CN113971641A - Wavelet threshold denoising method, device, equipment and medium - Google Patents
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Abstract
The present disclosure provides a wavelet threshold denoising method, including: acquiring a signal to be denoised and an ideal signal; initializing denoising parameters, and denoising a signal to be denoised by using the denoising parameters to obtain a first noise signal; calculating the mean square error between the signal to be denoised and the ideal signal as a first fitness; calculating the mean square error between the first noise signal and the ideal signal to be used as a second fitness; comparing the first fitness with the second fitness, updating the denoising parameter if the second fitness is smaller than the first fitness, and denoising the signal to be denoised by using the updated denoising parameter to obtain a second noise signal; calculating the mean square error between the second noise signal and the ideal signal to serve as a third fitness; comparing the third fitness with the second fitness, if the third fitness is smaller than the second fitness, updating the denoising parameters to perform denoising and fitness calculation, and iterating until the minimum fitness is obtained; and denoising the signal to be denoised by utilizing the denoising parameter corresponding to the minimum fitness.
Description
Technical Field
The present disclosure relates to the field of signal denoising technologies, and in particular, to a wavelet threshold denoising method, apparatus, device, and medium.
Background
The existing wavelet denoising methods mainly comprise three methods: a wavelet correlation denoising method, a wavelet modulus maximum denoising method and a wavelet threshold denoising method. The wavelet correlation denoising method is suitable for high signal-to-noise ratio signals, large in calculation amount and required to estimate noise variance. The wavelet mode maximum denoising method is suitable for the condition that a signal with a high signal-to-noise ratio contains more singular points, and the calculation speed is very slow during reconstruction. The wavelet threshold denoising method has strong data-removing correlation according to wavelet transformation, so that signal energy is concentrated in some large wavelet coefficients, and the wavelet coefficients are small because the noise energy is distributed in the whole wavelet domain. The method is suitable for various different noise and signal conditions, noise is almost completely eliminated, characteristic peak points reflecting initial signals are well reserved, and the method has wide adaptability. However, the method is easily affected by five factors, namely a wavelet basis function, a decomposition reconstruction layer number, a threshold estimation criterion, a threshold function form and a threshold scaling mode, and the quality of the denoising effect mainly depends on the suitability of the selection of the parameters, so that how to select the five parameters is the key of the wavelet threshold denoising method.
Aiming at the problems, many improved wavelet threshold denoising methods are provided, some of which only perform a large number of research attempts on a certain specific signal, then compare denoising effects, summarize parameter selection experiences when the wavelet threshold denoising method is used for processing the signal and noise, or some of which only perform optimization improvement on a certain main influence factor such as a threshold function form so as to improve the adaptability of threshold selection, such as a wavelet threshold denoising method based on a genetic algorithm, a wavelet threshold denoising method based on particle swarm optimization, a wavelet denoising method based on a swarm algorithm and a wavelet denoising method with a parameter threshold function, and the like. The method obviously has certain defects, such as the experimental method obtained by the trial has no universality due to single signal and noise types, and the integral self-adaption degree of the denoising method is still limited due to single optimization parameter.
The five influencing factors of the wavelet threshold denoising method all have various different parameter selection types, but no general rule can be followed when the parameters in the influencing factors are selected, and the corresponding optimal parameters can be determined by multiple attempts aiming at different signals and noises. In reality, actual signals and noise are mostly changed, and in order to achieve a better denoising effect, the parameters need to be manually adjusted to adapt to signals and noise with different characteristics, so that the adaptability of the wavelet threshold denoising algorithm is limited, and meanwhile, when the types of the parameters are more, the parameters which are manually adjusted in an attempt cannot be guaranteed to be optimal.
BRIEF SUMMARY OF THE PRESENT DISCLOSURE
Based on this, one aspect of the present disclosure provides a wavelet threshold denoising method, including: acquiring a signal to be denoised and an ideal signal; initializing denoising parameters, and denoising the signal to be denoised by using the initialized denoising parameters to obtain a first noise signal; calculating the mean square error between the signal to be denoised and the ideal signal to be used as a first fitness; calculating a mean square error between the first noise signal and the ideal signal as a second fitness; comparing the first fitness with the second fitness, updating a denoising parameter if the second fitness is smaller than the first fitness, and denoising the signal to be denoised by using the updated denoising parameter to obtain a second noise signal; calculating a mean square error between the second noise signal and the ideal signal as a third fitness; comparing the third fitness with the second fitness, if the third fitness is smaller than the second fitness, continuously updating denoising parameters to perform denoising and fitness calculation, and iterating until the minimum fitness is obtained; and denoising the signal to be denoised by utilizing the denoising parameter corresponding to the minimum fitness.
According to an embodiment of the present disclosure, the updating the denoising parameter includes: and respectively updating the denoising parameters in a global search mode or a local search mode.
According to the embodiment of the disclosure, the denoising parameters comprise a wavelet basis function, a decomposition reconstruction layer number, a threshold estimation criterion, a threshold function form and a threshold scaling mode; in the global search mode, the following steps are carried out:
and updating the denoising parameters, wherein,
represents the current value of the ith parameter in the five parameters during the t iteration updating,
representing the global optimum value of the ith parameter at the current iteration, L being the search step size.
