CN114417920A - Signal denoising method and device based on DE optimization wavelet parameters - Google Patents
Signal denoising method and device based on DE optimization wavelet parameters Download PDFInfo
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Abstract
The invention discloses a signal denoising method and device based on DE optimization wavelet parameters. The method comprises the following steps: selecting an initial wavelet basis function, and performing wavelet decomposition on the noise-containing signal according to the number of initial decomposition layers and an initial layering threshold value under each decomposition scale to obtain a detail coefficient under each decomposition scale and an approximate coefficient under the maximum decomposition scale; taking the initial wavelet basis function, the initial decomposition layer number and the initial layering threshold value under each decomposition scale as position parameters of an initial population in a DE algorithm, and acquiring an optimal wavelet basis function, an optimal decomposition layer number and an optimal layering threshold value under each decomposition scale based on the DE algorithm; and denoising each detail coefficient according to the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale to obtain a target detail coefficient, and reconstructing a signal by combining the target detail coefficient and the approximate coefficient to obtain a target signal. The invention can optimize the decomposition layer number and the layering threshold value by using a DE algorithm and improve the denoising effect.
Description
Technical Field
The invention relates to the technical field of signal processing, in particular to a DE-noising method and a DE-noising device for optimizing wavelet parameters.
Background
With the development of information technology, people have higher and higher requirements on the communication quality of wireless communication. In the wireless communication, signal transmission is performed through an atmospheric channel, and the communication quality is easily reduced due to external interference in the transmission process, so that the received noise-containing signal needs to be denoised.
Donoho and Johnstone proposed the idea of wavelet threshold denoising in 1994, which is widely used for signal denoising due to its multi-resolution, low entropy and decorrelation. Wavelet threshold denoising can be used to identify noise in a signal and suppress high frequency noise to reconstruct the signal. Although Donoho et al theoretically demonstrated and found the optimal universal threshold, the effect of the universal threshold in practical applications is not ideal in wavelet transform because the magnitude of the wavelet coefficients of noise decreases with increasing scale, while the magnitude of the wavelet coefficients of signal does not decrease with increasing scale. In this respect, when the wavelet threshold denoising method is applied, a layered threshold may be adopted, that is, each decomposition scale adopts a different threshold, so as to overcome the technical defect of the general threshold. The size of each layered threshold is the core of thresholding, if the threshold is selected too large, part of noise cannot be filtered, the denoising effect is poor, and if the threshold is selected too small, signal distortion of filtered effective signals is brought. Therefore, how to accurately determine the hierarchical threshold and determine the decomposition scale of the signal in the denoising process for different signal features are currently in urgent need of consideration.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a signal denoising method and device based on DE optimization wavelet parameters, which can optimize the decomposition layer number and the layering threshold value by using a DE algorithm and improve the denoising effect.
In order to solve the above technical problem, in a first aspect, an embodiment of the present invention provides a signal denoising method based on DE optimized wavelet parameters, including:
selecting an initial wavelet basis function, and performing wavelet decomposition on the noise-containing signal according to the number of initial decomposition layers and an initial layering threshold value under each decomposition scale to obtain detail coefficients under each decomposition scale and approximate coefficients under the maximum decomposition scale;
taking the initial wavelet basis function, the initial decomposition layer number and the initial layering threshold value under each decomposition scale as position parameters of an initial population in a DE algorithm, and acquiring an optimal wavelet basis function, an optimal decomposition layer number and an optimal layering threshold value under each decomposition scale based on the DE algorithm;
and denoising each detail coefficient according to the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale to obtain a target detail coefficient, and performing signal reconstruction by combining the target detail coefficient and the approximate coefficient to obtain a target signal.
Further, the obtaining of the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold under each decomposition scale based on the DE algorithm specifically includes:
initializing parameters: setting population scale, maximum iteration times and fitness function, and defining a layering threshold value of each individual in the population under each decomposition scale;
calculating the fitness value of each individual in the population according to the fitness function, and when the current iteration times reach the maximum iteration times, selecting the population with the minimum fitness value as the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale according to all the fitness values;
and when the current iteration times do not reach the maximum iteration times, performing cross operation on the variant individuals and the original individuals in the population, taking the variant individuals and/or the original individuals with the fitness values smaller than a preset fitness value as a next generation population, and performing differential evolution operation in a circulating mode until the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale are obtained when the maximum iteration times are reached or the fitness function requirement is met.
