Signal noise processing method and system
Patent Information
- Application Number
- PCT/CN2025/085118
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2025-03-26
- Publication Date
- 2026-10-01
Smart Images
Figure CN2025085118_01102026_PF_FP_ABST
Abstract
Description
Noise processing methods and systems for signals Technical Field
[0001] This application relates to the field of signal processing technology, and in particular to a method and system for noise processing of signals. Background Technology
[0002] In signal processing, noise is a key factor affecting data quality. Existing denoising methods are inefficient in complex environments, especially when dealing with large samples and multiple noise sources, making it difficult to maintain stable performance. Therefore, developing efficient denoising algorithms is crucial. Summary of the Invention
[0003] Therefore, it is necessary to provide a noise processing method and system for signals to address the above-mentioned technical problems, which can accurately remove noise in the case of multiple noise sources and avoid losing the original information carried by the initial signal as much as possible.
[0004] Firstly, this application provides a noise processing method for a signal, the noise processing method comprising:
[0005] The initial signal is decomposed using CEEMDAN to obtain multiple IMF signals;
[0006] Wavelet threshold denoising is performed on at least a portion of the IMF signals one by one to obtain the wavelet coefficients of each layer of each IMF signal;
[0007] The wavelet coefficients of each layer are subjected to inverse wavelet transform to reconstruct the denoised IMF signals of each layer.
[0008] The denoised initial signal is obtained from the denoised IMF signals of all layers.
[0009] In one embodiment, the step of performing CEEMDAN decomposition on the initial signal to obtain multiple IMF signals further includes:
[0010] Step 1: Generate multiple additive white Gaussian noises, and add each additive white Gaussian noise to the initial signal one by one to obtain the loaded signal:
[0011]
[0012] Among them, the The parameters are the loading signal after adding the additive white Gaussian noise. The signal-to-noise ratio for each decomposition level, The additive white Gaussian noise, It is a positive integer;
[0013] Step 2: Perform EMD decomposition on each of the loaded signals and obtain the first-level IMF signal and the first-level residual component, wherein the first-level IMF signal is:
[0014]
[0015] in, This is the first-level IMF signal. For each of the loaded signals, the first level of the IMF signal, and ;
[0016] The residual components of the first level are:
[0017] ;
[0018] Step 3: Perform EMD decomposition on each additive white Gaussian noise, and obtain the second-level IMF signal and the second-level residual component from the corresponding first-level residual component of the decomposed additive white Gaussian noise. The second-level IMF signal is as follows:
[0019] ,
[0020] The residual components of the second level are:
[0021] ;
[0022] Step 4: Obtain the residual components of the Kth level based on the residual components of the second level in Step 3, where the residual components of the Kth level are:
[0023] ,
[0024] Where k = 2, 3, ..., K, and K is the highest decomposition level;
[0025] Step 5: Obtain the IMF signal of the (K+1)th level based on the residual component of the Kth level, wherein the IMF signal of the (K+1)th level is:
[0026] ;
[0027] Step 6: Repeat steps 4 and 5 iteratively until the residual components become constants or monotonic functions, obtaining the decomposition expression of the initial signal, which is:
[0028] ;
[0029] Step 7: Output the IMF signal sequence arranged from high frequency to low frequency and a residual signal component.
[0030] In one embodiment, the step of performing EMD decomposition on each of the loaded signals further includes:
[0031] Step S11: Obtain the local maxima and local minima of the initial signal, and use a preset degree spline interpolation function to fit the local maxima and local minima respectively to obtain the upper envelope and lower envelope respectively;
[0032] Step S12: Obtain the first signal component based on the upper and lower envelopes, and determine whether the first signal component conforms to the characteristics of an IMF signal;
[0033] If the conditions are met, the first signal component is taken as the first-level IMF signal;
[0034] Subtracting the first-level IMF signal from the initial signal yields the first-level residual signal component;
[0035] If it does not meet the requirements, the first signal component is replaced with the initial signal, and steps S11 and S12 are repeated until the Kth signal component meets the characteristics of the IMF signal.
[0036] In one embodiment, the step of performing wavelet threshold denoising on at least a portion of the IMF signals one by one further includes:
[0037] For each IMF signal, a single-level wavelet decomposition is performed under each type of wavelet basis to obtain the first-level detail coefficients and the first-level approximation coefficients. The optimal wavelet basis for each level is obtained based on the first-level detail coefficients and the first-level approximation coefficients.
[0038] To obtain the optimal number of wavelet decomposition levels;
[0039] Perform wavelet decomposition with the optimal number of decomposition levels on each IMF signal. Obtain the optimal wavelet basis for each decomposition level, retain the detail coefficients of the first level obtained by decomposition, and use the approximation coefficients of the first level as the signal input for the next level. Decompose to obtain new detail coefficients of the first level and new approximation coefficients of the first level, until the decomposition is completed.