According to the embodiment of the disclosure, the denoising parameters comprise a wavelet basis function, a decomposition reconstruction layer number, a threshold estimation criterion, a threshold function form and a threshold scaling mode; in the local search mode, the following steps are performed:
and updating the denoising parameters, wherein,
represents the current value of the ith parameter in the five parameters during the t iteration updating,
and
showing that any two of the local parameters of the ith parameter at the time of the t-th iteration update are different from each other
Epsilon is a proportionality coefficient with an interval of (0, 1) and obeying uniform distribution. .
According to the embodiment of the disclosure, the denoising parameters comprise a wavelet basis function, a decomposition reconstruction layer number, a threshold estimation criterion, a threshold function form and a threshold scaling mode; denoising the signal to be denoised by using denoising parameters comprises: performing wavelet transformation on the de-noised signal by using a wavelet basis function; decomposing the signals and the noise in the signals to be denoised into different scales according to the decomposition reconstruction layer number; determining a threshold for processing wavelet coefficients under each scale according to a threshold estimation criterion and a threshold scaling mode; utilizing a threshold function form to perform zero setting, reduction or retention processing on the wavelet coefficients under each scale; and performing wavelet inverse transformation on the wavelet coefficients under each scale after processing by using the wavelet basis functions and the decomposition reconstruction layer number to obtain denoised signals.
According to an embodiment of the present disclosure, the method further comprises: setting a conversion probability; and selecting a global search mode or a local search mode according to the conversion probability.
According to the embodiment of the disclosure, the denoising parameters comprise a wavelet basis function, a decomposition reconstruction layer number, a threshold estimation criterion, a threshold function form and a threshold scaling mode; the method further comprises the following steps: and establishing a corresponding relation between all selectable types of the denoising parameters and the global search mode or local search mode search range, wherein the search range is referred to by a number.
Another mode of the embodiments of the present disclosure further provides a wavelet threshold denoising device, including: the acquisition module is used for acquiring a signal to be denoised and an ideal signal; the initialization module is used for initializing denoising parameters and denoising the signal to be denoised by using the initialized denoising parameters to obtain a first noise signal; the computing module is used for computing the mean square error between the signal to be denoised and the ideal signal to serve as a first fitness; calculating a mean square error between the first noise signal and the ideal signal as a second fitness; the updating module is used for comparing the first fitness with the second fitness and updating the denoising parameter if the second fitness is smaller than the first fitness; the denoising module is used for denoising the signal to be denoised by using the updated denoising parameter to obtain a second noise signal; the calculation module is further configured to calculate a mean square error between the second noise signal and the ideal signal as a third fitness; the updating module is further configured to compare the third fitness with the second fitness, and if the third fitness is smaller than the second fitness, continue to update the denoising parameter; and carrying out iteration on the calculation module, the updating module and the denoising module until the minimum fitness is obtained, and denoising the signal to be denoised by using the denoising parameter corresponding to the minimum fitness.
Another aspect of the present disclosure also provides an electronic device, including: one or more processors; memory for storing one or more programs, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method described above.
Another aspect of the present disclosure also provides a computer-readable storage medium having stored thereon executable instructions that, when executed by a processor, cause the processor to implement the method described above.
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The above and other objects, features and advantages of the present disclosure will become more apparent from the following description of embodiments of the present disclosure with reference to the accompanying drawings, in which:
fig. 1 schematically illustrates a flowchart of an improved wavelet threshold denoising method provided by an embodiment of the present disclosure.
Fig. 2 schematically illustrates a graph of the fitness function provided by an embodiment of the present disclosure as a function of the number of iterations.
Fig. 3 schematically shows a flowchart of parameter optimization provided by the embodiment of the present disclosure.
Fig. 4 schematically shows an ideal signal diagram corresponding to a radar signal, an electrocardiogram signal and a test signal provided by the embodiment of the disclosure.
Fig. 5 schematically illustrates a radar signal and a noise waveform thereof provided by an embodiment of the disclosure.
Fig. 6 schematically shows a result diagram of three noise removals of radar signals by using four wavelet denoising methods according to an embodiment of the present disclosure.
Fig. 7 schematically illustrates an electrocardiogram signal and its noise waveform provided by an embodiment of the present disclosure.
Fig. 8 schematically shows a result diagram of three noise removals on a electrocardiogram signal by using four wavelet denoising methods according to an embodiment of the present disclosure.
Fig. 9 schematically illustrates a test signal and its noise waveform provided by an embodiment of the present disclosure.
Fig. 10 schematically illustrates a result diagram of removing noise in a test signal by using four wavelet denoising methods according to an embodiment of the present disclosure.
Fig. 11 schematically shows a structural block diagram of a wavelet threshold denoising device provided by an embodiment of the present disclosure.
Fig. 12 schematically shows a block diagram of an electronic device adapted to implement the above described method according to an embodiment of the present disclosure.
Detailed Description
For the purpose of promoting a better understanding of the objects, aspects and advantages of the present disclosure, reference is made to the following detailed description taken in conjunction with the accompanying drawings. It is to be understood that the described embodiments are only a few, and not all, of the disclosed embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments disclosed herein without making any creative effort, shall fall within the protection scope of the present disclosure.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. The terms "comprises," "comprising," and the like, as used herein, specify the presence of stated features, steps, operations, and/or components, but do not preclude the presence or addition of one or more other features, steps, operations, or components.
