CN107516065B - The sophisticated signal denoising method of empirical mode decomposition combination dictionary learning - Google Patents
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Abstract
A kind of sophisticated signal denoising method of empirical mode decomposition combination dictionary learning: EMD decomposition is carried out to noise-containing signal, obtains the intrinsic mode function signal of one group of order from low to high；Noise-containing intrinsic mode function is denoised using Wavelet Soft-threshold Denoising Method；Intrinsic mode function after denoising is added to obtain denoised signal with remaining intrinsic mode function, residual error is added to obtain noise contribution；Denoised signal is divided into one group of training sample, one group of signal dictionary is therefrom trained using KSVD algorithm；Noise contribution is divided into one group of training sample, one group of noise dictionary is therefrom trained using KSVD algorithm；Signal dictionary and noise dictionary is combined to obtain mixing dictionary；The signal denoised will be needed to carry out sparse decomposition on mixing dictionary, one group of sparse vector is obtained, by the corresponding coefficient zero setting of noise atom in sparse vector；Mixing dictionary, sparse vector is multiplied with treated, obtains final denoised signal.The present invention can effectively remove a variety of noise contributions.
Description
Technical field
The present invention relates to a kind of sophisticated signal denoising methods.More particularly to a kind of empirical mode decomposition combination dictionary learning
Sophisticated signal denoising method.
Background technique
It is related to the field of data processing machinery vibration analysis, image and speech recognition, the interpretation of meteorological data etc. are numerous
In all suffer from a common problem: data are inevitably mixed into different types of noise signal in acquisition, transmission process,
This brings great difficulty to the data processing in later period, and the validity and accuracy of processing result are affected.Therefore,
Noise how is eliminated or inhibits, it is a very valuable research that useful signal component is restored from contaminated signal
Project, many scientific research personnel are dedicated to the research of the theme.
Untiringly make great efforts by each field scholar decades, signal denoising research have been achieved with many gratifying progress and at
Fruit, wherein more representational algorithm has: the signal antinoise method based on Fourier transformation, the signal based on wavelet transformation are gone
Method for de-noising and the signal antinoise method based on linear transformation etc..Signal antinoise method based on Fourier transformation is by signals and associated noises
Frequency domain is transformed to, retains effective signal component using the characteristic of signal and noise on frequency domain with different distributions and rejects and make an uproar
Sound ingredient, the signal denoised finally by Fourier inversion.The wherein linear filtering of more famous method, wiener filter
Wave and Kalman filtering work as signal component and noise contribution in frequency domain weight although linear filtering principle is simple, is easily achieved
With regard to helpless when conjunction；Wiener filtering realizes signal by minimizing the mean square error between denoised signal and original signal
The purpose of denoising, but this method is only effective to stationary signal；Kalman filtering introduces the state-space model of signal and noise
Filtering theory, obtains recurrence estimation algorithm, is later still by minimizing the mean square error between denoised signal and original signal
Signal is denoised, but this method needs to know the statistical property of signal and noise, cause algorithm in practical applications by
Limit.Denoising method based on wavelet transformation, overcomes the shortcomings that Fourier transformation is confined to frequency, by signal in time domain and frequency domain
Combine analysis, extend temporal locality and frequency local addresses analysis, not only the characteristic by signal on frequency domain shows
Incisively and vividly, while also it is demonstrated by the variation characteristic of signal in each period, improves denoising effect, however Wavelet Denoising Method is imitated
Fruit depends on the selection of wavelet basis, and the stationarity of wavelet basis function causes the adaptivity of Wavelet noise-eliminating method poor.It is based on
It is answered in the signal antinoise method of linear transformation with independent component analysis (Independent Component Analysis, ICA)
With the most extensively, main thought is to regard signals and associated noises as signal and noise and mixed with certain unknown manner, mutually
The subspace of independent signal and noise forms independent base, further according to certain denoising criterion to isolated component at
Reason, stick signal subspace finally does inverse transformation and obtains denoised signal.The algorithm generally requires known multiple signals, but real
Border signal often only has a kind of signals with noise, and which results in the limitations of the denoising method.