[0040] For the detail coefficients of the first level of each layer, a denoising threshold is calculated, and thresholding is performed on all detail coefficients of each layer based on the denoising threshold.
[0041] Perform a single-level inverse wavelet transform on the detail coefficients and approximation coefficients of each level to obtain new approximation coefficients for the next level. Then, continue to perform a single-level inverse wavelet transform using the same wavelet basis used in the previous level decomposition. Repeat this process until the IMF signal is reconstructed and the denoised IMF signal is obtained.
[0042] In one embodiment, the step of obtaining the optimal wavelet basis for each layer based on the detail coefficients of the first level and the approximation coefficients of the first level further includes:
[0043] For each IMF signal, a single-level wavelet decomposition is performed under a single-level wavelet basis to obtain the first-level detail coefficients and the first-level approximation coefficients.
[0044] The total signal energy of each single layer is calculated based on the approximation coefficients of all first-level waveslet bases under each single layer.
[0045] The energy probability distribution of each detail coefficient is calculated based on the total signal energy of each single layer, and the corresponding wavelet entropy is obtained.
[0046] For each single layer, the wavelet basis function that minimizes the wavelet entropy value is selected as the optimal wavelet basis for that layer.
[0047] In one embodiment, prior to the step of performing single-layer wavelet decomposition under a single-layer wavelet basis for each IMF signal, the method further includes:
[0048] Establish a wavelet family selection library to store various wavelet basis functions to be used.
[0049] In one embodiment, the step of performing single-layer wavelet decomposition on a single-layer wavelet basis for each IMF signal further includes:
[0050] For each input IMF signal, all wavelet basis functions are iterated over to perform single-level wavelet decomposition.
[0051] In one embodiment, the step of calculating the total signal energy of each single layer based on the approximation coefficients of all first-level layers under each single-layer wavelet basis further includes:
[0052] The total signal energy is calculated using the following formula:
[0053]
[0054] in, The total signal energy, Let represent the approximation coefficients of the i-th first level under each single-layer wavelet basis, where i = 1, 2, ..., N, and N is the number of approximation coefficients of the first level.
[0055] In one embodiment, the step of calculating the energy probability distribution of each detail coefficient based on the total signal energy of each single layer further includes: the energy probability distribution satisfies the following relationship:
[0056]
[0057] in, This represents the energy probability distribution.
[0058] The step of obtaining the corresponding wavelet entropy further includes:
[0059] The wavelet entropy WE satisfies the following relationship:
[0060]
[0061] In one embodiment, the step of obtaining the optimal wavelet decomposition level further includes:
[0062] Estimate the maximum wavelet decomposition level based on the input IMF signal:
[0063] The IMF signal is decomposed into the maximum number of decomposition levels. The optimal wavelet basis is obtained at each level, and the detail coefficients obtained at each level are retained. The approximation coefficients are used as the signal input for the next level of wavelet decomposition. New detail coefficients and new approximation coefficients are obtained until the decomposition is completed.
[0064] For any given level, calculate the sparsity of the approximation coefficients for that level, and calculate the sparsity variation between levels.
[0065] When the sparsity variation value meets the preset variation threshold, the decomposition level at this time is selected as the optimal decomposition level.
[0066] In one embodiment, the step of obtaining the denoised initial signal based on the denoised IMF signals of all layers further includes:
[0067] The residual components of the initial signal are accumulated with the denoised IMFs of each level to obtain the denoised initial signal.
[0068] Secondly, this application also provides a noise processing system for a signal, the system comprising:
[0069] The decomposition module is used to perform CEEMDAN decomposition on the initial signal to obtain multiple IMF signals;
[0070] A denoising module is used to perform wavelet threshold denoising on at least a portion of the IMF signals one by one to obtain the wavelet coefficients of each layer of each IMF signal.
[0071] The first reconstruction module is used to perform inverse wavelet transformation on the wavelet coefficients of each layer to reconstruct the denoised IMF signals of each layer.
[0072] The second reassembly module is used to obtain the denoised signal of the initial signal based on the denoised IMF signals of all layers.
