CN105827221A - Denoising technology based on recombinant product function waveform smoothing - Google Patents

Abstract

The invention discloses a noise reduction technology based on the waveform smoothing of the re-integrated function, which is characterized in that the method comprises the following steps: 1) extraction of the instantaneous envelope and pure frequency modulation components; 2) construction of the integral function components; 3) product Identification of function noise characteristics; 4) Energy distribution analysis of noisy product functions; 5) Superposition and reorganization of noisy high-order product function components; 6) Outlier value detection and elimination of product functions; 7) Miniature peak elimination and regularization based on waveform smoothing deal with. The beneficial effect of the invention is that the method design is reasonable, the flow is clear and the noise elimination effect is good.

Description

Noise Removal Technology Based on Waveform Smoothing of Recombined Product Function

technical field

The present invention is based on the signal processing theory, because the high-order noise product function composed of the instantaneous envelope of the noise-polluted signal and the pure frequency modulation component has significant dual pulse characteristics, and the multi-level local mean value decomposition and the high-order noise product function component superposition are applied Recombination, outlier detection and waveform smoothing technology eliminates pulse components step by step and restores the real source signal, finally achieving the purpose of eliminating noise. This denoising technology has laid a theoretical foundation for solving the problems of weak signal detection and extraction, signal purification and purification, and noise interference elimination in many fields.

Background technique

In the integral function obtained by "pure" noise signal after local mean value decomposition processing, especially in the high-order integral function components, the impulse component occupies a dominant position and forms an obvious energy concentration, unlike the empirical mode decomposition for each "pure" The energy of the noise eigenmode function component is basically evenly distributed on the entire waveform. In addition, the energy distribution of the "pure" noise signal is obviously different from the logarithmic decay law obtained based on the empirical mode decomposition ^[1] , which is obviously caused by the principle difference of the two signal decomposition algorithms.

Although the first-order integral function component of the noisy observation signal is mainly composed of noise components, which is similar to the result of empirical mode decomposition ^[2] , there is also a relatively obvious concentration of pulse energy. This pulse energy concentration effect becomes more pronounced in higher order integrator functions. Therefore, in the context of denoising applications based on mean decomposition, the existing wavelet-based threshold denoising ^[3] or empirical mode decomposition-based denoising ^[4] based on the amplitude filtering principle is no longer applicable, and new research is needed. denoising principle or method.

Contents of the invention

The purpose of the present invention is to solve the above-mentioned problems, and develops a noise-removing technology based on the waveform smoothing of the re-integrated function.

Achieving the above-mentioned purpose The technical solution of the present invention is, a kind of denoising technique based on the waveform smoothing of re-product function, it is characterized in that, this method comprises the following steps:

1) Extraction of instantaneous envelope and pure FM component;

2) Construction of integral function components;

3) Identification of the noise characteristics of the product function;

4) Analysis of energy distribution with noise product function;

5) Superposition and recombination of noisy high-order integral function components;

6) Detection and elimination of product function outliers;

7) Miniature peak elimination and regularization processing based on waveform smoothing.

The extraction formula of the instantaneous envelope and the pure frequency modulation component is:

In the formula, h _ij (t) is the signal after removing the local mean value from the original noise-polluted signal x(t), and a _i (t) is the instantaneous envelope component extracted in the i-th step, also called the instantaneous amplitude. s _in (t) is the pure frequency modulation component extracted in the i step.

The construction formula of the integral function component is:

In the formula, P _i (t) is the integral function component extracted in the i-th step.

The identification principle of the noise characteristic of the integral function is:

where E _1n is the energy of the first integral function component P _1n extracted from the "pure" noise signal by local mean decomposition. E _i is the noise energy estimate of the i-th integral function component P _i extracted from the original noise-polluted signal x(t) through local mean decomposition. median(.) is the median estimate.

The energy distribution analysis formula of the noise product function is:

where C is a constant. ê _i is the noise energy estimate of the i-th order integral function component P _i . E _1n is the energy of the first order "pure" noise product function component P _1n . For a specific local mean decomposition process, the parameter and Mainly depends on the number of iterations of local mean decomposition.

The superposition and reorganization calculation formula of the noisy high-order integral function component is:

In the formula, i is the series of multi-level local mean decomposition. Superimpose the extracted high-order integral function components of the second order and above (including the residual component u _K ⁽ⁱ⁾ ) P ₂ ⁽ⁱ⁾ ,…,P _K ⁽ⁱ⁾ , u _K ⁽ⁱ⁾ to form Recombination signal P ⁽ⁱ⁾ .