Further, before the performing the crossover operation on the variant individuals and the original individuals in the population, the method further comprises:
and carrying out mutation operation on the original individuals in the population based on a predefined difference strategy to obtain the variant individuals.
Further, the performing a cross operation on the variant individuals and the original individuals in the population specifically includes:
and carrying out cross operation on the variant individuals and the original individuals of the population through a binomial cross model.
Further, the fitness function is:
wherein MAX is the maximum amplitude of the input signal, RMSE is the root mean square error of the noisy signal,
n is the length of the noisy signal, w (k) is the wavelet coefficients of the input signal,
for the wavelet coefficients after the thresholding,
λ represents the hierarchical threshold at each decomposition scale.
In a second aspect, an embodiment of the present invention provides a DE-noising apparatus for optimizing wavelet parameters based on DE, including:
the wavelet decomposition module is used for selecting an initial wavelet basis function, and performing wavelet decomposition on the noise-containing signal according to the number of initial decomposition layers and the initial layering threshold value under each decomposition scale to obtain detail coefficients under each decomposition scale and approximate coefficients under the maximum decomposition scale;
the parameter optimization module is used for taking the initial wavelet basis function, the initial decomposition layer number and the initial layering threshold value under each decomposition scale as position parameters of an initial population in a DE algorithm and acquiring an optimal wavelet basis function, an optimal decomposition layer number and an optimal layering threshold value under each decomposition scale based on the DE algorithm;
and the signal denoising module is used for denoising each detail coefficient according to the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale to obtain a target detail coefficient, and performing signal reconstruction by combining the target detail coefficient and the approximate coefficient to obtain a target signal.
Further, the obtaining of the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold under each decomposition scale based on the DE algorithm specifically includes:
initializing parameters: setting population scale, maximum iteration times and fitness function, and defining a layering threshold value of each individual in the population under each decomposition scale;
calculating the fitness value of each individual in the population according to the fitness function, and when the current iteration times reach the maximum iteration times, selecting the population with the minimum fitness value as the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale according to all the fitness values;
and when the current iteration times do not reach the maximum iteration times, performing cross operation on the variant individuals and the original individuals in the population, taking the variant individuals and/or the original individuals with the fitness values smaller than a preset fitness value as a next generation population, and performing differential evolution operation in a circulating mode until the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale are obtained when the maximum iteration times are reached or the fitness function requirement is met.
Further, before the performing the crossover operation on the variant individuals and the original individuals in the population, the method further comprises:
and carrying out mutation operation on the original individuals in the population based on a predefined difference strategy to obtain the variant individuals.
Further, the performing a cross operation on the variant individuals and the original individuals in the population specifically includes:
and carrying out cross operation on the variant individuals and the original individuals of the population through a binomial cross model.
Further, the fitness function is:
wherein MAX is the maximum amplitude of the input signal, RMSE is the root mean square error of the noisy signal,
n is the length of the noisy signal, w (k) is the wavelet coefficients of the input signal,
for the wavelet coefficients after the thresholding,
λ represents the hierarchical threshold at each decomposition scale.
The embodiment of the invention has the following beneficial effects:
the method comprises the steps of selecting an initial wavelet basis function, performing wavelet decomposition on a noise-containing signal according to the number of initial decomposition layers and an initial layering threshold value under each decomposition scale to obtain detail coefficients under each decomposition scale and an approximation coefficient under the maximum decomposition scale, taking the initial wavelet basis function, the number of initial decomposition layers and the initial layering threshold value under each decomposition scale as position parameters of an initial population in a DE algorithm, obtaining an optimal wavelet basis function, the optimal decomposition layers and an optimal layering threshold value under each decomposition scale based on the DE algorithm, performing denoising processing on each detail coefficient according to the optimal wavelet basis function, the optimal decomposition layers and the optimal layering threshold value under each decomposition scale to obtain a target detail coefficient, performing signal reconstruction according to the target detail coefficient and the approximation coefficient to obtain a target signal, and completing signal denoising. Compared with the prior art, the embodiment of the invention obtains the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale based on the DE algorithm, and performs denoising processing on the noise-containing signal by using the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale based on discrete wavelet transform, so that the decomposition layer number and the layering threshold value can be optimized by using the DE algorithm, and the denoising effect is improved.