[0073] The above describes a noise processing method and system for signals. The noise processing method includes: performing CEEMDAN decomposition on an initial signal to obtain multiple IMF signals; performing wavelet threshold denoising on at least a portion of the IMF signals one by one to obtain wavelet coefficients for each layer of each IMF signal; performing inverse wavelet transform on each layer of wavelet coefficients to reconstruct the denoised IMF signals for each layer; and obtaining the denoised initial signal based on the denoised IMF signals for all layers. Therefore, this application uses a combination of CEEMDAN decomposition and wavelet denoising to perform noise reduction on the initial signal, which has strong signal denoising capabilities and high computational efficiency. This method is suitable for non-stationary complex signal processing tasks with large sample sizes and multiple noise sources. Attached Figure Description
[0074] Figure 1 is a schematic flowchart of a noise processing method for a signal provided in an embodiment of this application;
[0075] Figure 2 is a flowchart illustrating another noise processing method for a signal provided in an embodiment of this application;
[0076] Figure 3 is a flowchart illustrating another noise processing method for a signal provided in an embodiment of this application;
[0077] Figure 4 is a flowchart illustrating another noise processing method for a signal provided in an embodiment of this application;
[0078] Figure 5 is a flowchart illustrating another noise processing method for a signal provided in an embodiment of this application;
[0079] Figure 6 is a flowchart illustrating another noise processing method for a signal provided in an embodiment of this application;
[0080] Figure 7 is a schematic diagram of the structure of a noise processing system for a signal provided in an embodiment of this application;
[0081] Figure 8 is a basic structural block diagram of the computer device in this embodiment. Detailed Implementation
[0082] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0083] Please refer to Figure 1, which is a flowchart illustrating a noise processing method for a signal according to an embodiment of this application. As shown in Figure 1, the noise processing method includes the following steps:
[0084] Step S1: Perform CEEMDAN decomposition on the initial signal to obtain multiple IMF signals.
[0085] Before performing CEEMDAN decomposition on the initial signal, the original signal is first acquired by a sensor. Taking into account the environmental noise and instrument noise that may exist during the signal acquisition process, the original signal is preprocessed by using a bandpass Butterworth filter and a fixed frequency filter (usually 60Hz) to obtain the initial signal.
[0086] CEEMDAN decomposition, or Adaptive Noise-Complete Empirical Mode Decomposition, is an improved Empirical Mode Decomposition (EMD) method. Based on EMD decomposition, CEEMDAN not only addresses the mode mixing problem inherent in EMD decomposition by adding specific noise at each stage of the decomposition but also resolves the issue of noise residue after signal reconstruction. Furthermore, CEEMDAN decomposition can enhance the spectral separation capability of modes with lower computational complexity.
[0087] After the initial signal is decomposed by CEEMDAN, multiple IMF signals are obtained. That is, the initial signal is decomposed into multiple IMF signal components, and then noise denoising is performed on the IMF signal components to make the denoised signal granularity smaller and the noise can be effectively removed.
[0088] Step S2: Perform wavelet threshold denoising on at least a portion of the IMF signals one by one to obtain the wavelet coefficients of each layer of each IMF signal.
[0089] Wavelet thresholding denoising is implemented using wavelet transform algorithms, a type of time-frequency domain signal processing method characterized by multi-resolution properties. This means the signal has a smaller time scale for high-frequency components and a larger time scale for low-frequency components. Wavelet denoising theory is based on the sparsity of wavelet coefficients, where signal energy is concentrated in only a few coefficients, while noise energy is widely distributed across all coefficients in the wavelet domain. Therefore, denoising can be achieved by applying appropriate thresholding operations to each wavelet coefficient. This application denoises the IMF signals at each level rather than the original signal, proposing improvements to traditional wavelet thresholding denoising methods.
[0090] In this step, wavelet threshold denoising is performed only on high-frequency IMF signals. For example, after sorting the IMF signals from high frequency to low frequency, the first two-thirds of the IMF signals are selected for denoising.
[0091] Step S3: Perform inverse wavelet transform on the wavelet coefficients of each layer to reconstruct the denoised IMF signals of each layer.
[0092] Step S4: Obtain the denoised initial signal based on the denoised IMF signals of all layers.
[0093] Therefore, this embodiment decomposes the initial signal into multiple IMF signals, each reflecting the signal's characteristics at different scales. Then, noise is assessed for each IMF signal, and wavelet thresholding is used to denoise the high-frequency components of the IMF signal, such as the first two-thirds mentioned earlier, generating a denoised signal. This embodiment combines CEEMDAN decomposition with wavelet denoising to map the IMF features of the initial signal into the time, frequency, and wavelet domains, achieving accurate separation and noise removal of the initial signal's features at different scales.
[0094] Please refer to Figure 2, which is a flowchart illustrating another signal noise processing method provided in an embodiment of this application. As shown in Figure 2, the step S1 above, "performing CEEMDAN decomposition on the initial signal to obtain multiple IMF signals," further includes the following steps:
[0095] Step 1: Generate multiple additive white Gaussian noises, and add each additive white Gaussian noise to the initial signal one by one to obtain the loaded signal:
[0096]
[0097] Among them, the The loaded signal is the one after adding the additive white Gaussian noise. As the initial signal, the parameters The signal-to-noise ratio for each decomposition level, The additive white Gaussian noise, It is a positive integer.