The outlier detection and elimination formula of the product function is:

In the formula, M ₀ is the median value of the signal P ⁽ⁱ⁾ ={P ⁽ⁱ⁾ _j ,j=1,2,…,n}. E _bi and s _bi are double-weighted estimates of the mean and variance of P ⁽ⁱ⁾ , respectively. In the formula, M ₁ is the median value of the absolute deviation, that is, the median value of the absolute deviation of the data sample point P ⁽ⁱ⁾ _j relative to the signal median value M ₀ . The parameter c controls the offset distance of each data point relative to the data distribution center, usually 6<c<9. For the case of |u _j |>1.0, it is always set as u _j =0. The two statistics of E _bi and s _bi have strong anti-outlier performance, and can be applied after obtaining the estimates of E _bi and s _bi The inspection technique performs outlier detection. Assuming that P ⁽ⁱ⁾ _k is determined to be an outlier, the median value of the signal P ⁽ⁱ⁾ is used to replace the outlier to achieve outlier elimination.

The micro-peak elimination and regularization processing formula based on waveform smoothing is:

In the formula, it is assumed that t _j =j, t={t _j ,j=1,2,...,n}. A polynomial of degree m was used to fit the data. Solve the polynomial coefficients a ₀ , a ₁ ,…,am by the least square _criterion , and then realize the smoothing of the waveform with the noise product function component, the miniature peak elimination and the normalization processing.

Description of drawings

Fig. 1 is the implementation flow diagram of the denoising technology based on the re-product function waveform smoothing of the present invention;

Fig. 2 The signal denoising algorithm flow based on the waveform smoothing of the re-integrated product function;

Figure 3 Signal and its multi-level local mean value decomposition product function waveform

Figure 4 is the signal waveform of the high-order noise product function after superposition and recombination;

Figure 5 is the signal waveform of the product function after wild point detection and elimination;

Figure 6 is the denoised signal waveform after waveform smoothing and regularization;

Figure 7 Comparison of the denoising results of various denoising techniques for "AM-FM signal"

detailed description

The present invention is described in detail below in conjunction with the accompanying drawings. Fig. 1 is a schematic diagram of the implementation process of the denoising technology based on the waveform smoothing of the re-integrated product function according to the present invention. Extract the instantaneous envelope and pure frequency modulation components from the polluted signal, and based on the product function reconstruction, high-order noise product function component superposition and recombination, wild point detection and waveform smoothing, and regular processing technology, the pulse component is gradually eliminated and the real source is restored. signal, and finally achieve the purpose of noise removal.

This technical solution takes the signal polluted by white noise as an example to illustrate the signal denoising process. The basic denoising principle is: the noisy high-order integral function component signal has a significant dual pulse characteristic, and this duality is in the high-order It is universal in signals with noise product function components. After superposition and recombination, most of the dual pulse components are eliminated; for the remaining local pulse components, they are regarded as outliers that obviously deviate from the center of the overall data distribution, and the outlier detection and elimination are performed by statistical testing methods; Spikes are resolved by waveform smoothing and regularization.

Example 1

Denoising of "heavysine" signal polluted by white noise

Based on multi-level local mean decomposition, the instantaneous envelope a _i (t) and the pure frequency modulation component s _in (t) are extracted layer by layer to form integral function components , as shown in Figure 3. In the figure, s is the pure "heavysine" signal, x is the virtual observation signal polluted by white noise, and PF1-i, i=1, 2, 3, 4 are the four integral function components respectively. Several pairs of dual pulses are marked, such as "①+ and ①-", "②+ and ②-", and "③+ and ③-".

The noise characteristics of the four integral functions are identified, and the results show that the noise energy contained in the first-order integral function component PF1-x exceeds 85% of the energy of the first-order integral function component extracted from the "pure" noise signal, so It belongs to the complete noise component and can be directly removed; the other three components belong to (partial) noisy product function components and need to be retained and further denoised.

By superimposing and recombining the three noisy high-order integral function components obtained from the first-level local mean decomposition, the reorganized integral function components can be obtained Figure 4. The obvious pulse reduction effect can be seen, and the trend characteristics of the source signal s waveform change are also very clear.

