed, including:

[0044] Step S1: Perform binary wavelet decomposition on the original noisy insulation monitoring signal as shown Figure 2 to obtain wavelet coefficients of each layer and the highest-layer scale coefficient. The mother wavelet used for wavelet decomposition is selected according to the index that the cross-correlation coefficient between the mother wavelet and the theoretical insulation damage signal is the largest. The selection range of the mother wavelet includes the db series, sym series, and coif series; since insulation damage signals are more likely to appear on the high-voltage side of the generator-motor, and the insulation damage signals measured at the neutral point have passed through the propagation of the stator winding and mainly obtained the double-exponential oscillation decay pulse type, the optimal mother wavelet is selected as db8; the decomposition layer number is selected as 6 layers according to experience. At this time, the signal components in the decomposition coefficients are less, and there is no need to continue decomposition; therefore, in the embodiment, the original noisy signal is decomposed by the db8 mother wavelet for 6 layers to obtain the wavelet coefficients cD1 - cD6 of the 1st to 6th layers and the scale coefficient cA6 of the 6th layer;

[0045] Step S2: Calculate the kurtosis of each coefficient in the wavelet coefficients cD1 to cD6 of the 1st to 6th layers and the scale coefficient cA6 of the 6th layer respectively. Kurtosis is a statistical feature of the amplitude distribution of the coefficient sequence. Therefore, it is necessary to calculate using the local coefficient sequence around the coefficient to be calculated. The sequence length should be less than half of the wave length of the damage pulse signal. At this time, there is a need for signal extension at both ends. Common extension methods include mirror extension, zero-padding extension, etc. However, considering the endpoint effect of wavelet denoising, that is, the amplitudes at both ends of the denoised signal are not accurate. Therefore, in the process of kurtosis calculation, a simple treatment is adopted where some coefficients at both ends are not calculated. Specifically, for the cD1 wavelet coefficient sequence with a length of 400006, the sequence length for calculating kurtosis is 40. Therefore, 20 coefficients at both the head and tail of cD1 are not calculated for kurtosis and are default set to 0.

[0046] Step S3: Identify the coefficients with kurtosis less than the preset threshold T K = 3.5 as the coefficients corresponding to noise. Therefore, 20 coefficients at both the head and tail of cD1 are default considered as the coefficients corresponding to noise. Due to the endpoint effect of wavelet denoising, this treatment will not cause a large deviation. Coupled with the sparse distribution of the generator insulation damage pulses, usually it does not affect the detection of insulation signals;

[0047] Step S4: Use the 3σ criterion to calculate the thresholds of the coefficients corresponding to noise in the wavelet coefficients cD1 to cD6 of the 1st to 6th layers and the scale coefficient cA6 of the 6th layer respectively as the wavelet thresholds of this layer, that is, the wavelet threshold a_thr = 3σ, where σ is the standard deviation of the coefficients corresponding to noise in the wavelet coefficients cD1 to cD6 of the 1st to 6th layers and the scale coefficient cA6 of the 6th layer;

[0048] Step S5: Extract the coefficients corresponding to pulses from the wavelet coefficients cD1 to cD6 of the 1st to 6th layers and the scale coefficient cA6 of the 6th layer by combining the wavelet threshold and the chi-square energy window method;

[0049] Step S6: Set to zero the coefficients in the wavelet coefficients cD1 to cD6 of the 1st to 6th layers and the scale coefficient cA6 of the 6th layer except for the coefficients corresponding to pulses to obtain the processed wavelet coefficients cD1' to cD6' of the 1st to 6th layers and the scale coefficient cA6' of the 6th layer;

[0050] Step S7: Reconstruct using the processed wavelet coefficients cD1' to cD6' of the 1st to 6th layers and the scale coefficient cA6' of the 6th layer to obtain Figure 3 the denoised signal shown.

[0051] For comparison, in this embodiment, three commonly used methods in the field of insulation damage signal denoising, such as the general threshold combined with the hard threshold denoising method (Method 1), the layer-related threshold combined with the hard threshold (Method 2), and the layer-related threshold combined with the soft threshold (Method 3), are introduced for comparison to obtain Figure 4The denoising results shown are, for the convenience of comparison, only the denoising results within 0.2 ms are shown in the figure. The blue is the original noisy signal, and the red is the denoised signal. The denoising results of this embodiment and Methods 1-3 are shown from top to bottom. The abscissa in the figure is time, with the unit of ms, and the ordinate is amplitude, with the unit of V.

