CN106645943A - Weak signal denoising method based on wavelet theory and EEMD - Google Patents
Weak signal denoising method based on wavelet theory and EEMD Download PDFInfo
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- CN106645943A CN106645943A CN201610825420.2A CN201610825420A CN106645943A CN 106645943 A CN106645943 A CN 106645943A CN 201610825420 A CN201610825420 A CN 201610825420A CN 106645943 A CN106645943 A CN 106645943A
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Abstract
The invention, which relates to the denoising technology of weak signals, provides a weak signal denoising method based on a wavelet theory and ensemble empirical mode decomposition (EEMD). With the method, a problem of poor signal-to-noise improvement effect in the prior art can be solved. The method comprises: an original signal is obtained and EEMD is carried out on the obtained signal to obtain an intrinsic mode function set, and an intrinsic modal function for reconstruction is determined based on an energy relation of intrinsic modal functions; for each intrinsic mode function for reconstruction, an extreme value absolute value between each two zero crossing points is compared with a threshold value and noise removing processing is carried out; a sampling position of a first intrinsic mode function is changed randomly to obtain different noise including ways of the original signal, and each noise including way is processed to obtain a reconstructed signal; and average taking is carried out on the signal obtained after reconstruction to obtain a signal after denoising. Targeted denoising processing can be carried out by combining different signal characteristics adaptively; and the signal-to-noise improvement ratio for a target weak signal is larger than 15dB and the root-mean-square error is small.
Description
Technical field
The present invention relates to it is a kind of based on wavelet theory and the denoising method of the small-signal of EEMD, belong to signal denoising neck
Domain.
Technical background
In Modern Information war, the electromagnetic property of noncooperative target increasingly has low detectivity, target emanation
Electromagnetic signal be submerged in noise, signal power defines small-signal well below noise power, it is difficult to perceived to obtain
Take.For the relatively low block signal research denoising method of signal to noise ratio, this will have the design to the detection identification after intercepted signal
Significance.
In signal denoising field, many scholars do a lot of work in terms of using wavelet method denoising.Its reason is,
First wavelet theory possesses good time-frequency characteristic, and in addition Wavelet noise-eliminating method also has decorrelation, selects the spies such as base flexibility
Property.In concrete operations, through decomposing, three parts of wavelet coefficient process and reconstruct, you can obtain reasonable denoising effect.But
In the case where signal to noise ratio is extremely low, common Wavelet Denoising Method is embodied in almost without effect：Noise improves than almost nil,
Square error is very big.This is nonsensical for signal denoising.Therefore consider to explore new denoising approach.Empirical mode decomposition
(Empirical Mode Decomposition, EMD) method is a kind of signal transacting for causing scholar extensively to note in recent years
Method, sophisticated signal can be resolved into some typical empirical mode signals by it, and very sensitive to noise, be easy to follow-up
Research.But, EMD algorithms have some deficiency itself can not be overcome, such as modal overlap problem, and this will make the signal after decomposition
There is serious distortion, for this problem, we adopt to be based on and wavelet theory is applied into set empirical mode decomposition
The block signal that the method for (Ensemble Empirical Mode Decomposition, EEMD) is relatively low to signal to noise ratio is carried out
Denoising.
The content of the invention
The present invention is to solve existing conventional denoising method when small-signal is processed, for signal to noise ratio improvement
Bad problem, and propose a kind of based on wavelet theory and the small-signal denoising method of EEMD.
It is a kind of based on wavelet theory and the small-signal denoising method of EEMD, methods described includes：
Step one, acquisition primary signal simultaneously carry out EEMD decomposition to it, intrinsic mode function set are obtained, by described
Levy each intrinsic mode function in mode function set energy relationship determine for reconstruct intrinsic mode function, wherein EEMD
To gather empirical mode decomposition；
Step 2, extreme value absolute value and threshold that each is used in intrinsic mode function of reconstruct between each two zero crossing
Value relatively and do cancelling noise process；
Step 3, the sampling location by changing first intrinsic mode function at random, obtain primary signal different band and make an uproar
Form, does respectively the process of step 2, the signal after being reconstructed to every kind of band form of making an uproar；
Step 4, the signal to obtaining after the reconstruct are averaged, and obtain the signal after denoising.