Drawings
Fig. 1 is a schematic flow chart of a signal denoising method based on DE optimized wavelet parameters in a first embodiment of the present invention;
FIG. 2 is a schematic flowchart illustrating an exemplary signal denoising method based on DE optimized wavelet parameters according to a first embodiment of the present invention;
fig. 3 is a schematic flowchart illustrating an exemplary process of obtaining an optimal decomposition layer number and an optimal hierarchical threshold value under each decomposition scale based on a DE algorithm in the first embodiment of the present invention;
FIG. 4 is a signal diagram of an exemplary noisy signal in a first embodiment of the present invention;
FIG. 5 is a signal diagram of an exemplary target signal in a first embodiment of the present invention;
fig. 6 is a schematic structural diagram of a signal denoising apparatus based on DE optimized wavelet parameters in a second embodiment of the present invention.
Detailed Description
The technical solutions in the present invention will be described clearly and completely with reference to the accompanying drawings, and it is obvious that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that, the step numbers in the text are only for convenience of explanation of the specific embodiments, and do not serve to limit the execution sequence of the steps. The method provided by the embodiment can be executed by the relevant terminal device, and the following description takes a processor as an execution subject as an example.
As shown in fig. 1, a first embodiment provides a DE-noising method based on DE-optimized wavelet parameters, which includes steps S1 to S3:
s1, selecting an initial wavelet basis function, and performing wavelet decomposition on the noisy signals according to the number of initial decomposition layers and the initial layering threshold value under each decomposition scale to obtain detail coefficients under each decomposition scale and approximate coefficients under the maximum decomposition scale;
s2, taking the initial wavelet basis function, the initial decomposition layer number and the initial layering threshold value under each decomposition scale as position parameters of an initial population in the DE algorithm, and acquiring the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale based on the DE algorithm;
s3, denoising each detail coefficient according to the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale to obtain a target detail coefficient, and reconstructing a signal by combining the target detail coefficient and the approximate coefficient to obtain a target signal.
The Differential Evolution (DE) algorithm solves the optimization problem through cooperation and competition of individuals in a population, and has strong global convergence capability. The process of the Differential Evolution (DE) algorithm is similar to other evolution algorithms and comprises operations of mutation, intersection and selection, but compared with other algorithms, the Differential Evolution (DE) algorithm has the advantages of stable operation, high convergence speed and lower complexity.
As shown in fig. 2, in step S1, an initial wavelet basis function is selected from db1, sym1, and coif1, or another type of wavelet basis function may be selected as the initial wavelet basis function, and a noise-containing signal is wavelet decomposed according to the number of initial decomposition layers and the initial hierarchical threshold at each decomposition scale, so as to obtain detail coefficients at each decomposition scale and approximation coefficients at the maximum decomposition scale.
In step S2, the initial wavelet basis function, the initial decomposition level number, and the initial hierarchical threshold value under each decomposition scale are used as position parameters of the initial population in the DE algorithm, and the optimal wavelet basis function and the optimal decomposition level number are obtained based on the DE algorithm, so that the hierarchical threshold value is optimized based on the DE algorithm to obtain the optimal hierarchical threshold value under each decomposition scale.
In step S3, an optimal wavelet basis function is selected, denoising processing is performed on the detail coefficients in each decomposition scale according to the optimal decomposition layer number and the optimal layering threshold in each decomposition scale, a target detail coefficient is obtained, signal reconstruction is performed by combining the target detail coefficient and the approximation coefficient, a target signal is obtained, and signal denoising is completed.
In the embodiment, the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale are obtained based on the DE algorithm, and denoising processing is performed on the noise-containing signal by using the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale based on discrete wavelet transform, so that the decomposition layer number and the layering threshold value can be optimized by using the DE algorithm, and the denoising effect is improved.