In the present disclosure, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integral; can be mechanically connected, electrically connected or can communicate with each other; either directly or indirectly through intervening media, either internally or in any other suitable relationship. The specific meaning of the above terms in the present disclosure can be understood by those of ordinary skill in the art as appropriate.
In the description of the present disclosure, it is to be understood that the terms "longitudinal," "length," "circumferential," "front," "rear," "left," "right," "top," "bottom," "inner," "outer," and the like are used in the orientation or positional relationship indicated in the drawings for convenience in describing the present disclosure and for simplicity in description, and are not intended to indicate or imply that the referenced subsystems or elements must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present disclosure.
Throughout the drawings, like elements are represented by like or similar reference numerals. Conventional structures or constructions will be omitted when they may obscure the understanding of the present disclosure. And the shapes, sizes and positional relationships of the components in the drawings do not reflect the actual sizes, proportions and actual positional relationships. Furthermore, in the claims, any reference signs placed between parentheses shall not be construed as limiting the claim.
Similarly, in the above description of exemplary embodiments of the disclosure, various features of the disclosure are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various disclosed aspects. Reference to the description of the terms "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the disclosure. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present disclosure, "a plurality" means at least two, e.g., two, three, etc., unless explicitly specifically limited otherwise.
Aiming at the problems that the single processing object is lack of universality, the single adaptive degree of an optimized parameter is limited and the like in the existing wavelet threshold denoising improvement method, the disclosure provides an improved wavelet threshold denoising method based on a multi-target optimization algorithm. On the basis of the wavelet threshold denoising method, an intelligent optimization algorithm is utilized to determine the optimal parameter types of the parameters corresponding to the five influencing factors in the threshold denoising process, so that the wavelet threshold denoising effect can be optimal for different characteristic signals and noises. The method is not limited to a certain special signal and noise, only one influence factor is optimized, manual parameter adjustment is not needed, multiple parameters can be adjusted for multiple different signals and noises in a self-adaptive mode, and finally five optimal parameters of the wavelet threshold denoising method under the current signals and noises are determined.
The global optimal solution is solved by seeking the minimum value of the fitness function through multiple iterations, so that the parameter type with the best denoising effect under the current signal and noise is determined, and the method has higher universality due to the fact that the fitness function is definite and is suitable for various signals. By setting the number of the optimized targets in the initial stage of the algorithm, a plurality of target parameters can be simultaneously regulated and controlled in the optimization process of the algorithm, so that multi-parameter combination optimization can be efficiently carried out, and the overall adaptability of the wavelet threshold denoising algorithm is further improved. The following detailed description is to be read in connection with specific embodiments.
Fig. 1 schematically illustrates a flowchart of an improved wavelet threshold denoising method provided by an embodiment of the present disclosure.
As shown in fig. 1, the signal processing method may include, for example, operations S101 to S106.
In operation S101, a signal to be denoised and an ideal signal are acquired.
According to an embodiment of the present disclosure, the signal to be denoised may include, for example, a radar echo signal, an ECG electrocardiogram signal, a test signal, and the like.
In operation S102, a denoising parameter is initialized,
according to an embodiment of the present disclosure, the denoising parameters may include a wavelet basis function, a number of decomposition reconstruction layers, a threshold estimation criterion, a threshold function form, and a threshold scaling manner.
In operation S103, a signal to be denoised is denoised by using the initialized denoising parameters, so as to obtain a first noise signal.
According to an embodiment of the present disclosure, the denoising process may include: and performing wavelet transformation on the de-noised signal by using the wavelet basis function. And decomposing the signals and the noise in the signals to be denoised to different scales according to the decomposition reconstruction layer number. And determining the threshold for processing the wavelet coefficient under each scale according to a threshold estimation criterion and a threshold scaling mode. And carrying out zero setting, reduction or retention processing on the wavelet coefficients under each scale by using a threshold function form. And performing wavelet inverse transformation on the wavelet coefficients under each scale after processing by using the wavelet basis functions and the decomposition reconstruction layer number to obtain denoised signals.
Operation S104 is performed to calculate a mean square error between the signal to be denoised and the ideal signal as a first fitness, and calculate a mean square error between the first noise signal and the ideal signal as a second fitness.
According to the embodiment of the disclosure, the mean square error between the denoised signal and the ideal signal is taken as the fitness function of the denoising parameter optimization algorithm. The selection of the fitness function is important, and the fitness function is not only a judgment index for judging whether the signal denoising effect is good or bad, but also a judgment standard for judging whether the parameter selection result is appropriate or not. The embodiment of the present disclosure selects Mean Square Error (MSE), which is a measure reflecting the degree of difference between the estimated quantity and the estimated quantity, and the formula is as follows:
wherein x (m) is an ideal signal,
is a denoised signal.
Fig. 2 schematically illustrates a graph of the fitness function provided by an embodiment of the present disclosure as a function of the number of iterations.
As shown in fig. 2, the MSE gradually decreases through a plurality of iterations, and when it reaches a minimum value, the corresponding global optimal solution is the optimal parameter type to be found.
In operation S105, the first fitness and the second fitness are compared, and if the second fitness is smaller than the first fitness, the denoising parameter is updated.
After the denoising parameter is updated according to the embodiment of the present disclosure, the operation S103 is returned, the signal to be denoised is denoised by using the updated denoising parameter to obtain a second noise signal, and the operation S103 to the operation S105 are continuously and repeatedly performed to perform iterative computation until the minimum fitness is obtained.