Since many complicated signals have the characteristic of nonlinear and nonstationary, it is difficult to adopt the basic function carry out table of rule
Sign, and contained noise type can not be predicted in advance, be difficult to obtain satisfied denoising effect so as to cause existing Denoising Algorithm.Needle
To deficiency existing for existing Denoising Algorithm, and fully consider that the basic characteristics of sophisticated signal, the present invention propose empirical mode decomposition
In conjunction with the complex time series signal antinoise method of dictionary learning.
Summary of the invention
The technical problem to be solved by the invention is to provide the experiences that a kind of denoising effect is substantially better than other denoising methods
The sophisticated signal denoising method of mode decomposition combination dictionary learning.
The technical scheme adopted by the invention is that: a kind of sophisticated signal denoising side of empirical mode decomposition combination dictionary learning
Method includes the following steps:
1) EMD decomposition is carried out to noise-containing signal, obtains the intrinsic mode function signal of one group of order from low to high；
2) noise-containing intrinsic mode function is denoised using Wavelet Soft-threshold Denoising Method；
3) intrinsic mode function after denoising that step 2) obtains is added with remaining intrinsic mode function, obtains denoising letter
NumberFor signal dictionary training later, the residual error that step 2) is obtained is added to obtain noise contribution n (x), after being used for
Noise dictionary training；
4) by the denoised signal in step 3)It is divided into one group of training sample, therefrom trains one using KSVD algorithm
Group signal dictionary D1, wherein atom number is m；
5) the noise contribution n (x) in step 3) is divided into one group of training sample, therefrom trains one using KSVD algorithm
Group noise dictionary D2, wherein atom number is n；
6) by signal dictionary D1With noise dictionary D2Combination obtains mixing dictionary D,
D={ D1:D2} (6)；
7) signal denoised will be needed to carry out sparse decomposition on mixing dictionary D, obtains one group of sparse vector (x1,x2,…,
xm+n), by sparse vector (x1,x2,…,xm+n) in the corresponding coefficient zero setting of noise atom:
8) mixing dictionary D, sparse vector is multiplied with treated, obtains final denoised signal
Step 1) includes:
(1) local minimum and local maximum for finding original signal y (t), will using the method for cubic curve interpolation
The minimum found is connected with maximum, further obtains minimum envelope ymin(t) and maximum envelope ymax(t)；
(2) the temporal average m (t), i.e., each moment minimum envelope y of original signal y (t) are calculatedmin(t) and greatly
It is worth envelope ymax(t) mean value:
(3) temporal average m (t) is cut with original signal y (t), obtains a new sequences h (t):
H (t)=y (t)-m (t) (2)；
(4) according to following two characteristics of intrinsic mode function, determine whether new sequences h (t) is intrinsic mode function:
1. the number of extreme point is equal to zero crossing number or the two at most differs one；
2. at arbitrary point, the mean value of local minimum envelope and local maximum envelope is zero；
If new sequences h (t) has above-mentioned two characteristic, using new sequences h (t) as first intrinsic mode function
imf1, it is denoted as c1(t)；Otherwise, (1) step~the (3) step is repeated, until finding an intrinsic mode function c1(t)；Eigen mode
State function c1(t) high frequency section in original signal is represented, it is separated from original signal, obtains remainder r1(t):
y(t)-c1(t)=r1(t) (3)；
(5) continue to remainder r1(t) (1) step~the (4) step is repeated, next intrinsic mode function is decomposited:
Precision as defined in reaching when the difference of front and back decomposition result twice stops decomposing, and the decomposition result finally obtained is made
For the last one intrinsic mode function.
Wavelet transformation first is done to each noise-containing intrinsic mode letter in step 2), then does soft-threshold denoising processing,
Finally carry out wavelet transformation reconstruct, intrinsic mode function and noise after being denoised.
The sophisticated signal denoising method of empirical mode decomposition combination dictionary learning of the invention, major advantage and characteristic embody
Following aspects:
1, the characteristics of nonlinear and nonstationary that the method for the present invention generally has first against complex time series signal, uses
The empirical mode decomposition method of above-mentioned signal can be effectively decomposed, so that noise contribution focuses only on a small number of intrinsic mode functions
In, it is ensured that noise contribution is effectively separated from these intrinsic mode functions.