In a preferred embodiment, the obtaining an optimal wavelet basis function, an optimal decomposition layer number and an optimal layering threshold under each decomposition scale based on the DE algorithm specifically includes: initializing parameters: setting population scale, maximum iteration times and fitness function, and defining a layering threshold value of each individual in the population under each decomposition scale; calculating the fitness value of each individual in the population according to the fitness function, and when the current iteration times reach the maximum iteration times, selecting the population with the minimum fitness value as an optimal wavelet basis function, an optimal decomposition layer number and an optimal layering threshold under each decomposition scale according to all the fitness values; and when the current iteration times do not reach the maximum iteration times, performing cross operation on the variant individuals and the original individuals in the population, taking the variant individuals and/or the original individuals with the fitness values smaller than the preset fitness values as a next generation population, and performing differential evolution operation in a circulating mode until the maximum iteration times are reached or the fitness function requirements are met to obtain the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale.
As shown in fig. 3, as an example, obtaining an optimal wavelet basis function, an optimal decomposition layer number and an optimal layering threshold under each decomposition scale based on a DE algorithm specifically includes the steps of:
s2-1, parameter initialization: setting a population size NP, a maximum iteration number G, a scaling factor F, a crossover operator CR and a fitness function F (X), and defining each individual X in the populationiRepresenting a layering threshold value under each scale, wherein the population dimension is D;
s2-2, calculating individual fitness value, judging whether iteration termination conditions are met or not, if the current iteration times reach the maximum iteration times, judging that the iteration termination conditions are met, and taking the population with the minimum current fitness value as the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale, otherwise, continuing to perform the step S2-3;
s2-3, carrying out mutation operation on NP individuals in the population to generate difference individuals and variant individuals;
s2-4, in order to improve the diversity of the population, carrying out cross operation on the variant individuals generated in the S2-3 and the original individuals of the population through a binomial cross model;
s2-5, arranging according to the sequence of the individual fitness values from small to large, selecting the individual with the smaller fitness value to enter the next generation of the population, and ensuring that the population evolves towards the optimal solution;
and S2-6, continuing to circularly carry out differential evolution operation by using the optimal learning search equation until an iteration termination condition is met, namely when the current iteration times reach the maximum iteration times, taking the population with the minimum current fitness value as the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale.
The implementation process of initializing the population-scale NPs in step S2-1 is as follows:
s2-11, initializing wavelet basis functions, and selecting the wavelet basis functions as db1, sym1 and coif2, namely:
r1＝round(1+1.9*r(1)) (1)；
wherein r1 is a wavelet basis function, and round () is a rounding operation;
s2-12, initializing the number of decomposition layers, setting the range of the number of decomposition layers to be 3 to 8, namely:
r2＝round(3+5.9*r(3)) (2)；
wherein r2 is the number of decomposition layers;
s2-13, initializing a hierarchical threshold, namely:
rp＝r(3:2+r2) (3)；
where rp is the tiered threshold.
In a preferred embodiment, before the performing the crossover operation on the variant individuals and the original individuals in the population, the method further comprises: and carrying out mutation operation on the original individuals in the population based on a predefined difference strategy to obtain the variant individuals.
As an example, based on a predefined difference strategy, mutation operations are performed on the original individuals in the population, namely:
wherein the content of the first and second substances,
selecting three different vectors randomly from the population, wherein r1, r2, i belongs to NP;
for the difference vector, F is the scaling factor of the DE algorithm, and is typically taken as [0,1 ]]Controlling the amplification effect of the differential vector; vi tThe variation vector is represented.
In a preferred embodiment, the performing a crossover operation on the variant individuals and the original individuals in the population specifically includes: and carrying out cross operation on the variant individuals and the original individuals of the population through a binomial cross model.
Illustratively, to improve population diversity, the binomial cross model employed operates as follows:
wherein the content of the first and second substances,
is an experimental vector
The (g) th gene fragment of (1),
is a variation vector
The jth gene fragment of (1), randb is [0,1 ]]A random number in between; CR is a crossover operator, controlling the binomial crossover process, usually at [0,1 ]]The larger the CR value, the more likely hybridization will occur; j is a function ofrandIs [1, D ]]Internally randomly generated numbers, can ensure
J (d) ofrandThe bit is from
The method can ensure that the experimental vector is different from the target vector variation vector, and avoid invalid hybridization.
In a preferred embodiment, the fitness function is:
where MAX is the maximum amplitude of the input signal, RMSE is the root mean square error of the noisy signal,
n is the length of the noisy signal, w (k) is the wavelet coefficients of the input signal,
for the wavelet coefficients after the thresholding,
λ represents the hierarchical threshold at each decomposition scale.