In operation S106, the signal to be denoised is denoised by using the denoising parameter corresponding to the minimum fitness.
Specifically, a wavelet threshold denoising function is called, the optimally selected optimal parameter is used as an input parameter of the function, the obtained signal to be denoised is used as an input signal, wavelet threshold denoising is carried out, and the output signal is the denoised signal.
According to an embodiment of the present disclosure, the updating the denoising parameter may include: and respectively updating the denoising parameters in a global search mode or a local search mode.
Specifically, the parameter optimization process of the embodiment of the present disclosure is mainly completed through a global search link and a local search link. The two search links are determined by transforming the values of the probability parameter p and the random number rand, wherein the rand is uniformly distributed according to (0, 1). And through multiple iterations, the search is continuously switched between the global and the local, and finally the global optimal solution is found.
Fig. 3 schematically shows a flowchart of parameter optimization provided by the embodiment of the present disclosure.
As shown in fig. 3, the optimization process may include:
1. and setting parameters, namely setting a search point number N, a cycle iteration number N and a conversion probability p.
2. Initializing, initializing an optimization range, solutions Sol of all parameters, Fitness Fitness, global optimal Fitness Fmin and global optimal solution Best.
3. And global optimization is carried out, and the solution S of all the parameters found at present is updated.
4. The new fitness Fnew is calculated according to the fitness function.
5. And acquiring the current Fitness Fitness, and comparing the new Fitness Fnew with the current Fitness Fitness. If Fnew is less than Fitness, replacing Fitness with Fnew, and replacing Sol with S, otherwise, not changing;
6. and obtaining the current global optimal fitness Fmin, comparing the new fitness Fnew with the current global optimal fitness Fmin, if the Fnew is less than the Fmin, replacing the Fmin with the Fnew, replacing the Best with the S, and otherwise, keeping the fitness unchanged.
7. And (5) finishing the loop iteration to obtain the optimal value Best of the wavelet threshold denoising parameter, and otherwise, returning to 3 until all loop iterations are finished.
In the global search mode, the following may be used:
and updating the denoising parameters, wherein,
represents the current value of the ith parameter in the five parameters during the t iteration updating,
is shown at the current iterationL is the search step size, which obeys the levy distribution. Wherein, the L vy distribution formula is as follows:
where Γ (λ) is a standard gamma function, this distribution is valid for step sizes s > 0, where λ typically takes 1.5.
In the local search mode, the method can be according to:
and updating the denoising parameters, wherein,
represents the current value of the ith parameter in the five parameters during the t iteration updating,
and
showing that any two of the local parameters of the ith parameter at the time of the t-th iteration update are different from each other
Epsilon is a proportionality coefficient with an interval of (0, 1) and obeying uniform distribution.
According to the embodiment of the disclosure, since only numbers can be processed in the actual parameter optimization process, a specific number is required to be set as a 'comparison table' to refer to the parameter type, so that the optimization algorithm and the wavelet threshold denoising are combined.
Specifically, the least common multiple of all the selectable types of the five parameters is used as the maximum range of algorithm search, the wavelet basis functions have 60 selection types, the decomposition reconstruction layer number has 10 selection types, the threshold function form has 2 selection types, the threshold estimation criterion has 4 selection types, and the threshold scaling mode has 3 selection types, so that the least common multiple is 60, namely the algorithm search range is a number from 1 to 60. Secondly, the numbers are distributed to each parameter type in the order from small to large according to the principle of equal probability, all the optional types of the five target parameters can be in one-to-one correspondence with the algorithm search range, and the comparison table is established.
The selectable type ranges of five parameters of wavelet threshold denoising and the corresponding algorithm search ranges thereof are shown in the following table 1:
according to the content in the table 1, each natural number uniquely refers to a certain parameter selectable type, so that the optimal parameter type scheme in all parameter types can be determined by the global optimal numerical solution finally given by the algorithm and comparing the table.
According to the improved wavelet threshold denoising method provided by the embodiment of the disclosure, the denoising parameter is continuously updated in an iterative manner, and the mean square error between the signal subjected to denoising by the denoising parameter and the ideal signal is used as the fitness to measure whether the current denoising parameter is the optimal denoising parameter, so that the optimal denoising parameter is adaptively found to denoise the signal to be denoised, and the denoising accuracy is improved.
To verify the advantages of improved wavelet threshold denoising provided by the embodiments of the present disclosure, the following is further described with reference to three specific examples.
Example 1
The method comprises the steps of carrying out denoising processing on three common additive noises in radar echo signals, namely environment noise (white Gaussian noise WGN), clutter noise (Gaussian color noise CGN) and non-stationary noise (non-stationary Gaussian noise), comparing denoising results, and finally analyzing denoising performances of a wavelet correlation denoising method, a wavelet modulus maximum denoising method, a wavelet threshold denoising method and the wavelet threshold denoising method provided by the embodiment of the disclosure by combining two evaluation indexes of SNR and MSE.
Fig. 4 schematically shows an ideal signal diagram corresponding to a radar signal, an electrocardiogram signal and a test signal provided by the embodiment of the disclosure.
The simulation waveform of the radar signal is shown as a 1 st graph in fig. 4, and the formula is as follows:
fig. 5 schematically illustrates a radar signal and a noise waveform thereof provided by an embodiment of the disclosure.