[0052] Further, the kurtosis calculation formula for each coefficient described in step S2 is:

[0053]

[0054] where x i (i = 1, 2, …, N) is the coefficient sequence centered on each coefficient for which the kurtosis is to be calculated. N is the length of the coefficient sequence, and N should be less than the half-wave length of the insulation damage pulse signal. Therefore, it is also related to the corresponding frequency bands of each layer of wavelet coefficients and the highest-layer scale coefficients. The greater the frequency of the corresponding frequency band of the coefficient, the more pulse-corresponding coefficients of the same pulse are decomposed into the wavelet coefficients of this layer. Therefore, N is also larger. μ is the average value of the coefficient sequence, and σ is the standard deviation of the coefficient sequence. The length N of the coefficient sequence satisfies: the N used for the highest-layer wavelet coefficients is the same as the N used for the highest-layer scale coefficients, and the N used for the sub-highest-layer wavelet coefficients is twice the N used for the highest-layer wavelet coefficients, and so on to determine the N used for each layer of wavelet coefficients.

[0055] Further, the value range of the preset threshold is [2, 5]. The purpose of using kurtosis and the preset threshold is to obtain the coefficients corresponding to pure white noise, rather than extracting all the noise-corresponding coefficients in the coefficients. Therefore, the value of the preset threshold can be specifically determined according to the noise characteristics.

[0056] For a white noise coefficient sequence n(i) with a standard deviation of σ within an energy window of length M = 20, n(i) / σ is independently and identically distributed according to the standard normal distribution N(0, 1). Therefore, the nominal cumulative energy E of the energy window of n(i)

[0057]

[0058] obeys the chi-square distribution with M degrees of freedom, and satisfies P(E≥40) = 0.005. That is, it is a small-probability event that the nominal cumulative energy of a white noise coefficient sequence of length 20 is greater than or equal to 40. It can be reasonably considered that when E≥40, the sequence contains pulse-corresponding coefficients. Therefore, by moving this energy window, the pulse-corresponding coefficients can be identified. After identifying the pulse-corresponding coefficients, setting the remaining coefficients to zero can complete the wavelet threshold processing. Therefore, first, use the above wavelet threshold a_thr = 3σ to complete the discovery of pulse coefficients, and then combine the energy statistical characteristics of white noise to determine the position of x(n) in the sliding window according to the sliding direction, so as to obtain a more accurate pulse boundary centered on x(n).

[0059] Therefore, the current chi-square energy window method is improved to form the process as described in Figure 4 which specifically includes:

[0060] Step S51: Set the energy window width M = 20 according to the lower limit of the pulse width;

[0061] Step S52: Compare the absolute value of the coefficient with the wavelet threshold a_thr point by point. The coefficient x(n) whose absolute value is greater than a_thr is the coefficient corresponding to the pulse;

[0062] Step S53: Starting from the identified x(n), the energy window with x(n) as the end point slides forward point by point. When the nominal cumulative energy E of the energy window is less than the energy threshold e_thr, the coefficient corresponding to the end point of the energy window is the starting point of the pulse, where

[0063]

[0064] Step S54: Starting from the identified x(n), the energy window with x(n) as the starting point slides backward point by point. When the nominal cumulative energy E of the energy window is less than the energy threshold e_thr, the coefficient corresponding to the starting point of the energy window is the end point of the pulse, and the coefficients between the end point of the pulse and the starting point of the pulse described in Step S53 are all the coefficients corresponding to the pulse, where

[0065]

[0066] Step S55: Starting from the next coefficient that is M points away from the end point of the pulse identified in Step S54, repeat Steps S52 to S55 until the end of the coefficients;

[0067] where x(i) is the coefficient sequence within the energy window, and σ is the standard deviation of the coefficients corresponding to the noise in each layer of wavelet coefficients or the coefficients of the highest layer scale.

[0068] The energy threshold e_thr = 40 is obtained by querying the chi-square distribution table based on the chi-square energy window width M = 20 and the probability value P = 0.005.