It will be appreciated that the signal length is the number of signal samples.
Illustratively, an optimal target vector or an optimal experimental vector is selected through a fitness function f (x) to serve as an individual entering a next generation population, and the population is ensured to evolve towards an optimal solution, wherein the process is as follows:
and after the step is finished, the differential evolution operation is continuously and circularly carried out until the iteration times or the fitness function requirement is met, and the algorithm is terminated.
Optionally, the fitness function is calculated as follows:
where SNR represents the signal-to-noise ratio of the noisy signal, delta is an additional factor,
mean () is the signal averaging operation, U is the voltage amplitude of the noisy signal, and R is the resistance.
In step S3, wavelet decomposition is performed on the noisy signal by using the decomposition scale of the individual with the optimal fitness selected in step S2, that is, the optimal number of decomposition layers, where the discrete wavelet can be represented as:
wherein a is a scale parameter, b is a translation parameter,
and performing discrete processing. At this time j is a region of integer value, a0I.e. a fixed telescopic step with a value greater than 1. For b, take
Wherein b is0>0 and related to the specific form of the wavelet ψ (t), k being an integer。
The discretized wavelet coefficients can be expressed as:
wherein s (n) is a noisy signal.
The wavelet threshold denoising utilizes the characteristic that noise is mainly distributed in a high-frequency part, a received signal is decomposed into a useful signal and a signal with the noise through wavelet transformation, and then an appropriate wavelet basis function is selected to decompose a signal containing the noise to obtain an approximate coefficient and a detail coefficient. The detail coefficient obtained by wavelet decomposition is thresholded to reduce noise of signal, XiI.e. the optimal threshold values at different decomposition scales. The detail coefficients after threshold processing can form new approximate coefficients and detail coefficients, and the wavelet coefficients reaching the optimal decomposition scale are used for reconstructing and forming the denoised signals. The reconstruction process is as follows:
where C is a constant independent of the signal.
Optionally, the wavelet basis of the wavelet reconstruction is determined by algorithm optimization.
The size of the signal-to-noise ratio can effectively reflect the noise reduction effect of the target signal and the deviation of the target signal and the noise-containing signal, and the noise reduction effect is better when the signal-to-noise ratio is larger.
In order to verify the effectiveness of the invention, the signal-to-noise ratio is used as an evaluation index of the denoising performance, and the evaluation index can be calculated by the ratio of the signal power to the noise power, and the calculation formula is as follows:
the signal-to-noise ratios of the resulting noisy signal and the target signal are shown in table 1:
TABLE 1 Signal-to-noise ratio contrast (dB) of signals before and after de-noising
| Before denoising | After denoising |
| 23.543 | 31.109 |
The signal diagrams of the noisy signal and the target signal are respectively shown in fig. 4 and 5, and as can be seen from fig. 4 and 5, the DE-optimization wavelet parameter-based signal denoising method provided by the embodiment can effectively improve the denoising effect.
Based on the same technical concept as the first embodiment, the second embodiment provides a DE-noising apparatus for DE-optimizing wavelet parameters, as shown in fig. 6, including: the wavelet decomposition module is used for selecting an initial wavelet basis function, and performing wavelet decomposition on the noise-containing signal according to the number of initial decomposition layers and the initial layering threshold value under each decomposition scale to obtain detail coefficients under each decomposition scale and approximate coefficients under the maximum decomposition scale; the parameter optimization module is used for taking the initial wavelet basis function, the initial decomposition layer number and the initial layering threshold value under each decomposition scale as position parameters of an initial population in the DE algorithm and acquiring the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale based on the DE algorithm; and the signal denoising module is used for denoising each detail coefficient according to the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale to obtain a target detail coefficient, and reconstructing a signal by combining the target detail coefficient and the approximate coefficient to obtain a target signal.