For the case of the radar system with the environmental noise interference, the present embodiment is simulated by the white gaussian noise WGN, the probability density function follows gaussian distribution, and the power spectral density function follows uniform distribution, and the waveform is shown in the first line of fig. 5. For the condition that clutter is mixed in the radar echo, the radar echo is simulated by using gaussian color noise CGN, the probability density function of the radar echo is subjected to gaussian distribution, the power spectral density function of the radar echo is subjected to non-uniform distribution, and the waveform is shown in the second line chart of fig. 5. Because of some objective factors, the signal strength suddenly changes, the present embodiment is simulated by using non-stationary gaussian noise, the probability density function follows gaussian distribution, the power spectral density function is a step function, and the waveform is shown in the third line chart of fig. 5.
Fig. 6 schematically shows a result diagram of three noise removals of radar signals by using four wavelet denoising methods according to an embodiment of the present disclosure.
As shown in fig. 6, first, subjective analysis and judgment are performed by human eye observation. The three oscillograms in the row 1 in fig. 6 are effect graphs of the wavelet correlation method after removing three kinds of noise, and it can be seen from the graphs that the de-noised signals have more obvious "burrs", and are relatively rough and have poor de-noising effect; the three waveforms in row 2 in fig. 6 are graphs of the effect of the wavelet modulus maximum value method on three types of noise after being removed, and it can be seen from the graphs that the signals after being removed of noise are improved as compared with the signals in the previous row, but some "burrs" still exist, and are slightly rough, and the noise removal effect is general; the three oscillograms in the 3 rd row in fig. 6 are effect graphs of the wavelet threshold method after removing three kinds of noise respectively, and it can be seen from the graphs that the denoised signals are obviously improved compared with the signals in the two rows, the signals are smooth and have no 'burr', but some details are slightly deformed and distorted, and the denoising effect is good; the three waveforms in row 4 of fig. 6 are graphs of the effect of the improved wavelet threshold method on removing three kinds of noise, respectively, and it can be seen from the graphs that the de-noised signals are cleaner and smoother than the signals in the upper row, the deformation at the details is reduced, only the intensity at the individual peak valley is slightly fluctuated compared with the ideal signals, and the de-noising effect is the best among the four methods.
In order to further verify that the denoising effect of the method is the best, two denoising effect evaluation indexes, namely the signal-to-noise ratio (SNR) and the Mean Square Error (MSE), of the denoised signal are compared through various methods, and objective analysis and judgment are conducted. According to the principle that the MSE is larger and the denoising effect is smaller and the better, the denoising effects of various methods are compared, as shown in Table 2:
the table index data further shows that for three additive noises in radar signals, the improved wavelet threshold denoising method provided by the disclosure has a denoising effect obviously superior to that of other three traditional wavelet denoising methods.
Example two:
in the embodiment, denoising processing is respectively performed on three common additive noises in an ECG signal, namely environmental noise (white Gaussian noise WGN), baseline drift noise (PLN) and electromyographic interference noise (EMG), and denoising results are compared, and finally a wavelet correlation denoising method, a wavelet modulus maximum denoising method, a wavelet threshold denoising method and an improved wavelet threshold denoising method are analyzed by combining two evaluation indexes of SNR and MSE.
The simulated waveform of the ECG signal is generated based on the Fourier series principle while combining the measured ECG signal characteristics, as shown in FIG. 4, panel 2.
Fig. 7 schematically illustrates an electrocardiogram signal and its noise waveform provided by an embodiment of the present disclosure.
For the case of environmental noise interference in the ECG signal, the present embodiment is modeled by white gaussian noise WGN, the probability density function follows gaussian distribution, the power spectral density function follows uniform distribution, and the waveform is shown in the first line of fig. 7; for the case of ECG baseline wander, this embodiment simulates it with a sine function, as shown below, with the waveform shown in the second row of FIG. 7;
NPLN＝200sin(0.002πt) t＝0，1，2...1024
for the case of electromyographic interference of the ECG, the present embodiment is modeled with uniform noise, the probability density function follows a uniform distribution, and the waveform is shown in the third row of FIG. 7.
Fig. 8 schematically shows a result diagram of three noise removals on a electrocardiogram signal by using four wavelet denoising methods according to an embodiment of the present disclosure.
The four wavelet denoising methods respectively remove the three noise results,
as shown in fig. 8, first, subjective analysis and judgment were performed by human eye observation. The three oscillograms in the row 1 in fig. 8 are effect graphs of the wavelet correlation method after removing three kinds of noise, and it can be seen from the graphs that the de-noised signals have more obvious "burrs", and are relatively rough and have poor de-noising effect; the three oscillograms in the 2 nd row in fig. 8 are the effect graphs of the wavelet modulus maximum value method after removing the three kinds of noise respectively, and it can be seen from the graphs that the signal distortion after denoising is serious, especially the characteristic peak is basically removed as noise, and the denoising effect is very poor; the three oscillograms in the 3 rd row in fig. 8 are effect graphs of the wavelet threshold method after removing three kinds of noise respectively, and it can be seen from the graphs that the denoised signals are obviously improved compared with the signals in the two rows, the signals are smooth and have no obvious 'burr', but some details still have noise obviously remained, and the denoising effect is better; the three waveforms in row 4 in fig. 8 are graphs of the effect of the improved wavelet threshold method on removing three kinds of noise, respectively, and it can be seen from the graphs that the denoised signal is closer to an ideal signal than the signal in the upper row, the residual noise at the details is slightly reduced, and the denoising effect is the best among the four methods.