[0098] Additive white Gaussian noise conforms to: ~N(0,1). Typically, the parameter... For data primarily composed of high-frequency signals, set a smaller amplitude; for data primarily composed of low-frequency signals, set a larger amplitude. When i is 1, for , representing the undecomposed signal-to-noise ratio.
[0099] Step 2: Perform EMD decomposition on each of the loaded signals and obtain the first-level IMF signal and the first-level residual component, wherein the first-level IMF signal is:
[0100]
[0101] in, This is the first-level IMF signal. For each of the loaded signals, the first level of the IMF signal, and In other words, each loaded signal can first be decomposed using EMD to obtain its corresponding first-level IMF signal. Then, all the first-level IMF signals can be summed and averaged to obtain the final first-level IMF signal. .
[0102] The residual components of the first level are:
[0103] ;
[0104] That is, the residual component of the first level is the difference between the initial signal and the IMF signal of the first level.
[0105] Step 3: Perform EMD decomposition on each additive white Gaussian noise, and obtain the second-level IMF signal and the second-level residual component from the corresponding first-level residual component of the decomposed additive white Gaussian noise. The second-level IMF signal is as follows:
[0106] ,
[0107] The residual components of the second level are:
[0108] ;
[0109] Step 4: Obtain the residual components of the Kth level based on the residual components of the second level in Step 3, where the residual components of the Kth level are:
[0110]
[0111] Where k = 2, 3, ..., K, and K is the highest decomposition level;
[0112] Step 5: Obtain the IMF signal of the (K+1)th level based on the residual component of the Kth level, wherein the IMF signal of the (K+1)th level is:
[0113] ;
[0114] That is, obtaining the residual components of the k-th level. Then, similar to step 3, the next level, namely the K+1 level IMF signal, is obtained.
[0115] Step 6: Repeat steps 4 and 5 iteratively until the residual components become constants or monotonic functions, obtaining the decomposition expression of the initial signal, which is:
[0116] ;
[0117] Step 7: Output the IMF signal sequence arranged from high frequency to low frequency and a residual signal component.
[0118] That is, it outputs a series of IMF signals.
[0119] Please refer to Figure 3, where step 2 above, "perform EMD decomposition on each of the loaded signals," further includes the following steps:
[0120] Step S11: Obtain the local maxima and local minima of the initial signal, and use a preset degree spline interpolation function to fit the local maxima and local minima respectively to obtain the upper envelope and lower envelope respectively.
[0121] In one embodiment, the preset number of predictions can be 3. It should be understood that the number of predictions can also be 2, 4, 5, etc., and is not limited here.
[0122] Step S12: Obtain the first signal component based on the upper and lower envelopes, and determine whether the first signal component conforms to the characteristics of an IMF signal.
[0123] Specifically, the average value of the first upper envelope and the first lower envelope can be calculated first. The first signal component is calculated using this average value, satisfying the following relationship:
[0124]
[0125] in, The first signal component, This is the initial signal.
[0126] The specific scheme for determining whether the first signal component conforms to the characteristics of an IMF signal is as follows: The first signal component should meet two conditions: First, the sum of the number of local maxima and local minima must meet a preset threshold, for example, the sum of the two is equal to the number of zero-crossing points of the signal or the maximum difference is 1; Second, the average value of the first upper envelope and the first lower envelope of the signal is 0. If the first signal component meets both of the above conditions, it is considered a first-level IMF signal.
[0127] In this step, if the judgment result is satisfactory, proceed to step S13; if the judgment result is unsatisfactory, proceed to step S15.
[0128] Step S13: Use the first signal component as the first-level IMF signal.
[0129] Step S14: Subtract the first-level IMF signal from the initial signal to obtain the first-level residual signal component.
[0130]
[0131] in, This is the first-level residual signal component. This is the first-level IMF signal.
[0132] Step S15: Replace the initial signal with the first signal component and repeat steps S11 and S12 until the Kth signal component satisfies the characteristics of the IMF signal.
[0133] The first signal component is about to be After replacing the initial signal, repeat steps S11 and S12 to obtain new upper and lower envelopes. Then, take the average value of the new upper and lower envelopes and the new second signal component, satisfying the following relationship:
[0134]
[0135] For the new second signal component, This represents the average of the new upper and lower envelopes.
[0136] Repeat this step K times, eliminating oscillations by repeatedly subtracting the envelope, until the Kth signal component satisfies the characteristics of an IMF signal, then the following relationship is satisfied:
[0137] .