For the superimposed and recombined high-order noisy product function components, apply Outlier detection and elimination are carried out by the inspection method. Figure 5. It can be seen that the remaining pulses in the signal are greatly reduced, and only some tiny pulses remain locally. In order to eliminate its adverse effect on signal denoising, it is necessary to further smooth and regularize the signal waveform.

Further smoothing, miniature peak elimination and normalization are performed on the waveform with noise product function components. Figure 6. Apparently, the local tiny pulse remaining in the signal - the spike component is further reduced to obtain a smoother signal waveform, and the effect of denoising is obvious.

So far, the first level of denoising processing is completed. If a higher level of denoising processing is required for the noisy observation x, just repeat the above processing steps. Of course, the number of levels of denoising processing should not be too high, generally no more than 3 levels, if the number of levels is too high, the denoising performance of the algorithm will be degraded. In addition, it is necessary to carefully set parameters such as distance control parameters, polynomial order, and number of smoothing cycles. It is ensured that the processed signal has enough extreme points, so that the next-level decomposition of the multi-level local mean decomposition can proceed smoothly.

Example 2

Denoising "AM-FM" signal polluted by white noise

The denoising results of different techniques on the "AM-FM" signal polluted by white noise are compared respectively. In addition to the denoising technology based on the waveform smoothing of the re-product function (ML-LMD-OS), the primary local mean decomposition-based denoising technology (LMD-H and LMD-S), and the wavelet-based translation-invariant threshold denoising technology (WT-H and WT-S) and improved empirical mode decomposition based denoising algorithms (EMD-H and EMD-S). Among them, "H" and "S" represent rigid and soft thresholding, respectively. SNR1 is the signal-to-noise ratio of the noisy observation, and _SNR2 is the signal-to-noise ratio of the denoised signal. The primary local mean decomposition base denoising algorithm here is to directly perform amplitude filtering and denoising on the integral function components. Figure 7.

It can be seen that the denoising technology based on the waveform smoothing of the re-integrated product function has achieved a better and stable denoising effect. In general, rigid thresholding (H) is generally better than soft thresholding (S) for the same denoising algorithm. The advantages of the denoising technology based on the smooth waveform of the re-integrated product function are reflected in the middle of the observed signal-to-noise ratio (-7dB<SNR ₁ <2dB). At this time, it performs best and shows better comprehensive denoising performance, especially suitable for High-precision denoising of signals with medium and high signal-to-noise ratios.

references

[1] FLANDRINP, RILLINGG, and GONCALVESP. EM Dequivalent filter banks, from interpretation to applications. In Hilbert-Huang Transform and Its Applications, HUANGNE and SHENS, Eds., 1sted. Singapore: World Scientific, 2005.

[2] KOPSINISY and MCLAUGHLINS. Development of EMD-Based Denoising Methods Inspired by Wavelet Thresholding. IEEE Transactions on Signal Processing, 2009, 57(4): 1351-1362.

[3] H.C. Huang and N. Cressie. Deterministic/stochastic wavelet decomposition for recovery of signal from noisy data. Technometrics, 2000, 42: 262-276.

[4] VIJAYABASKARV, RAJENDRANV, and PHILIPMM. EMD Based Denoising of Underwater Acoustic Signal. Journal of the Instrument Society of India, 2012, 42(2): 125-127.

The above-mentioned technical solutions only reflect the preferred technical solutions of the technical solutions of the present invention, and some changes that those skilled in the art may make to certain parts reflect the principles of the present invention and fall within the 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 formula_ijT () is the signal after removing local average from original noise polluted signal x (t), a_iT () is the instantaneous envelope component of the i-th step extraction, also referred to as instantaneous amplitude, s_inT () 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 formula_iT () 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 formula_1nFirst Product function component P of extraction from " pure " noise signal is decomposed for local average_1nEnergy,

E_iPollute signal x (t) for raw noise and decompose the i-th Product function component P of extraction through local average_iEstimation 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,

ê_iIt is the i-th rank Product function component P_iEstimation of noise energy,

E_1nIt is the first rank " pure " noise Product function component P_1nEnergy,

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 u_K ⁽ⁱ⁾) P₂ ⁽ⁱ⁾,…,P_K ⁽ⁱ⁾,u_K ⁽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},

E_biWith s_biIt 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 | u_j| > situation of 1.0, it is set to u the most without exception_j=0,

E_biWith s_biTwo statistics all have stronger anti-outlier performance, it is thus achieved that E_biWith s_biEstimation 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 t_j=j, t={t_j, 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,…,a_m, and then realize the waveform smoothing processing of signal.