Beneficial effects of the present invention are：
The present invention takes full advantage of the flexibility that wavelet theory and EEMD methods are combined, by pending signals with noise
The energy relationship research of each intrinsic mode function obtained after EEMD decomposes, selects the intrinsic mode letter for reconstruct
Number.The threshold denoising thought of wavelet theory is applied in these intrinsic mode functions.Determine all zero in each intrinsic mode
Two adjacent zero crossings points are defined as gap by cross-point locations, and respective threshold process is carried out in each gap.To original letter
First intrinsic mode function sampling location change at random produces new signal in number, and above-mentioned threshold denoising behaviour is repeated to new signal
Make, finally by it is all after threshold process intrinsic mode functions reconstruct, so as to obtain denoising after signal.This denoising side
The characteristics of method adaptively can combine unlike signal, targetedly denoising, through experiment to Target Weak Signal
Noise improves than being more than 15dB, and root-mean-square error is less.
Description of the drawings：
Fig. 1 is the flow chart of the present invention；
Fig. 2 (a)-Fig. 2 (c) is directly using the effect obtained after the decomposed and reconstituted denoisings of EEMD and interval denoising, iterated denoising
The schematic diagram of the embodiment of fruit contrast；
Fig. 3 be after iterated denoising process after denoising signal to noise ratio with the relation of original signal to noise ratio schematic diagram；
Fig. 4 is the schematic diagram of the IMF contrasts after the IMF after the signal decomposition with noise decomposes with pure noise signal.
Specific embodiment
Specific embodiment one：
Present embodiment it is a kind of based on wavelet theory and the denoising method of the small-signal of EEMD, methods described includes mesh
Mark signal modeling decomposes pretreatment and two parts of denoising, realizes especially by following steps：
Step one, acquisition primary signal simultaneously carry out EEMD decomposition to it, intrinsic mode function set are obtained, by described
Levy each intrinsic mode function in mode function set energy relationship determine for reconstruct intrinsic mode function, wherein EEMD
To gather empirical mode decomposition；
It should be noted that because the invention belongs to Wavelet Denoising Method field, therefore primary signal of the present invention is also
Belong to the signal that Wavelet Denoising Method field can be processed.
In addition, " small-signal " implication mentioned in the present invention is to determine, " Detection of Weak Signals " in the art belongs to
Common technology term, it is meant that " measurement of small-signal in being submerged in ambient noise ", i.e., small-signal can be noise
Than relatively low, so that the signal being easily submerged in ambient noise.Therefore in specific practical application, judge original be whether
Small-signal can be contrasted primary signal with ambient noise, be judged according to concrete actual conditions.
Step 2, extreme value absolute value and threshold that each is used in intrinsic mode function of reconstruct between each two zero crossing
Value relatively and do cancelling noise process；The process of step 2 is properly termed as EEMD interval denoisings (EEMD-IT).
Step 3, the sampling location by changing first intrinsic mode function at random, obtain primary signal different band and make an uproar
Form, does respectively the process of step 2, the signal after being reconstructed to every kind of band form of making an uproar；
It should be noted that first intrinsic mode function arbitrarily takes, and sampling location is also by random manner
Select.
Step 4, the signal to obtaining after the reconstruct are averaged, and obtain the signal after denoising.
It should be noted that the present invention is being related to calculate and during formula, described " signal " refers to that signal amplitude (or claims
For signal amplitude).For example in step 4 " signal to obtaining after reconstruct is averaged " means the signal width to obtaining after reconstruct
Value is averaged.
Specific embodiment two：
From unlike specific embodiment one, step one, detailed process is,
Step one by one, obtain primary signal.
In an experiment can by setting up signal model come simulating actual conditions in various complicated signals constitute.
Specifically, by the research to typical small-signal, with multi-signal combination block signal as prototype, signal
Model.By taking formula (1.1) as an example.
Those skilled in that art it should be clear that the block signal in formula (1.1) is only the reference signal of artificial setting, its
In signal can also have a variety of forms, as the case may be can be by trigonometric function therein, parameter or span
Make and change.
Step one two, on the basis of signal, add signal to noise ratio be 5dB white Gaussian noise, produce small-signal.According to
Concrete condition is different, it is also possible to signal to noise ratio is made according to actual conditions and is changed.
Step one three, EEMD process is carried out to small-signal, obtain N number of intrinsic mode function；Because noise decomposes to EMD
As a result affect very big, can produce the phenomenon of modal overlap, therefore carry out to signal EEMD (Ensemble Empirical again
Mode Decomposition, gather empirical mode decomposition) process, so as to alleviate modal overlap, the denoising for being conducive to signal is imitated
Fruit improves.
Obtain to be calculated the energy of each IMF after N number of intrinsic mode function, decompose with white Gaussian noise
To each IMF energy contrasted respectively, in one embodiment, find before M IMF energy it is almost suitable.So as to
Go out conclusion, the front M IMF that signals with noise is obtained after decomposing is mainly noise energy, then be letter by the energy in rear N-M IMF
Number leading, therefore it is defined as the IMF for reconstruct.