[0138] That is, the signal component hk+1(t) satisfies the two conditions for becoming an IMF signal. However, considering the possibility of convergence difficulties in practical applications, a new criterion can be used to replace the two conditions for an IMF signal. Specifically, a sufficiently small constant a is first set. During the a-th iteration, the standard deviation textSDk between the current component ha(t) and the component ha−1(t) obtained in the previous iteration is calculated, i.e.:
[0139]
[0140] Where N is the signal component and The length of SDj. If SDj is less than or equal to the constant a, then stop the iteration and... As a first-level IMF signal.
[0141] Please refer to Figure 4. The step of "performing wavelet threshold denoising on at least a portion of the IMF signals one by one" in step S3 above also includes the following steps:
[0142] Step S21: For each IMF signal, perform single-level wavelet decomposition under each type of wavelet basis to obtain the detail coefficients and approximation coefficients of the first level, and obtain the optimal wavelet basis for each level based on the detail coefficients and approximation coefficients of the first level.
[0143] Before step S21, a wavelet family selection library is first established to store various wavelet basis functions to be used, such as sym2, rbio1.3, and coif1. Specifically, in step S21, for each input IMF signal, all wavelet basis functions are iterated through to perform single-level wavelet decomposition, obtaining the first-level detail coefficients and the first-level approximation coefficients.
[0144] Please refer to Figure 5. Step S21, "obtaining the optimal wavelet basis for each layer based on the detail coefficients of the first layer and the approximation coefficients of the first layer," specifically includes the following steps:
[0145] Step S31: For each IMF signal, perform single-level wavelet decomposition under a single-level wavelet basis to obtain the detail coefficients and approximation coefficients of the first level.
[0146] Step S32: Calculate the total signal energy of each single-layer wavelet basis based on the approximation coefficients of all first-level levels. Specifically, the total signal energy is calculated using the following formula:
[0147]
[0148] in, The total signal energy, Let represent the approximation coefficients of the i-th first level under each single-layer wavelet basis, where i = 1, 2, ..., N, and N is the number of approximation coefficients of the first level.
[0149] Step S33: Calculate the energy probability distribution of each detail coefficient based on the total signal energy of each single layer, and obtain the corresponding wavelet entropy.
[0150] The energy probability distribution satisfies the following relationship:
[0151]
[0152] in, This represents the energy probability distribution.
[0153] Further define and obtain the corresponding wavelet entropy WE:
[0154] .
[0155] Step S34: For each single layer, select the wavelet basis function that minimizes the wavelet entropy value from the wavelet entropy values, and use it as the optimal wavelet basis for that layer.
[0156] Step S22: Obtain the optimal number of wavelet decomposition layers.
[0157] Please refer to Figure 6. The specific scheme for obtaining the optimal wavelet decomposition level includes the following steps:
[0158] S41: Estimate the maximum number of wavelet decomposition layers based on the input IMF signal.
[0159] First, the maximum wavelet decomposition level is estimated to satisfy the following relationship:
[0160]
[0161] Where N is the length of the input signal. The signal is decomposed into J levels.
[0162] S42: Decompose the IMF signal into the maximum number of decomposition levels. The optimal wavelet basis is obtained at each level, and the detail coefficients obtained from each level are retained. The approximation coefficients are used as the signal input for the next level of wavelet decomposition. New detail coefficients and new approximation coefficients are obtained until the decomposition is completed.
[0163] S43: For any given level, calculate the sparsity of the approximation coefficients for that level, and calculate the sparsity variation between levels. The sparsity of the approximation coefficients for that level satisfies the following relationship:
[0164]
[0165] in, To account for the sparsity of the approximation coefficients of this layer, For the sparsity variation between layers, Let be the number of detail coefficients at layer j, where 1 ≤ j ≤ J, and i be the index of the detail coefficient, i = 1, 2, ... . The following relationship must be satisfied: .
[0166] S44: When the sparsity variation value meets the preset variation threshold, select the decomposition level at this time as the optimal decomposition level.
[0167] The sparsity transform can be calculated starting from j=2, and S1 = 0 is defined. When the sparsity transform value Sj≥0.05, the optimal maximum layer of the signal is selected as Jmax=j−1.
[0168] Step S23: Perform wavelet decomposition with the optimal number of decomposition levels on each IMF signal. Obtain the optimal wavelet basis for each decomposition level, retain the detail coefficients of the first level obtained by decomposition, and use the approximation coefficients of the first level as the signal input of the next level. Decompose to obtain new detail coefficients of the first level and new approximation coefficients of the first level until the decomposition is completed.
[0169] Step S24: Calculate the denoising threshold for the detail coefficients of the first level of each layer, and perform thresholding on all detail coefficients of each layer according to the denoising threshold.