2, by learning respectively to a large amount of noise contribution and effective component, acquisition can be represented effectively the method for the present invention
The atom of two constituents, and it is combined into mixing dictionary.Signals and associated noises are decomposed using mixing dictionary, wherein noise is former for removal
It after the corresponding coefficient of son, then is multiplied with mixing dictionary, obtains denoised signal.Denoising method in the present invention can be effectively removed multiple
Noise contribution in miscellaneous signal, denoising effect are substantially better than other denoising methods.
3, the complex time series signal antinoise method of empirical mode decomposition combination dictionary learning proposed by the present invention is one
The completely new sophisticated signal denoising method of kind obtains and processing, image and Speech processing, geophysical exploration in heat transfer agent
Equal fields have broad application prospects.
Detailed description of the invention
Fig. 1 is the flow chart of the sophisticated signal denoising method of empirical mode decomposition combination dictionary learning of the present invention；
Fig. 2 a is the timing diagram of original Lorenz signal；
Fig. 2 b is the timing diagram for adding Lorenz signal of making an uproar；
Fig. 3 is original Lorenz signal and the spectrogram for adding Lorenz signal of making an uproar；
Fig. 4 is to adding Lorenz signal of making an uproar to do the imf component that EMD is decomposed；
Fig. 5 a is the timing diagram of wavelet soft-threshold denoising signal and original signal；
Fig. 5 b is the spectrogram of wavelet soft-threshold denoising signal and original signal；
Fig. 6 a is the timing diagram of EMD wavelet threshold denoising signal and original signal；
Fig. 6 b is the spectrogram of EMD wavelet threshold denoising signal and original signal；
Fig. 7 a is the timing diagram of the method for the present invention denoised signal and original signal；
Fig. 7 b is the spectrogram of the method for the present invention denoised signal and original signal.
Specific embodiment
It is denoised below with reference to sophisticated signal of the embodiment and attached drawing to empirical mode decomposition combination dictionary learning of the invention
Method is described in detail.
As shown in Figure 1, the sophisticated signal denoising method of empirical mode decomposition combination dictionary learning of the invention, including it is as follows
Step:
1) EMD decomposition is carried out to noise-containing signal, obtains the intrinsic mode function of one group of order from low to high
(Intrinsic Mode Function, imf) signal；Include:
(1) local minimum and local maximum for finding original signal y (t), will using the method for cubic curve interpolation
The minimum found is connected with maximum, further obtains minimum envelope ymin(t) and maximum envelope ymax(t)；
(2) the temporal average m (t), i.e., each moment minimum envelope y of original signal y (t) are calculatedmin(t) and greatly
It is worth envelope ymax(t) mean value:
(3) temporal average m (t) is cut with original signal y (t), obtains a new sequences h (t):
H (t)=y (t)-m (t) (2)；
(4) according to following two characteristics of intrinsic mode function, determine whether new sequences h (t) is intrinsic mode function:
1. the number of extreme point is equal to zero crossing number or the two at most differs one；
2. at arbitrary point, the mean value of local minimum envelope and local maximum envelope is zero；
If new sequences h (t) has above-mentioned two characteristic, using new sequences h (t) as first intrinsic mode function
imf1, it is denoted as c1(t)；Otherwise, (1) step~the (3) step is repeated, until finding an intrinsic mode function c1(t)；Eigen mode
State function c1(t) high frequency section in original signal is represented, it is separated from original signal, obtains remainder r1(t):
y(t)-c1(t)=r1(t) (3)；
(5) continue to remainder r1(t) (1) step~the (4) step is repeated, next intrinsic mode function is decomposed:
Precision as defined in reaching when the difference of front and back decomposition result twice stops decomposing, and the decomposition result finally obtained is made
For the last one intrinsic mode function.
2) noise-containing intrinsic mode function is denoised using Wavelet Soft-threshold Denoising Method；
Wavelet transformation first is done to each noise-containing intrinsic mode letter, then does soft-threshold denoising processing, is finally carried out
Wavelet transformation reconstruct, intrinsic mode letter and residual error after being denoised, wherein soft-threshold function is defined as follows:
Wherein sgn (x) is sign function.