Specific embodiment three：
From unlike specific embodiment one or two, step one two is specially：
1) population mean number of times M is set, i.e., repeatedly adds the number of times of white noise, and set the white noise amplitude of addition,
Make i=1；
2) to initial signal xiWhite noise signal n is added in (t)iT (), constitutes new signal x to be decomposedi(t), can represent
Into xi(t)=x (t)+ni(t), i=1,2 ... M, wherein, xiT () is the signal of i-th added white noise；niT () is i ＆ lt
The white noise of addition；
Step one three is specially：
3) signal to be decomposed in second, x are decomposed using EEMD algorithmsiT () is IMF sums, its computing formula isWherein, s is the quantity of IMF components；ri,sT () is survival function, embody averagely becoming for signal
Gesture, but for the extraction of signal time-frequency distributions has no practical significance, can be ignored, ci,sT () is IMF point of signal decomposition
Amount, (ci,1,ci,2,…,ci,s) including the IMF components of different range frequency range from high to low；
4) repeat second and three to M time, then each EEMD decomposition adds the white noise that given amplitude is not quite similar
The set entered to IMF components obtained in initial signal can be expressed as：{c1,s(t)},{c2,s(t)},…,{cM,s(t) }, s=1,
2,…,S；
5) the IMF ensemble averages value obtained in the 4th is calculated as final value, then the IMF that signal Jing EEMD decomposition is obtained is：
Specific embodiment four：
From unlike specific embodiment two, two detailed process is the step of present embodiment：
Step 2 one：On the basis of step one, first IMF that can be used to reconstruct is chosen, determine its all zero crossing
zjPosition, by the position between two neighboring zero crossingIt is defined as gap；
Step 2 two, the threshold value adaptable with it is chosen according to each intrinsic mode function, specifically by testing wide
Adopted threshold valueWith Bayes's threshold valueBetween select the more preferable threshold value of performance, in formulaIt is white Gaussian noise
Variance,It is the variance of signal, noise criteria is poorObtained by the Robust filter device based on component intermediate value, especially by formulaCalculated；Wherein | ci| it is the signal amplitude absolute value of i-th zero crossing, median
It is median function.
Step 2 three, by the absolute value of the maximum value or minimum value in each gap | h(i) max| with obtain in step 2 two
Threshold value compare, comparison procedure pass through soft-threshold algorithmOr
Hard threshold algorithmRealize, whereinRepresent and use thresholding algorithm anterior diastema
In extreme value,Represent and use thresholding algorithm post gapIn extreme value.
By taking hard -threshold process as an example, when ratio of extreme values thresholding is big, then can illustrate that the energy in the gap is that signal is dominated
, all values are all remained in gap；When extreme value is less than thresholding, then illustrate that the energy in the gap is noise energy,
All values all zero setting in gap.When being processed with soft-threshold, principle is close.
Specific embodiment five：
From unlike specific embodiment 1, present embodiment and the step of three detailed processes be：
Step 3 one, on the basis of step one EEMD decomposition is done to original signal, N number of intrinsic mode function is obtained, after order
N-1 IMF is constant, is defined asN-1 IMF extreme value adds and for x after i.e.p(t)；
Step 3 two, the principle for using for reference translational invariant shrinkage denoising, equally spaced change the sample bits of first IMF
Put and obtain different from originalReconstruct the bands different from primary signal to make an uproar form, obtain
ArriveUsing the signals with noise x for newly obtainingaT () does EEMD decomposition；Wherein ALTER is for realization etc.
Interval changes the function of sampling location.Wherein ALTER is for realizing changing the function of sampling location, h at equal intervals(1)T () is the
The extreme value of 1 intrinsic mode function,It is through changing sampling location at equal intervals by the extreme value of the 1st intrinsic mode function
Value afterwards.
Step 3 three, to xaThe IMF that obtains does the denoising of EEMD gaps t () decomposes after, obtains original tape and makes an uproar letter
Number denoising formThree or two iteration of repeat step K-1 time, so as to obtain K denoising form of original signal
Finally, in step 4, signal after the denoising of gained is averaged
Claims (5)
1. a kind of based on wavelet theory and the denoising method of the small-signal of EEMD, it is characterised in that：The Weak Signal Processing
Method is realized by following steps：
Step one, acquisition primary signal simultaneously carry out EEMD decomposition to it, intrinsic mode function set are obtained, by the eigen mode
The energy relationship of each intrinsic mode function determines the intrinsic mode function for reconstruct in state function set, and wherein EEMD is collection
Close empirical mode decomposition；
Step 2, extreme value absolute value and threshold value ratio that each is used in intrinsic mode function of reconstruct between each two zero crossing
Relatively and do cancelling noise process；
Step 3, the sampling location by changing first intrinsic mode function at random, obtain primary signal different band and make an uproar form,
Do the process of step 2, the signal after being reconstructed to every kind of band form of making an uproar respectively；
Step 4, the signal to obtaining after the reconstruct are averaged, and obtain the signal after denoising.