[0170] For example, for the detail coefficients of the first level of the j-th layer, 1≤j≤Jmax, the denoising threshold is calculated as follows:
[0171]
[0172] in The median of the detail coefficients of the first level in the j-th layer. Let be the number of detail coefficients in layer j. Thresholding is applied to the detail coefficients of each level in layer j, satisfying the following formula:
[0173]
[0174] Where sgn(cD) i,j Let be the symbol for the detail coefficient, i be the index of the detail coefficient, and T be an adjustable parameter. Thresholding is performed on all detail coefficients across all levels to obtain the i-th new detail coefficient of the j-th level, represented as: .
[0175] Step S25: Perform a single-level inverse wavelet transform on the detail coefficients and approximation coefficients of each level to obtain new approximation coefficients for the next level. Then, continue to perform a single-level inverse wavelet transform using the same wavelet basis used in the previous level decomposition. Repeat this process until the IMF signal is reconstructed and the denoised IMF signal is obtained.
[0176] Specifically, starting from the highest level, using the same wavelet basis used in the decomposition, a single-level inverse wavelet transform is performed on the detail coefficients and approximation coefficients to obtain new approximation coefficients for the next level. This single-level inverse wavelet transform is then performed again using the same wavelet basis used in the previous level's decomposition. This process is repeated until the signal is reconstructed, at which point the algorithm outputs the denoised IMF signal.
[0177] After obtaining the denoised IMF signal, as described in step S4 above: obtain the denoised initial signal based on the denoised IMF signals of all layers. Specifically, the residual components of the initial signal are accumulated with the denoised IMF signals of each layer to obtain the denoised initial signal.
[0178] Therefore, in this embodiment, after the initial signal is decomposed by the CEEMDAN algorithm, the algorithm iteratively performs wavelet threshold denoising on the IMF signals at each level, and after all denoising processes are completed, the signal is reconstructed to obtain the denoised signal.
[0179] The noise processing method described above can be used to train a neural network model using the denoised initial signal. Specifically, multiple initial signals are collected and used as inputs to the neural network model. These initial signals are then processed using the noise processing method described above to remove noise, resulting in denoised initial signals. These denoised initial signals serve as the training targets for the neural network model, which is then trained sequentially. The neural network model is considered complete when the difference between its output signal and the denoised initial signals falls within a preset range. The completed neural network model can then be directly used for signal denoising.
[0180] This application also provides a noise processing system for a signal, applied to the noise processing of the signal described above. Please refer to Figure 7 for details. Figure 7 is a schematic diagram of the structure of the noise processing system for a signal provided in this application embodiment. As shown in Figure 7, the system 70 includes:
[0181] The decomposition module 71 is used to perform CEEMDAN decomposition on the initial signal to obtain multiple IMF signals. The specific decomposition process is as described above and will not be repeated here.
[0182] The denoising module 72 is used to perform wavelet threshold denoising on at least a portion of the IMF signals one by one to obtain the wavelet coefficients of each layer of each IMF signal. The specific denoising process is as described above and will not be repeated here.
[0183] The first reconstruction module 73 is used to perform inverse wavelet transform on the wavelet coefficients of each layer to reconstruct the denoised IMF signals of each layer. The specific reconstruction process is as described above and will not be repeated here.
[0184] The second recombination module 74 is used to obtain the denoised signal of the initial signal based on the denoised IMF signals of all layers. The specific process is as described above and will not be repeated here.
[0185] To address the aforementioned technical problems, this application also provides a computer device. Please refer to Figure 8 for details; Figure 8 is a basic structural block diagram of the computer device according to this embodiment.
[0186] The computer device 6 includes a memory 61, a processor 62, and a network interface 63 that are interconnected via a system bus. It should be noted that only the computer device 6 with components 61-63 is shown in the figure; however, it should be understood that it is not required to implement all the shown components, and more or fewer components can be implemented alternatively. Those skilled in the art will understand that the computer device described here is a device capable of automatically performing numerical calculations and / or information processing according to pre-set or stored instructions, and its hardware includes, but is not limited to, microprocessors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), embedded devices, etc.
[0187] The computer device can be a desktop computer, laptop, handheld computer, or cloud server, etc. The computer device can interact with the user via a keyboard, mouse, remote control, touchpad, or voice control.
[0188] The memory 61 includes at least one type of readable storage medium, including flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the memory 61 may be an internal storage unit of the computer device 6, such as the hard disk or memory of the computer device 6. In other embodiments, the memory 61 may also be an external storage device of the computer device 6, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., equipped on the computer device 6. Of course, the memory 61 may also include both the internal storage unit and its external storage device of the computer device 6. In this embodiment, the memory 61 is typically used to store the operating system and various information management operating systems installed on the computer device 6, such as computer-readable instructions for signal noise processing methods. In addition, the memory 61 can also be used to temporarily store various types of data that have been output or will be output.