3) intrinsic mode function after denoising that step 2) obtains is added with remaining intrinsic mode function, obtains denoising letter
NumberFor signal dictionary training later, the residual error that step 2) is obtained is added to obtain noise contribution n (x), after being used for
Noise dictionary training；
4) by denoised signal obtained in step 3)It is divided into one group of training sample, is therefrom instructed using KSVD algorithm
Practise one group of signal dictionary D1, wherein atom number is m；
5) noise contribution n (x) obtained in step 3) is divided into one group of training sample, is therefrom trained using KSVD algorithm
One group of noise dictionary D out2, wherein atom number is n；
6) by signal dictionary D1With noise dictionary D2Combination obtains mixing dictionary D,
D={ D1:D2} (6)；
7) signal denoised will be needed to carry out sparse decomposition on mixing dictionary D, obtains one group of sparse vector (x1,x2,…,
xm+n), by sparse vector (x1,x2,…,xm+n) in the corresponding coefficient zero setting of noise atom:
8) mixing dictionary D, sparse vector is multiplied with treated, obtains final denoised signal
In the following, classical Lorenz signal denoising example and attached drawing is combined to explain empirical mode decomposition of the invention in detail
In conjunction with the sophisticated signal denoising method of dictionary learning:
Lorenz system is classical one of chaos system, its kinetic model is as follows:
δ=10, r=28, b=8/3 are enabled, initial value is (10,1,0), and t takes a point, length of time series every 0.01
10000 are gone, after the transient state point for removing front, in addition the white Gaussian noise that intensity is 5 decibels is used to do based Denoising.
1) the lorenz signal after making an uproar will be added to carry out EMD decomposition, obtained 12 imf components (as shown in Figure 4):
(imf1,imf2,…,imf12) (10)；
2) wavelet soft-threshold denoising is done to preceding 4 imf components, by after denoising intrinsic mode function and remaining 8 it is intrinsic
Mode function is added, and obtains denoised signalThe residual error of Wavelet Denoising Method is added, noise contribution n (x) is obtained:
3) willIt is divided into one group of training sample Y, 200 atoms are trained from sample using KSVD method, is constituted
Signal dictionary D1,
Wherein, Y is training sample matrix, and each column of Y are a training sample, D1It is the signal dictionary to be learnt, XyIt is
The matrix being made of sparse vector,It is XyI-th column, T is sparsity constraints；
4) n (x) is divided into one group of training sample N, 100 atoms is trained from sample using KSVD method, constituted
Noise dictionary D2,
Wherein, N is training sample matrix, and each column of N are a training sample, D2It is the noise dictionary to be learnt, XnIt is
The matrix being made of sparse vector,It is XnI-th column, T is sparsity constraints；
5) by signal dictionary D1With noise dictionary D2It is combined into mixing dictionary D:
D={ D1:D2} (13)；
6) one section of noisy lorenz signal as shown in Figure 2 b is carried out sparse decomposition on mixing dictionary, finds out signal
Sparse vector (x1,x2,…,x300), the corresponding coefficient of noise atom is set to 0:
7) mixing dictionary D, sparse vector is multiplied with treated, obtains final denoised signal
8) timing diagram (Fig. 7 a) and spectrogram (Fig. 7 b) of denoised signal and original signal are drawn, denoised signal and original are calculated
The relative error of beginning signal, such as table 1；
9) in order to verify the validity that the method for the present invention denoises, Traditional Wavelet soft-threshold denoising signal and original letter are depicted
Number timing diagram (Fig. 5 a) and spectrogram (Fig. 5 b), EMD wavelet threshold denoising signal and original signal timing diagram (Fig. 6 a) with
Spectrogram (Fig. 6 b), and the relative error of denoised signal and original signal that every kind of method obtains is calculated, such as table 1.
The relative error of table 1 various method denoised signals and original signal
As can be seen that passing from the comparison of timing diagram and spectrogram in Fig. 5 a, Fig. 5 b, Fig. 6 a, Fig. 6 b, Fig. 7 a and Fig. 7 b
The effect of system wavelet soft-threshold denoising is worst, and the relative error of denoised signal and original signal is 11.30%；EMD wavelet threshold
The effect of denoising improves to some extent, and relative error is reduced to 10.97%；The method of the present invention isolates noise from the noisy component of signal
Ingredient is respectively trained signal component and noise contribution, obtains the atom with the respective feature of the two, composition mixing word
Allusion quotation, by signals and associated noises when carrying out sparse decomposition on mixing dictionary, successively selection atom goes to approach noisy letter from mixing dictionary
Number, finally the corresponding coefficient of signal component coefficient corresponding with noise contribution is separated, achievees the purpose that signal denoising, from
It can be seen that the timing diagram and spectrogram of denoised signal and original signal are almost overlapped in the result of Fig. 7, only several places have
The relative error of significant difference, signal and original signal after the method for the present invention denoising only has 6.02%, hence it is evident that threshold softer than small echo
The effect of value denoising and EMD wavelet threshold denoising has very big promotion.