In a preferred embodiment, the obtaining an optimal wavelet basis function, an optimal decomposition layer number and an optimal layering threshold under each decomposition scale based on the DE algorithm specifically includes: initializing parameters: setting population scale, maximum iteration times and fitness function, and defining a layering threshold value of each individual in the population under each decomposition scale; calculating the fitness value of each individual in the population according to the fitness function, and when the current iteration times reach the maximum iteration times, selecting the population with the minimum fitness value as an optimal wavelet basis function, an optimal decomposition layer number and an optimal layering threshold under each decomposition scale according to all the fitness values; and when the current iteration times do not reach the maximum iteration times, performing cross operation on the variant individuals and the original individuals in the population, taking the variant individuals and/or the original individuals with the fitness values smaller than the preset fitness values as a next generation population, and performing differential evolution operation in a circulating mode until the maximum iteration times are reached or the fitness function requirements are met to obtain the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale.
In a preferred embodiment, before the performing the crossover operation on the variant individuals and the original individuals in the population, the method further comprises: and carrying out mutation operation on the original individuals in the population based on a predefined difference strategy to obtain the variant individuals.
In a preferred embodiment, the performing a crossover operation on the variant individuals and the original individuals in the population specifically includes: and carrying out cross operation on the variant individuals and the original individuals of the population through a binomial cross model.
In a preferred embodiment, the fitness function is:
where MAX is the maximum amplitude of the input signal, RMSE is the root mean square error of the noisy signal,
n is the length of the noisy signal, w (k) is the wavelet coefficients of the input signal,
for the wavelet coefficients after the thresholding,
λ represents the hierarchical threshold at each decomposition scale.
In summary, the embodiment of the present invention has the following advantages:
the method comprises the steps of selecting an initial wavelet basis function, performing wavelet decomposition on a noise-containing signal according to the number of initial decomposition layers and an initial layering threshold value under each decomposition scale to obtain detail coefficients under each decomposition scale and an approximation coefficient under the maximum decomposition scale, taking the initial wavelet basis function, the number of initial decomposition layers and the initial layering threshold value under each decomposition scale as position parameters of an initial population in a DE algorithm, obtaining an optimal wavelet basis function, the optimal decomposition layers and an optimal layering threshold value under each decomposition scale based on the DE algorithm, performing denoising processing on each detail coefficient according to the optimal wavelet basis function, the optimal decomposition layers and the optimal layering threshold value under each decomposition scale to obtain a target detail coefficient, performing signal reconstruction according to the target detail coefficient and the approximation coefficient to obtain a target signal, and completing signal denoising. According to the embodiment of the invention, the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale are obtained based on the DE algorithm, and denoising processing is carried out on the noise-containing signal by using the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale based on discrete wavelet transformation, so that the decomposition layer number and the layering threshold value can be optimized by using the DE algorithm, and the denoising effect is improved.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.
It will be understood by those skilled in the art that all or part of the processes of the above embodiments may be implemented by hardware related to instructions of a computer program, and the computer program may be stored in a computer readable storage medium, and when executed, may include the processes of the above embodiments. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.
Claims (10)
1. A signal denoising method based on DE optimization wavelet parameters is characterized by comprising the following steps:
selecting an initial wavelet basis function, and performing wavelet decomposition on the noise-containing signal according to the number of initial decomposition layers and an initial layering threshold value under each decomposition scale to obtain detail coefficients under each decomposition scale and approximate coefficients under the maximum decomposition scale;
taking the initial wavelet basis function, the initial decomposition layer number and the initial layering threshold value under each decomposition scale as position parameters of an initial population in a DE algorithm, and acquiring an optimal wavelet basis function, an optimal decomposition layer number and an optimal layering threshold value under each decomposition scale based on the DE algorithm;
and denoising each detail coefficient according to the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale to obtain a target detail coefficient, and performing signal reconstruction by combining the target detail coefficient and the approximate coefficient to obtain a target signal.
2. The DE-noising method based on optimized wavelet parameters according to claim 1, wherein the DE-based algorithm obtains an optimal wavelet basis function, an optimal number of decomposition layers, and optimal hierarchical thresholds at each decomposition scale, specifically:
initializing parameters: setting population scale, maximum iteration times and fitness function, and defining a layering threshold value of each individual in the population under each decomposition scale;
calculating the fitness value of each individual in the population according to the fitness function, and when the current iteration times reach the maximum iteration times, selecting the population with the minimum fitness value as the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale according to all the fitness values;
and when the current iteration times do not reach the maximum iteration times, performing cross operation on the variant individuals and the original individuals in the population, taking the variant individuals and/or the original individuals with the fitness values smaller than a preset fitness value as a next generation population, and performing differential evolution operation in a circulating mode until the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale are obtained when the maximum iteration times are reached or the fitness function requirement is met.