[0189] In some embodiments, the processor 62 may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip. The processor 62 is typically used to control the overall operation of the computer device 6. In this embodiment, the processor 62 is used to execute computer-readable instructions stored in the memory 61 or to process data, such as computer-readable instructions for noise processing methods of signals.
[0190] The network interface 63 may include a wireless network interface or a wired network interface, which is typically used to establish communication connections between the computer device 6 and other electronic devices.
[0191] This application also provides another embodiment, namely, a computer program product storing computer-readable instructions that can be executed by at least one processor to cause the at least one processor to perform the steps of the noise processing method for the signal described above.
[0192] This application provides a noise processing method and system for signals. The noise processing method includes: performing CEEMDAN decomposition on an initial signal to obtain multiple IMF signals; performing wavelet threshold denoising on at least a portion of the IMF signals one by one to obtain wavelet coefficients for each layer of each IMF signal; performing inverse wavelet transform on each layer of wavelet coefficients to reconstruct the denoised IMF signals for each layer; and obtaining the denoised initial signal based on the denoised IMF signals for all layers. Therefore, this application uses a combination of CEEMDAN decomposition and wavelet denoising to perform noise reduction on the initial signal, which has powerful signal denoising capabilities and efficient computational performance. This method is suitable for non-stationary complex signal processing tasks with large sample sizes and multiple noise sources.
[0193] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.
[0194] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0195] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.
Claims
1. A method of noise processing of a signal, wherein, The noise processing method includes: The initial signal is decomposed using CEEMDAN to obtain multiple IMF signals; Wavelet threshold denoising is performed on at least a portion of the IMF signals one by one to obtain the wavelet coefficients of each layer of each IMF signal; The wavelet coefficients of each layer are subjected to inverse wavelet transform to reconstruct the denoised IMF signals of each layer. The denoised initial signal is obtained from the denoised IMF signals of all layers.
2. The noise processing method of claim 1, wherein, The step of performing CEEMDAN decomposition on the initial signal to obtain multiple IMF signals further includes: Step 1: Generate multiple additive white Gaussian noises, and add each additive white Gaussian noise to the initial signal one by one to obtain the loaded signal: wherein the For loading the loaded signal after the additive white Gaussian noise, the parameters The signal-to-noise ratio for each decomposition level, for the additive white Gaussian noise, It is a positive integer; Step 2: Perform EMD decomposition on each of the loaded signals and obtain the first-level IMF signal and the first-level residual component, wherein the first-level IMF signal is: in, This is the first-level IMF signal. For each of the loaded signals, the first level of the IMF signal, and ； The residual components of the first level are: ； Step 3: Perform EMD decomposition on each additive white Gaussian noise, and obtain the second-level IMF signal and the second-level residual component from the corresponding first-level residual component of the decomposed additive white Gaussian noise. The second-level IMF signal is as follows: ， The residual components of the second level are: ； Step 4: Obtain the residual components of the Kth level based on the residual components of the second level in Step 3, where the residual components of the Kth level are: ， Where k = 2, 3, ..., K, and K is the highest decomposition level; Step 5: Obtain the IMF signal of the (K+1)th level based on the residual component of the Kth level, wherein the IMF signal of the (K+1)th level is: ； Step 6: Repeat steps 4 and 5 iteratively until the residual components become constants or monotonic functions, obtaining the decomposition expression of the initial signal, which is: ； Step 7: Output the IMF signal sequence arranged from high frequency to low frequency and a residual signal component.
3. The noise treatment method according to claim 2, wherein, The step of performing EMD decomposition on each of the loaded signals further includes: Step S11: Obtain the local maxima and local minima of the initial signal, and use a preset degree spline interpolation function to fit the local maxima and local minima respectively to obtain the upper envelope and lower envelope respectively; Step S12: Obtain the first signal component based on the upper and lower envelopes, and determine whether the first signal component conforms to the characteristics of an IMF signal; If the conditions are met, the first signal component is taken as the first-level IMF signal; Subtracting the first-level IMF signal from the initial signal yields the first-level residual signal component; If it does not meet the requirements, the first signal component is replaced with the initial signal, and steps S11 and S12 are repeated until the Kth signal component meets the characteristics of the IMF signal.