2. a kind of based on wavelet theory and the denoising method of the small-signal of EEMD according to claim 1, it is characterised in that
Step one detailed process is：
Step one by one, obtain primary signal；
Step one two, on the basis of the primary signal, add signal to noise ratio be 5dB white Gaussian noise, obtain small-signal；
Step one three, EEMD process is carried out to the small-signal, obtain at least one intrinsic mode function；
Step one four, according to the energy relationship obtain for reconstruct intrinsic mode function.
3. a kind of based on wavelet theory and the denoising method of the small-signal of EEMD according to claim 1, it is characterised in that
The detailed process of step 2 is：
Step 2 one：On the basis of step one, first intrinsic mode function for being used for reconstruct is chosen, determine its all zero passage
Point zjPosition, by the position between j-th and+1 zero crossing of jthGap is defined as, whereinRepresent
The position of j-th zero crossing of i-th intrinsic mode function；
Step 2 two, the threshold value adaptable with it is chosen according to each intrinsic mode function, specifically by testing in broad sense threshold
ValueWith Bayes's threshold valueBetween select the more preferable threshold value of performance, in formulaIt is the side of white Gaussian noise
Difference,It is the variance of signal, noise criteria is poorObtained by the Robust filter device based on component intermediate value, especially by formulaCalculated；Wherein | ci| it is the signal amplitude absolute value of i-th zero crossing, median
It is median function.
Step 2 three, by the absolute value of the maximum value or minimum value in each gap | h(i) max| with the threshold obtained in step 2 two
Value is compared, and comparison procedure passes through soft-threshold algorithmOr hard threshold
Value-based algorithmRealize, whereinRepresent and use thresholding algorithm anterior diastemaIn
Extreme value,Represent and use thresholding algorithm post gapIn extreme value.
4. a kind of according to claim 1,2 or 3 is based on wavelet theory and the denoising method of the small-signal of EEMD, and it is special
Levy is that the detailed process of step 3 is：
Step 3 one, on the basis of step one EEMD decomposition is done to original signal, N number of intrinsic mode function is obtained, N-1 after order
Intrinsic mode function is constant, is defined asxp(t) be rear N-1 intrinsic mode function extreme value plus and,
h(i)T () is the extreme value of i-th intrinsic mode function；
Step 3 two, the equally spaced sampling location of first intrinsic mode function of change obtain and original different intrinsic mode
Function, the procedural representation isReconstruct the bands different from primary signal to make an uproar form, obtain new
Signals with noiseUsing new signals with noise xaT () does EEMD decomposition, the eigen mode after being decomposed
State function；Wherein ALTER is for realizing changing the function of sampling location, h at equal intervals(1)T () is the 1st intrinsic mode function
Extreme value,It is the value by the extreme value of the 1st intrinsic mode function after changing sampling location at equal intervals；
Step 3 three, to xaT intrinsic mode function that () obtains after decomposing does the denoising of EEMD gaps, obtains original tape and makes an uproar
The denoising form of signalThree or two iteration of repeat step K-1 time, so as to obtain K denoising form of original signal
5. according to claim 3 a kind of based on wavelet theory and the denoising method of the small-signal of EEMD, its feature exists
In described to select the more preferable threshold value of performance between broad sense threshold value and Bayes's threshold value specifically, logical by experiment in step 2 two
The experimental result that experiment calculates respectively two kinds of threshold values is crossed, selects signal to noise ratio to improve big, and the little threshold value of root-mean-square error is used as property
Can more preferable threshold value.
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| CN114462458A (en) * | 2022-04-11 | 2022-05-10 | 自然资源部第一海洋研究所 | Ship underwater signal noise reduction and target enhancement method |
| CN115659128A (en) * | 2022-12-12 | 2023-01-31 | 浙江工业大学 | Signal noise reduction method based on ensemble empirical mode decomposition method and power spectrum |
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Cited By (4)
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| CN109580787A (en) * | 2018-12-08 | 2019-04-05 | 国网四川省电力公司广安供电公司 | The ultrasonic echo denoising method of for transformer bushing lead ultrasound detection |
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