3. The DE optimization wavelet parameter-based signal denoising method of claim 2, further comprising, before the crossover operation on the variant individuals and the original individuals in the population:
and carrying out mutation operation on the original individuals in the population based on a predefined difference strategy to obtain the variant individuals.
4. The DE optimization wavelet parameter-based signal denoising method of claim 2, wherein the crossover operation is performed on the variant individuals and the original individuals in the population, specifically:
and carrying out cross operation on the variant individuals and the original individuals of the population through a binomial cross model.
5. The DE-noising method of signals based on DE-optimized wavelet parameters of claim 2, wherein the fitness function is:
wherein MAX is the maximum amplitude of the input signal, RMSE is the root mean square error of the noisy signal,
n is the length of the noisy signal, w (k) is the wavelet coefficients of the input signal,
for the wavelet coefficients after the thresholding,
λ represents the hierarchical threshold at each decomposition scale.
6. A DE-optimization wavelet parameter-based signal denoising device is characterized by comprising:
the wavelet decomposition module is used for selecting an initial wavelet basis function, and performing wavelet decomposition on the noise-containing signal according to the number of initial decomposition layers and the initial layering threshold value under each decomposition scale to obtain detail coefficients under each decomposition scale and approximate coefficients under the maximum decomposition scale;
the parameter optimization module is used for taking the initial wavelet basis function, the initial decomposition layer number and the initial layering threshold value under each decomposition scale as position parameters of an initial population in a DE algorithm and acquiring an optimal wavelet basis function, an optimal decomposition layer number and an optimal layering threshold value under each decomposition scale based on the DE algorithm;
and the signal denoising module is used for denoising each detail coefficient according to the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale to obtain a target detail coefficient, and performing signal reconstruction by combining the target detail coefficient and the approximate coefficient to obtain a target signal.
7. The DE-noising device for signals based on optimized wavelet parameters according to claim 6, wherein the DE-based algorithm obtains an optimal wavelet basis function, an optimal number of decomposition layers and an optimal layering threshold at each decomposition scale, and specifically comprises:
initializing parameters: setting population scale, maximum iteration times and fitness function, and defining a layering threshold value of each individual in the population under each decomposition scale;
calculating the fitness value of each individual in the population according to the fitness function, and when the current iteration times reach the maximum iteration times, selecting the population with the minimum fitness value as the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale according to all the fitness values;
and when the current iteration times do not reach the maximum iteration times, performing cross operation on the variant individuals and the original individuals in the population, taking the variant individuals and/or the original individuals with the fitness values smaller than a preset fitness value as a next generation population, and performing differential evolution operation in a circulating mode until the optimal wavelet basis function, the optimal decomposition layer number and the optimal layering threshold value under each decomposition scale are obtained when the maximum iteration times are reached or the fitness function requirement is met.
8. The DE optimizing wavelet parameter-based signal denoising apparatus of claim 7, wherein prior to the crossover operation on the variant individuals and the original individuals in the population, further comprising:
and carrying out mutation operation on the original individuals in the population based on a predefined difference strategy to obtain the variant individuals.
9. The DE optimization wavelet parameter-based signal denoising apparatus of claim 7, wherein the crossover operation is performed on the variant individuals and the original individuals in the population, specifically:
and carrying out cross operation on the variant individuals and the original individuals of the population through a binomial cross model.
10. The DE-noising apparatus based on DE-optimized wavelet parameters of claim 7, wherein the fitness function is:
wherein MAX is the maximum amplitude of the input signal, RMSE is the root mean square error of the noisy signal,
n is the length of the noisy signal, w (k) is the wavelet coefficients of the input signal,
for the wavelet coefficients after the thresholding,
λ represents the hierarchical threshold at each decomposition scale.
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| CN117092206A (en) * | 2023-08-09 | 2023-11-21 | 国网四川省电力公司电力科学研究院 | Defect detection method for cable lead sealing area, computer equipment and storage medium |
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| CN117092206A (en) * | 2023-08-09 | 2023-11-21 | 国网四川省电力公司电力科学研究院 | Defect detection method for cable lead sealing area, computer equipment and storage medium |
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