In order to further verify that the denoising effect of the method is the best, two denoising effect evaluation indexes, namely the signal-to-noise ratio (SNR) and the Mean Square Error (MSE), of the denoised signal are compared through various methods, and objective analysis and judgment are conducted. According to the principle that the larger the SNR, the smaller the MSE and the better the denoising effect, the denoising effects of various methods are compared, as shown in Table 3:
as further illustrated by the index data in the table, for three additive noises in the ECG signal, the improved wavelet threshold denoising method provided by the disclosure has a significantly better denoising effect than the other three traditional wavelet denoising methods.
Example three:
the embodiment performs denoising processing and comparison on denoising results aiming at test signals and noises, and finally analyzes a wavelet correlation denoising method, a wavelet modulus maximum denoising method, a wavelet threshold denoising method and the denoising performance of an improved wavelet threshold denoising method by combining two evaluation indexes of SNR and MSE.
The waveform of the test signal is obtained by directly importing the data fdata, as shown in fig. 3 of fig. 4.
Fig. 9 schematically illustrates a test signal and its noise waveform provided by an embodiment of the present disclosure.
As shown in fig. 9. The noise of the test signal is also obtained by directly introducing the data fdata.
Fig. 10 schematically illustrates a result diagram of noise removal on a test signal by using four wavelet denoising methods according to an embodiment of the present disclosure.
As shown in fig. 10, first, subjective analysis and judgment were performed by human eye observation. The oscillogram in line 1 in fig. 10 is an effect graph of a wavelet correlation method after removing test noise, and it can be seen from the graph that a number of significant "burrs" exist at corners of a denoised signal, and the whole is rough and has a poor denoising effect; the oscillogram in line 2 in fig. 10 is an effect graph of the wavelet modulus maximum value method after removing the test noise, and it can be seen from the graph that the denoised signal is improved compared with the signal in the upper line, the signal is smooth and has no "burr", but abnormal peak points appear at the corners, and the whole is slightly rough, and the denoising effect is general; the oscillogram in the 3 rd row in fig. 10 is an effect graph of the wavelet threshold method after removing the test noise, and it can be seen from the graph that the denoised signal is smoother compared with the signals in the two rows, but the abnormal peak points at the corners are more obvious, and the denoising effect is more general; the waveform diagram in row 4 in fig. 10 is a diagram of the effect of the improved wavelet threshold method on the removal of the test noise, and it can be seen from the diagram that the denoised signal is cleaner and smoother than the above signal, the abnormal peak values at the corners are reduced, and the denoising effect is the best among the four methods.
In order to further verify that the denoising effect of the method is the best, two denoising effect evaluation indexes, namely the signal-to-noise ratio (SNR) and the Mean Square Error (MSE), of the denoised signal are compared through various methods, and objective analysis and judgment are conducted. According to the principle that the MSE is larger and the denoising effect is smaller and the better, the denoising effects of various methods are compared, as shown in Table 4:
as further illustrated by index data in the table, for the noise of a test signal, the denoising effect of the improved wavelet threshold denoising method provided by the disclosure is obviously superior to that of the other three traditional wavelet denoising methods.
In summary, the present disclosure provides an improved wavelet threshold denoising method based on an intelligent optimization algorithm. The method is used for adaptively optimizing and selecting five influence parameters required in the wavelet threshold denoising process aiming at signals in various actual lives such as radar echo signals, ECG (electrocardiogram) signals and the like, so that the optimal denoising effect can be achieved when the signals face different characteristic signals and noises, and the optimization algorithm is verified to maximize the wavelet threshold denoising capability and has strong universality and adaptability. Therefore, it is reasonable to believe that the present disclosure has a very wide application prospect, for example, the aspects of radar echo signal detection, physiological signal monitoring such as electrocardiogram and electroencephalogram, diffraction grating interference signal processing, power system harmonic detection, etc. all relate to the interference of noise on useful signals, so the present disclosure can be applied to these scientific research engineering fields as well.
Based on the same inventive concept, the disclosure also provides a wavelet threshold denoising device. Fig. 11 schematically shows a structural block diagram of a wavelet threshold denoising device provided by an embodiment of the present disclosure.
As shown in fig. 11, the wavelet threshold denoising apparatus 1100 may include, for example, an obtaining module 1110, an initializing module 1120, a calculating module 1130, an updating module 1140, and a denoising module 1150.
The obtaining module 1110 is configured to obtain a signal to be denoised and an ideal signal.
The initialization module 1120 is configured to initialize a denoising parameter, and denoise a signal to be denoised by using the initialized denoising parameter to obtain a first noise signal.
A calculating module 1130, configured to calculate a mean square error between the signal to be denoised and the ideal signal, as a first fitness; and calculating the mean square error between the first noise signal and the ideal signal as a second fitness.
The updating module 1140 is configured to compare the first fitness with the second fitness, and update the denoising parameter if the second fitness is smaller than the first fitness.
And the denoising module 1150 is configured to denoise the signal to be denoised by using the updated denoising parameter, so as to obtain a second noise signal.
The calculating module 1130 is further configured to calculate a mean square error between the second noise signal and the ideal signal as a third fitness.
