CN105827221A - Denoising technology based on recombinant product function waveform smoothing - Google Patents
Denoising technology based on recombinant product function waveform smoothing Download PDFInfo
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Abstract
The present invention discloses a denoising technology based on recombinant product function waveform smoothing. The invention is characterized in that the method comprises the steps of (1) the extraction of an instantaneous envelope and a pure frequency modulation component, (2) the construction of a product function component, (3) the identification of a product function noise characteristic, (4) band noise product function energy distribution analysis, (5) the superimposed recombination of band noise high order product function components, (6) product function outlier detection and elimination, and (7) micro spike elimination and smoothing processing based on waveform smoothing. The denoising technology has the advantages that the method design is rational, the process is clear, and the denoising effect is good.
Description
Technical field
The present invention is based on signal processing theory, the high-order band constituted due to instantaneous envelope and the pure frequency modulation component of noise polluted signal Product function of making an uproar has significant Dual pulse characteristic, apply multistage local average to decompose, Product function component superposition restructuring made an uproar by high-order band, wild point detects and waveform smoothing technique, eliminate pulse repetition step by step and recover real source signal, being finally reached the purpose eliminating noise.This noise cancellation technology is that the Testing of Feeble Signals related in the many fields of solution purifies with extraction, signal and the problem such as purification and noise jamming elimination has established theoretical basis.
Background technology
" pure " noise signal is in the Product function of local average resolution process gained, particularly high-order Product function component, pulse repetition occupies ascendancy, and forming obvious energy to concentrate, the energy of each unlike empirical mode decomposition " pure " noise intrinsic mode functions component is substantially uniform to be distributed on whole waveform.Additionally, the Energy distribution of " pure " noise signal is significantly different with the logarithmic decrement rule obtained based on empirical mode decomposition institute[1], it is clear that it is to be caused by the principle difference of two kinds of Algorithm of Signal Decomposition.
Although band is made an uproar, the first rank Product function component of observation signal is mainly made up of noise contribution, and this is similar with the result of empirical mode decomposition[2], but wherein there is also obvious pulse energy and concentrate.In high-order Product function, this pulse energy concentration effect becomes readily apparent from.Therefore, under the denoising application background decomposed based on average, existing wavelet basis threshold denoising[3]Or empirical mode decomposition base denoising[4]The amplitude filtering principle relied on is the most applicable, needs to study new denoising principle or method.
Summary of the invention
The invention aims to solve the problems referred to above, develop a kind of noise cancellation technology smooth based on restructuring Product function waveform.
Realize above-mentioned purpose the technical scheme is that, a kind of noise cancellation technology smooth based on restructuring Product function waveform, it is characterised in that the method comprises the steps:
1) instantaneous envelope and the extraction of pure frequency modulation component；
2) structure of Product function component；
3) identification of Product function noise characteristic；
4) band is made an uproar Product function Energy distribution analysis；
5) band make an uproar high-order Product function component superposition restructuring；
6) detection of Product function outlier and rejecting；
7) eliminate and regular process based on the miniature spike that waveform is smooth.
Described instantaneous envelope with the extraction-type of pure frequency modulation component is:
H in formulaijT () is the signal after removing local average from original noise polluted signal x (t), aiT () is the instantaneous envelope component of the i-th step extraction, also referred to as instantaneous amplitude.sinT () is the pure frequency modulation component of the i-th step extraction.
The structure formula of described Product function component is:
P in formulaiT () is the Product function component of the i-th step extraction.
The recognition principle of described Product function noise characteristic is:
E in formula1nFirst Product function component P of extraction from " pure " noise signal is decomposed for local average1nEnergy.EiPollute signal x (t) for raw noise and decompose the i-th Product function component P of extraction through local averageiEstimation of noise energy.Median (.) is mediant estimation.
Described band Product function Energy distribution analysis mode of making an uproar is:
In formula, C is constant.êiIt is the i-th rank Product function component PiEstimation of noise energy.E1nIt is the first rank " pure " noise Product function component P1nEnergy.For some specific local average catabolic process, parameterWithDepend primarily on the iterations that local average is decomposed.