[0069] Through the description of the above embodiments, those skilled in the art can clearly understand that the implementation of the present invention can be achieved by means of software plus a necessary general hardware platform. Embodiments of the present invention can be implemented using existing processors, or by a dedicated processor used for this purpose or other purposes in a suitable system, or by a hardwired system. Embodiments of the present invention also include non-transitory computer-readable storage media, which include machine-readable media for carrying or having machine-executable instructions or data structures stored thereon; such machine-readable media can be any available medium accessible by a general or special-purpose computer or other machine with a processor. For example, such machine-readable media can include RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk memories, magnetic disk memories or other magnetic storage devices, or any other medium that can be used to carry or store the required program code in the form of machine-executable instructions or data structures and can be accessed by a general or special-purpose computer or other machine with a processor. When information is transmitted or provided to a machine through a network or other communication connection (hardwired, wireless or a combination of hardwired or wireless), this connection is also regarded as a machine-readable medium.

[0070] So far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the protection scope of the present invention.

Claims

1. A wavelet denoising method, characterized in that, Including: Step S1: Perform wavelet decomposition on the noisy signal to obtain wavelet coefficients and scale coefficients of each layer; Step S2: Calculate the kurtosis of each coefficient in the wavelet coefficients and scale coefficients of each layer respectively; Step S3: Identify the coefficients with kurtosis less than the preset threshold as the coefficients corresponding to noise; Step S4: Use the 3σ criterion to calculate the threshold of the coefficients corresponding to noise in the wavelet coefficients and scale coefficients of each layer as the wavelet threshold a_thr = 3σ of this layer, where σ is the standard deviation of the coefficients corresponding to noise in the wavelet coefficients and scale coefficients of each layer; Step S5: Extract the coefficients corresponding to pulses from the wavelet coefficients and scale coefficients of each layer by combining the wavelet threshold and the chi-square energy window method; Step S6: Set to zero the coefficients other than the coefficients corresponding to pulses in the wavelet coefficients and scale coefficients of each layer to obtain the processed wavelet coefficients and scale coefficients of each layer; Step S7: Reconstruct the denoised signal using the processed wavelet coefficients and scale coefficients of each layer; In step S5, the chi-square energy window method includes: Step S51: Set the energy window width M according to the lower limit of the pulse width; Step S52: Compare the absolute value of the coefficient with the wavelet threshold a_thr point by point. The coefficient x(n) with an absolute value greater than a_thr is the coefficient corresponding to the pulse; Step S53: Starting from the identified x(n), the energy window with x(n) as the end point slides forward point by point. When the nominal cumulative energy E of the energy window is less than the energy threshold e_thr, the coefficient corresponding to the end point of the energy window is the starting point of the pulse, where Step S54: Starting from the identified x(n), the energy window with x(n) as the starting point slides backward point by point. When the nominal cumulative energy E of the energy window is less than the energy threshold e_thr, the coefficient corresponding to the starting point of the energy window is the end point of the pulse. The coefficients between the end point of the pulse and the starting point of the pulse described in step S53 are all coefficients corresponding to the pulse, where Step S55: Starting from the next coefficient that is M points away from the end point of the pulse identified in step S54, repeat steps S52 to S55 until the end of the coefficients; where, x(i) is the coefficient sequence in the energy window, and σ is the standard deviation of the coefficients corresponding to noise in the wavelet coefficients of each layer or the highest-layer scale coefficient; The energy threshold e_thr is obtained by querying the chi-square distribution table with the chi-square energy window width M; 2. The wavelet denoising method according to claim 1, characterized in that, The calculation formula for the kurtosis of each coefficient described in step S2 is: where x i (i = 1, 2, …, N) is a coefficient sequence centered on each coefficient for which the kurtosis is to be calculated, N is the length of the coefficient sequence, the value of N should be less than half the wave length of the pulse signal, μ is the average value of the coefficient sequence, and σ is the standard deviation of the coefficient sequence.

3. The wavelet denoising method according to claim 2, characterized in that The wavelet decomposition is binary wavelet decomposition. The length N of the coefficient sequence satisfies: The N used for the highest-layer wavelet coefficients is the same as the N used for the highest-layer scale coefficients. The N used for the second-highest-layer wavelet coefficients is twice the N used for the highest-layer wavelet coefficients, and so on to determine the N used for the wavelet coefficients of each layer; 4. A wavelet denoising method according to claim 1, characterized in that The value range of the preset threshold is [2, 5]; 5. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the wavelet denoising method according to any one of claims 1 to 4; 6. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the wavelet denoising method according to any one of claims 1 to 4.

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