The updating module 1140 is further configured to compare the third fitness with the second fitness, and if the third fitness is smaller than the second fitness, continue to update the denoising parameter.
The signal to be denoised is denoised by utilizing the denoising parameter corresponding to the minimum fitness until the minimum fitness is obtained through iteration of the calculating module 1130, the updating module 1140 and the denoising module 1150.
Any number of modules, sub-modules, units, sub-units, or at least part of the functionality of any number thereof according to embodiments of the present disclosure may be implemented in one module. Any one or more of the modules, sub-modules, units, and sub-units according to the embodiments of the present disclosure may be implemented by being split into a plurality of modules. Any one or more of the modules, sub-modules, units, sub-units according to embodiments of the present disclosure may be implemented at least in part as a hardware circuit, such as a Field Programmable Gate Array (FPGA), a Programmable Logic Array (PLA), a system on a chip, a system on a substrate, a system on a package, an Application Specific Integrated Circuit (ASIC), or may be implemented in any other reasonable manner of hardware or firmware by integrating or packaging a circuit, or in any one of or a suitable combination of software, hardware, and firmware implementations. Alternatively, one or more of the modules, sub-modules, units, sub-units according to embodiments of the disclosure may be at least partially implemented as a computer program module, which when executed may perform the corresponding functions.
For example, any plurality of the obtaining module 1110, the initializing module 1120, the calculating module 1130, the updating module 1140 and the denoising module 1150 may be combined and implemented in one module/unit/subunit, or any one of the modules/units/subunits may be split into a plurality of modules/units/subunits. Alternatively, at least part of the functionality of one or more of these modules/units/sub-units may be combined with at least part of the functionality of other modules/units/sub-units and implemented in one module/unit/sub-unit. According to an embodiment of the present disclosure, at least one of the obtaining module 1110, the initializing module 1120, the calculating module 1130, the updating module 1140 and the denoising module 1150 may be at least partially implemented as a hardware circuit, such as a Field Programmable Gate Array (FPGA), a Programmable Logic Array (PLA), a system on a chip, a system on a substrate, a system on a package, an Application Specific Integrated Circuit (ASIC), or may be implemented by hardware or firmware in any other reasonable manner of integrating or packaging a circuit, or implemented by any one of three implementations of software, hardware and firmware, or implemented by a suitable combination of any several of them. Alternatively, at least one of the obtaining module 1110, the initializing module 1120, the calculating module 1130, the updating module 1140 and the denoising module 1150 may be at least partially implemented as a computer program module, which may perform corresponding functions when executed.
It should be noted that, the signal processing apparatus portion in the embodiment of the present disclosure corresponds to the signal processing method portion in the embodiment of the present disclosure, and the specific implementation details thereof are also the same, and are not described herein again.
Fig. 12 schematically shows a block diagram of an electronic device adapted to implement the above described method according to an embodiment of the present disclosure. The electronic device shown in fig. 12 is only an example, and should not bring any limitation to the functions and the scope of use of the embodiments of the present disclosure.
As shown in fig. 12, an electronic apparatus 1200 according to an embodiment of the present disclosure includes a processor 1201 which can perform various appropriate actions and processes in accordance with a program stored in a Read Only Memory (ROM)1202 or a program loaded from a storage section 12012 into a Random Access Memory (RAM) 1203. The processor 1201 may include, for example, a general purpose microprocessor (e.g., a CPU), an instruction set processor and/or associated chipset, and/or a special purpose microprocessor (e.g., an Application Specific Integrated Circuit (ASIC)), among others. The processor 1201 may also include on-board memory for caching purposes. The processor 1201 may include a single processing unit or multiple processing units for performing the different actions of the method flows according to embodiments of the present disclosure.
In the RAM1203, various programs and data necessary for the operation of the electronic apparatus 1200 are stored. The processor 1201, the ROM1202, and the RAM1203 are connected to each other by a bus 1204. The processor 1201 performs various operations of the method flow according to the embodiments of the present disclosure by executing programs in the ROM1202 and/or the RAM 1203. Note that the programs may also be stored in one or more memories other than the ROM1202 and the RAM 1203. The processor 1201 may also perform various operations of method flows according to embodiments of the present disclosure by executing programs stored in the one or more memories.
According to embodiments of the present disclosure, method flows according to embodiments of the present disclosure may be implemented as computer software programs. For example, embodiments of the present disclosure include a computer program product comprising a computer program embodied on a computer readable storage medium, the computer program containing program code for performing the method illustrated by the flow chart. In such an embodiment, the computer program may be downloaded and installed from a network through the communication section 1209, and/or installed from the removable medium 1211. The computer program, when executed by the processor 1201, performs the above-described functions defined in the system of the embodiments of the present disclosure. The systems, devices, apparatuses, modules, units, etc. described above may be implemented by computer program modules according to embodiments of the present disclosure.
The present disclosure also provides a computer-readable storage medium, which may be contained in the apparatus/device/system described in the above embodiments; or may exist separately and not be assembled into the device/apparatus/system. The computer-readable storage medium carries one or more programs which, when executed, implement the method according to an embodiment of the disclosure.
According to an embodiment of the present disclosure, the computer-readable storage medium may be a non-volatile computer-readable storage medium. Examples may include, but are not limited to: a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the present disclosure, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.
For example, according to embodiments of the present disclosure, a computer-readable storage medium may include the ROM1202 and/or the RAM1203 and/or one or more memories other than the ROM1202 and the RAM1203 described above.