Described band make an uproar high-order Product function component superposition restructuring calculating formula be:
In formula, i is the progression that multistage local average is decomposed.The second-order extracted and above high-order Product function component (are included residual component uK (i)) P2 (i),…,PK (i),uK (i)It is overlapped processing, forms recombination signal P(i)。
The detection of described Product function outlier with rejecting formula is:
M in formula0For signal P(i)={P(i) j, j=1,2 ..., the intermediate value of n}.EbiWith sbiIt is respectively P(i)Double kernel estimators values of average and variance.M in formula1For absolute deviation intermediate value, i.e. data sample point P(i) jRelative to signal intermediate value M0The intermediate value of absolute deviation.Parameter c controls each data point offset distance relative to data distribution center, generally takes 6 < c < 9.For | uj| > situation of 1.0, it is set to u the most without exceptionj=0。EbiWith sbiTwo statistics all have stronger anti-outlier performance, it is thus achieved that EbiWith sbiEstimation after can applyInspection technology carries out outlier detection.Assume P(i) kIt is judged as outlier, then uses signal P(i)Intermediate value replace this outlier to realize unruly-value rejecting.
The described miniature spike smooth based on waveform eliminates and with regular process formula is:
Formula sets tj=j, t={tj,j=1,2,…,n}.M order polynomial is used to carry out data matching.Multinomial coefficient a is solved by criterion of least squares0,a1,…,am, and then realize band and make an uproar that the waveform of Product function component is smooth, miniature spike eliminates and regularization.
Accompanying drawing explanation
Fig. 1 is the implementing procedure schematic diagram of the noise cancellation technology smooth based on restructuring Product function waveform of the present invention；
The Signal denoising algorithm flow process that Fig. 2 smooths based on restructuring Product function waveform；
The Product function waveform that Fig. 3 signal and multistage local average thereof are decomposed
Fig. 4 high-order band after superposition is recombinated is made an uproar the signal waveform of Product function；
The signal waveform of Fig. 5 Product function after the detection of open country point with rejecting；
Signal waveform after Fig. 6 denoising after waveform is smooth with regular process；
Fig. 7 multiple noise cancellation technology de-noising Comparative result to " AM/FM amplitude modulation/frequency modulation signal "
Detailed description of the invention
Below in conjunction with the accompanying drawings the present invention is specifically described, if Fig. 1 is the implementing procedure schematic diagram of the noise cancellation technology smooth based on restructuring Product function waveform of the present invention, as shown in the figure, the multistage local average of use in conjunction is decomposed and is extracted instantaneous envelope and pure frequency modulation component from by the signal of sound pollution, and make an uproar based on Product function reconstruct, high-order band that Product function component superposition restructuring, wild some detection be smooth with waveform, regular treatment technology, eliminate pulse repetition step by step and recover real source signal, being finally reached the purpose of noise remove.
The technical program is with process that the signal that polluted by white noise is that example illustrates signal noise silencing, its basic denoising principle is: the high-order Product function component signal that band is made an uproar has significant Dual pulse characteristic, and this duality has universality in Product function component signal made an uproar by the band of high-order.After superposition is recombinated, major part Dual pulse composition therein is eliminated；For remaining local pulse component, it is considered as deviating considerably from the outlier of conceptual data distribution center, carries out outlier detection by Statistical Identifying Method and reject；For micro-peeks remaining in signal, solve with regular process by waveform is smooth.
Embodiment 1
" heavysine " signal noise silencing polluted by white noise
Decompose based on multistage local average, successively extraction instantaneous envelope ai(t) and pure frequency modulation component sinT (), forms Product function component, such as Fig. 3.In figure, s is pure " heavysine " signal, and x is the virtual observation signal after being polluted by white noise, PF1-i, i=1, and 2,3,4 are respectively four Product function components.Wherein mark multipair Dual pulse, such as " 1.+with 1.-", " 2.+with 2.-" and " 3.+with 3.-".
The noise characteristic of four Product function is identified, result shows that the noise energy that the first rank Product function component PF1-x is comprised exceeds the 85% of the energy of the first rank Product function component extracted from " pure " noise signal, it is consequently belonging to complete noise component(s), can directly reject；Other three components belong to (part) band and make an uproar Product function component, need to retain and also carry out denoising further.
To first order local average decompose gained three bands make an uproar high-order Product function component be overlapped restructuring, can obtain recombinate Product function componentSuch as Fig. 4.It can be seen that obvious pulsecutting effect, and the trend feature of source signal s waveform change is also clear that.
The high-order band of superposition restructuring is made an uproar Product function component, applicationThe method of inspection carries out outlier detection and rejects.Such as Fig. 5.It will be seen that pulse remaining in signal is greatly cut down, only locally lying in some small pulse residuals.In order to eliminate its adverse effect to signal denoising, need further signal waveform to be made smooth and regular process.