Claims (2)
1. a kind of sophisticated signal denoising method of empirical mode decomposition combination dictionary learning, which comprises the steps of:
1) EMD decomposition is carried out to noise-containing signal, obtains the intrinsic mode function signal of one group of order from low to high；
2) noise-containing intrinsic mode function is denoised using Wavelet Soft-threshold Denoising Method, is first to contain to each
The intrinsic mode letter of noise does wavelet transformation, then does soft-threshold denoising processing, wavelet transformation reconstruct is finally carried out, after obtaining denoising
Intrinsic mode function and noise；
3) intrinsic mode function after denoising that step 2) obtains is added with remaining intrinsic mode function, obtains denoised signalFor signal dictionary training later, the noise that step 2) is obtained is added to obtain noise contribution n (x), for later
Noise dictionary training；
4) by the denoised signal in step 3)It is divided into one group of training sample, one group of letter is therefrom trained using KSVD algorithm
Number dictionary D1, wherein atom number is m；
5) the noise contribution n (x) in step 3) is divided into one group of training sample, therefrom trains one group using KSVD algorithm and makes an uproar
Sound dictionary D2, wherein atom number is n；
6) by signal dictionary D1With noise dictionary D2Combination obtains mixing dictionary D,
D={ D1:D2} (6)；
7) signal denoised will be needed to carry out sparse decomposition on mixing dictionary D, obtains one group of sparse vector (x1,x2,…,
xm+n), by sparse vector (x1,x2,…,xm+n) in the corresponding coefficient zero setting of noise atom:
8) mixing dictionary D, sparse vector is multiplied with treated, obtains final denoised signal
2. the sophisticated signal denoising method of empirical mode decomposition combination dictionary learning according to claim 1, feature exist
In step 1) includes:
(1) local minimum and local maximum for finding original signal y (t) will be found using the method for cubic curve interpolation
Minimum connected with maximum, further obtain minimum envelope ymin(t) and maximum envelope ymax(t)；
(2) the temporal average m (t), i.e., each moment minimum envelope y of original signal y (t) are calculatedmin(t) and maximum packet
Network ymax(t) mean value:
(3) temporal average m (t) is cut with original signal y (t), obtains a new sequences h (t):
H (t)=y (t)-m (t) (2)；
(4) according to following two characteristics of intrinsic mode function, determine whether new sequences h (t) is intrinsic mode function:
1. the number of extreme point is equal to zero crossing number or the two at most differs one；
2. at arbitrary point, the mean value of local minimum envelope and local maximum envelope is zero；
If new sequences h (t) has above-mentioned two characteristic, using new sequences h (t) as first intrinsic mode function imf1, it is denoted as
c1(t)；Otherwise, (1) step~the (3) step is repeated, until finding an intrinsic mode function c1(t)；Intrinsic mode function c1
(t) high frequency section in original signal is represented, it is separated from original signal, obtains remainder r1(t):
y(t)-c1(t)=r1(t) (3)；
(5) continue to remainder r1(t) (1) step~the (4) step is repeated, next intrinsic mode function is decomposited:
Precision as defined in reaching when the difference of front and back decomposition result twice stops decomposing, using the decomposition result finally obtained as most
The latter intrinsic mode function.
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| CN110146929B (en) * | 2019-05-21 | 2020-11-10 | 东华理工大学 | Low-frequency magnetotelluric data denoising method based on over-complete dictionary and compressed sensing reconstruction algorithm |
| CN110426569B (en) * | 2019-07-12 | 2021-09-21 | 国网上海市电力公司 | Noise reduction processing method for acoustic signals of transformer |
| CN110940524B (en) * | 2019-12-06 | 2021-07-06 | 西安交通大学 | Bearing fault diagnosis method based on sparse theory |
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