4. The noise treatment method according to claim 1, wherein, The step of performing wavelet threshold denoising on at least a portion of the IMF signals also includes: For each IMF signal, a single-level wavelet decomposition is performed under each type of wavelet basis to obtain the first-level detail coefficients and the first-level approximation coefficients. The optimal wavelet basis for each level is obtained based on the first-level detail coefficients and the first-level approximation coefficients. To obtain the optimal number of wavelet decomposition levels; Perform wavelet decomposition with the optimal number of decomposition levels on each IMF signal. Obtain the optimal wavelet basis for each decomposition level, retain the detail coefficients of the first level obtained by decomposition, and use the approximation coefficients of the first level as the signal input for the next level. Decompose to obtain new detail coefficients of the first level and new approximation coefficients of the first level, until the decomposition is completed. For the detail coefficients of the first level of each layer, a denoising threshold is calculated, and thresholding is performed on all detail coefficients of each layer based on the denoising threshold. Perform a single-level inverse wavelet transform on the detail coefficients and approximation coefficients of each level to obtain new approximation coefficients for the next level. Then, continue to perform a single-level inverse wavelet transform using the same wavelet basis used in the previous level decomposition. Repeat this process until the IMF signal is reconstructed and the denoised IMF signal is obtained.
5. The noise treatment method according to claim 4, wherein, The step of obtaining the optimal wavelet basis for each layer based on the detail coefficients of the first level and the approximation coefficients of the first level further includes: For each IMF signal, a single-level wavelet decomposition is performed under a single-level wavelet basis to obtain the first-level detail coefficients and the first-level approximation coefficients. The total signal energy of each single layer is calculated based on the approximation coefficients of all first-level waveslet bases under each single layer. The energy probability distribution of each detail coefficient is calculated based on the total signal energy of each single layer, and the corresponding wavelet entropy is obtained. For each single layer, the wavelet basis function that minimizes the wavelet entropy value is selected as the optimal wavelet basis for that layer.
6. The noise treatment method according to claim 5, wherein, Before the step of performing single-layer wavelet decomposition under a single-layer wavelet basis for each IMF signal, the method further includes: Establish a wavelet family selection library to store various wavelet basis functions to be used.
7. The noise treatment method according to claim 6, wherein, The step of performing single-layer wavelet decomposition on a single-layer wavelet basis for each IMF signal further includes: For each input IMF signal, all wavelet basis functions are iterated over to perform single-level wavelet decomposition.
8. The noise treatment method according to claim 5, wherein, The step of calculating the total signal energy of each single-layer wavelet basis based on the approximation coefficients of all first-level approximations also includes: The total signal energy is calculated using the following formula: in, The total signal energy, Let represent the approximation coefficients of the i-th first level under each single-layer wavelet basis, where i = 1, 2, ..., N, and N is the number of approximation coefficients of the first level.
9. The noise treatment method according to claim 8, wherein, The step of calculating the energy probability distribution of each detail coefficient based on the total signal energy of each single layer also includes: the energy probability distribution satisfies the following relationship: in, This represents the energy probability distribution. The step of obtaining the corresponding wavelet entropy further includes: The wavelet entropy WE satisfies the following relationship:
10. The noise processing method according to claim 6, wherein, The step of obtaining the optimal wavelet decomposition level further includes: Estimate the maximum wavelet decomposition level based on the input IMF signal: The IMF signal is decomposed into the maximum number of decomposition levels. The optimal wavelet basis is obtained at each level, and the detail coefficients obtained at each level are retained. The approximation coefficients are used as the signal input for the next level of wavelet decomposition. New detail coefficients and new approximation coefficients are obtained until the decomposition is completed. For any given level, calculate the sparsity of the approximation coefficients for that level, and calculate the sparsity variation between levels. When the sparsity variation value meets the preset variation threshold, the decomposition level at this time is selected as the optimal decomposition level.
11. The noise processing method according to claim 2, wherein, The step of obtaining the denoised initial signal based on the denoised IMF signals of all layers further includes: The residual components of the initial signal are accumulated with the denoised IMFs of each level to obtain the denoised initial signal.
12. A noise processing system for a signal, wherein, The system includes: The decomposition module is used to perform CEEMDAN decomposition on the initial signal to obtain multiple IMF signals; A denoising module is used to perform wavelet threshold denoising on at least a portion of the IMF signals one by one to obtain the wavelet coefficients of each layer of each IMF signal. The first reconstruction module is used to perform inverse wavelet transformation on the wavelet coefficients of each layer to reconstruct the denoised IMF signals of each layer. The second recombination module is used to obtain the denoised signal of the initial signal based on the denoised IMF signals of all layers.
13. A computer device, wherein, The computer device includes a memory and a processor, the memory storing computer-readable instructions, and the processor executing the computer-readable instructions to implement the steps of the method as described in any one of claims 1 to 11.
14. A computer program product, wherein, The computer program product includes a computer program that, when executed by a computer, performs the method according to any one of claims 1 to 11.