The waveform of Product function component of making an uproar band further smooths, miniature spike eliminates and regularization.Such as Fig. 6.The small pulse in the local residual spike composition being clearly, there are in signal is cut down further, it is thus achieved that more smooth signal waveform, the good results are evident in de-noising.
So far, first order denoising completes.If band is made an uproar by needs, observation x carries out the denoising of higher level, repeats above process step.Certainly, the progression of denoising can not be the highest, is usually no more than 3 grades, the too high denoising performance that will deteriorate algorithm of progression.In addition, need meticulously to arrange the parameters such as distance controlling parameter, polynomial order and smooth cycle-index, total principle is: after should ensureing superposition restructuring, the outlier in signal obtains the smoothness that more sufficiently rejecting and waveform reach certain, signal after guarantee processes again has abundant extreme point so that the next stage that multistage local average is decomposed decomposes and can be smoothed out.
Embodiment 2
" AM/FM amplitude modulation/frequency modulation " signal noise silencing polluted by white noise
Compared for different technologies respectively and " AM/FM amplitude modulation/frequency modulation " signal polluted by white noise is carried out the result of denoising.In addition to the noise cancellation technology (ML-LMD-OS) smooth based on restructuring Product function waveform, also provide a comparison primary local average and decompose base noise-removed technology (LMD-H and LMD-S), wavelet basis translation invariant threshold denoising technology (WT-H and WT-S) and empirical mode decomposition base Denoising Algorithm (EMD-H and EMD-S) improved.Wherein, " H " and " S " represent that rigidity processes with compliance thresholdization respectively.SNR1 is that band is made an uproar observation signal to noise ratio, SNR2For denoised signal signal to noise ratio.Here primary local average decomposes base Denoising Algorithm, it is simply that directly Product function component is carried out amplitude filtering and noise reduction.Such as Fig. 7.
Preferably denoising effect is stablized it will be seen that obtain based on the noise cancellation technology that restructuring Product function waveform is smooth.In general, rigidity thresholdsization is used to process (H) for same Denoising Algorithm typically more preferable than the effect that compliance threshold change processes (S).Advantage based on the smooth noise cancellation technology of restructuring Product function waveform is embodied in the stage casing (-7dB < SNR of observation signal to noise ratio1< 2dB), now it is put up the best performance, and demonstrates the most comprehensive de-noising performance, the high accuracy de-noising of the signal being particularly suitable under middle and high state of signal-to-noise.
List of references
[1]FLANDRINP,RILLINGG,andGONCALVESP.EMDequivalentfilterbanks,frominterpretationtoapplications.InHilbert-HuangTransformandItsApplications,HUANGNEandSHENS,Eds.,1sted.Singapore:WorldScientific,2005.
[2]KOPSINISYandMCLAUGHLINS.DevelopmentofEMD-BasedDenoisingMethodsInspiredbyWaveletThresholding.IEEETransactionsonSignalProcessing,2009,57(4):1351-1362.
[3]H.C.HuangandN.Cressie.Deterministic/stochasticwaveletdecompositionforrecoveryofsignalfromnoisydata.Technometrics,2000,42:262-276.
[4]VIJAYABASKARV,RAJENDRANV,andPHILIPMM.EMDBasedDenoisingofUnderwaterAcousticSignal.JournaloftheInstrumentSocietyofIndia,2012,42(2):125-127.
Technique scheme only embodies the optimal technical scheme of technical solution of the present invention, and some variations that some of which part may be made by those skilled in the art all embody the principle of the present invention, within belonging to protection scope of the present invention.
Claims (8)
1. the noise cancellation technology smoothed based on restructuring Product function waveform, it is characterised in that the method comprises the steps:
1) instantaneous envelope and the extraction of pure frequency modulation component；
2) structure of Product function component；
3) identification of Product function noise characteristic；
4) band is made an uproar Product function Energy distribution analysis；
5) band make an uproar high-order Product function component superposition restructuring；
6) detection of Product function outlier and rejecting；
7) eliminate and regular process based on the miniature spike that waveform is smooth.