The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams or flowchart illustration, and combinations of blocks in the block diagrams or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions. Those skilled in the art will appreciate that various combinations and/or combinations of features recited in the various embodiments and/or claims of the present disclosure can be made, even if such combinations or combinations are not expressly recited in the present disclosure. In particular, various combinations and/or combinations of the features recited in the various embodiments and/or claims of the present disclosure may be made without departing from the spirit or teaching of the present disclosure. All such combinations and/or associations are within the scope of the present disclosure.
Claims (10)
1. A wavelet threshold denoising method comprises the following steps:
acquiring a signal to be denoised and an ideal signal;
initializing denoising parameters, and denoising the signal to be denoised by using the initialized denoising parameters to obtain a first noise signal;
calculating the mean square error between the signal to be denoised and the ideal signal to be used as a first fitness; calculating a mean square error between the first noise signal and the ideal signal as a second fitness;
comparing the first fitness with the second fitness, updating a denoising parameter if the second fitness is smaller than the first fitness, and denoising the signal to be denoised by using the updated denoising parameter to obtain a second noise signal;
calculating a mean square error between the second noise signal and the ideal signal as a third fitness;
comparing the third fitness with the second fitness, if the third fitness is smaller than the second fitness, continuously updating denoising parameters to perform denoising and fitness calculation, and iterating until the minimum fitness is obtained;
and denoising the signal to be denoised by utilizing the denoising parameter corresponding to the minimum fitness.
2. The wavelet threshold denoising method of claim 1, wherein the updating denoising parameters comprises:
and respectively updating the denoising parameters in a global search mode or a local search mode.
3. The wavelet threshold denoising method of claim 2, wherein the denoising parameters include a wavelet basis function, a number of decomposition reconstruction layers, a threshold estimation criterion, a threshold function form, and a threshold scaling manner;
in the global search mode, the following steps are carried out:
and updating the denoising parameters, wherein,
represents the current value of the ith parameter in the five parameters during the t iteration updating,
representing the global optimum value of the ith parameter at the current iteration, L being the search step size.
4. The wavelet threshold denoising method of claim 2, wherein the denoising parameters include a wavelet basis function, a number of decomposition reconstruction layers, a threshold estimation criterion, a threshold function form, and a threshold scaling manner;
in the local search mode, the following steps are performed:
and updating the denoising parameters, wherein,
represents the current value of the ith parameter in the five parameters during the t iteration updating,
and
showing that any two of the local parameters of the ith parameter at the time of the t-th iteration update are different from each other
Epsilon is a proportionality coefficient with an interval of (0, 1) and obeying uniform distribution.
5. The wavelet threshold denoising method of claim 1, wherein the denoising parameters include a wavelet basis function, a number of decomposition reconstruction layers, a threshold estimation criterion, a threshold function form, and a threshold scaling manner;
denoising the signal to be denoised by using denoising parameters comprises:
performing wavelet transformation on the de-noised signal by using a wavelet basis function;
decomposing the signals and the noise in the signals to be denoised into different scales according to the decomposition reconstruction layer number;
determining a threshold for processing wavelet coefficients under each scale according to a threshold estimation criterion and a threshold scaling mode;
utilizing a threshold function form to perform zero setting, reduction or retention processing on the wavelet coefficients under each scale;
and performing wavelet inverse transformation on the wavelet coefficients under each scale after processing by using the wavelet basis functions and the decomposition reconstruction layer number to obtain denoised signals.
6. The wavelet threshold denoising method of claim 2, the method further comprising:
setting a conversion probability;
and selecting a global search mode or a local search mode according to the conversion probability.
7. The wavelet threshold denoising method of claim 2, wherein the denoising parameters include a wavelet basis function, a number of decomposition reconstruction layers, a threshold estimation criterion, a threshold function form, and a threshold scaling manner;
the method further comprises the following steps:
and establishing a corresponding relation between all selectable types of the denoising parameters and the global search mode or local search mode search range, wherein the search range is referred to by a number.
8. A wavelet threshold denoising apparatus, comprising:
the acquisition module is used for acquiring a signal to be denoised and an ideal signal;
the initialization module is used for initializing denoising parameters and denoising the signal to be denoised by using the initialized denoising parameters to obtain a first noise signal;
the computing module is used for computing the mean square error between the signal to be denoised and the ideal signal to serve as a first fitness; calculating a mean square error between the first noise signal and the ideal signal as a second fitness;
the updating module is used for comparing the first fitness with the second fitness and updating the denoising parameter if the second fitness is smaller than the first fitness;
the denoising module is used for denoising the signal to be denoised by using the updated denoising parameter to obtain a second noise signal;
the calculation module is further configured to calculate a mean square error between the second noise signal and the ideal signal as a third fitness;
the updating module is further configured to compare the third fitness with the second fitness, and if the third fitness is smaller than the second fitness, continue to update the denoising parameter;
and carrying out iteration on the calculation module, the updating module and the denoising module until the minimum fitness is obtained, and denoising the signal to be denoised by using the denoising parameter corresponding to the minimum fitness.
9. An electronic device, comprising:
one or more processors;
a memory for storing one or more programs,
wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of any of claims 1-7.
10. A computer readable storage medium having stored thereon executable instructions which, when executed by a processor, cause the processor to carry out the method of any one of claims 1 to 7.
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