The noise cancellation technology smooth based on restructuring Product function waveform the most according to claim 1, it is characterised in that described instantaneous envelope with the extraction-type of pure frequency modulation component is:
H in formulaijT () is the signal after removing local average from original noise polluted signal x (t), aiT () is the instantaneous envelope component of the i-th step extraction, also referred to as instantaneous amplitude, sinT () is the pure frequency modulation component of the i-th step extraction.
The noise cancellation technology smooth based on restructuring Product function waveform the most according to claim 1, it is characterised in that the structure formula of described Product function component is:
P in formulaiT () is the Product function component of the i-th step extraction.
The noise cancellation technology smooth based on restructuring Product function waveform the most according to claim 1, it is characterised in that the recognition principle of described Product function noise characteristic is:
E in formula1nFirst Product function component P of extraction from " pure " noise signal is decomposed for local average1nEnergy,
EiPollute signal x (t) for raw noise and decompose the i-th Product function component P of extraction through local averageiEstimation of noise energy,
Median (.) is mediant estimation.
The noise cancellation technology smooth based on restructuring Product function waveform the most according to claim 1, it is characterised in that described band Product function Energy distribution analysis mode of making an uproar is:
In formula, C is constant,
êiIt is the i-th rank Product function component PiEstimation of noise energy,
E1nIt is the first rank " pure " noise Product function component P1nEnergy,
For some specific local average catabolic process, parameterWithDepend primarily on the iterations that local average is decomposed.
The noise cancellation technology smooth based on restructuring Product function waveform the most according to claim 1, it is characterised in that the make an uproar superposition restructuring calculating formula of high-order Product function component of described band is:
In formula, i is the progression that multistage local average is decomposed,
The second-order extracted and above high-order Product function component (are included residual component uK (i)) P2 (i),…,PK (i),uK (i)It is overlapped processing, forms recombination signal P(i)。
The noise cancellation technology smooth based on restructuring Product function waveform the most according to claim 1, it is characterised in that the detection of described Product function outlier with rejecting formula is:
M in formula0For signal P(i)={P(i) j, j=1,2 ..., the intermediate value of n},
EbiWith sbiIt is respectively P(i)Double kernel estimators values of average and variance,
M in formula1For absolute deviation intermediate value, i.e. data sample point P(i) jRelative to signal intermediate value M0The intermediate value of absolute deviation,
Parameter c controls each data point offset distance relative to data distribution center, generally takes 6 < c < 9,
For | uj| > situation of 1.0, it is set to u the most without exceptionj=0,
EbiWith sbiTwo statistics all have stronger anti-outlier performance, it is thus achieved that EbiWith sbiEstimation after can applyInspection technology carries out outlier detection,
Assume P(i) kIt is judged as outlier, then uses signal P(i)Intermediate value replace this outlier to realize unruly-value rejecting.
The noise cancellation technology smooth based on restructuring Product function waveform the most according to claim 1, it is characterised in that the described miniature spike smooth based on waveform eliminates and with regular process formula be:
Formula sets tj=j, t={tj, j=1,2 ..., n},
M order polynomial is used to carry out data matching,
Multinomial coefficient a is solved by criterion of least squares0,a1,…,am, and then realize the waveform smoothing processing of signal.
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| CN101822548A (en) * | 2010-03-19 | 2010-09-08 | 哈尔滨工业大学（威海） | Ultrasound signal de-noising method based on correlation analysis and empirical mode decomposition |
| US20120207325A1 (en) * | 2011-02-10 | 2012-08-16 | Dolby Laboratories Licensing Corporation | Multi-Channel Wind Noise Suppression System and Method |
| CN104182625A (en) * | 2014-08-15 | 2014-12-03 | 重庆邮电大学 | Electrocardiosignal denoising method based on morphology and EMD (empirical mode decomposition) wavelet threshold value |
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| CN101822548A (en) * | 2010-03-19 | 2010-09-08 | 哈尔滨工业大学（威海） | Ultrasound signal de-noising method based on correlation analysis and empirical mode decomposition |
| US20120207325A1 (en) * | 2011-02-10 | 2012-08-16 | Dolby Laboratories Licensing Corporation | Multi-Channel Wind Noise Suppression System and Method |
| CN104182625A (en) * | 2014-08-15 | 2014-12-03 | 重庆邮电大学 | Electrocardiosignal denoising method based on morphology and EMD (empirical mode decomposition) wavelet threshold value |
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| CN107045543A (en) * | 2017-03-02 | 2017-08-15 | 杭州变啦网络科技有限公司 | A kind of fat reducing data sharing method of application LPF algorithm |
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