CN100592667C - Wavelet noise-eliminating method for time frequency compactly supported signal - Google Patents

Abstract

This invention relates to a method for eliminating noises with small waves for time frequency compactly supported signals, which regulates the central frequency and bandwidth of the mother small wavebased on the band property of the Gauss small wave to quickly match the central frequency of signals containing noises with the band width to eliminate the Gauss white noise in the signal effectivelywhich is particularly suitable for testing weak signals. This invention also provides an example for processing pulse supersonic signals with this method.

Description

The Wavelet noise-eliminating method of time frequency compactly supported signal

Technical field:

The present invention relates to a kind of time frequency compactly supported or approximate compactly supported signal denoising method, utilize the frequency bandwidth characteristics of small echo,, can tightly prop up or be similar to the tight signal that props up to time-frequency domain and carry out denoising effectively by centre frequency and the bandwidth of adjusting its female small echo based on wavelet technique.This method is applicable to Detection of weak, for white Gaussian noise good denoising effect is arranged, and in addition, for random noise and multiplicative noise certain denoising effect is arranged also.This method realizes easy, quick.

Background technology:

Main application of the present invention is the pulse ultrasonic wave signal, thus in following elaboration, with this signal as setting forth object.

The impulse ultrasound echo is a kind of transient state, non-stationary time varying signal, and its time domain waveform and frequency spectrum all have approximate tight support.This characteristic and wavelet function are closely similar.This also makes small echo become one of the strongest instrument of analyzing the impulse ultrasound echo.Wavelet function can be regarded the band pass filter of quality factor such as a group as, if can design a kind of wavelet filter, make it have the spectrum distribution function that is complementary with ultrasonic signal, then can play the effect of filtering, useful composition in the stick signal, the noise in the filtered signal.

Utilizing the wavelet filter that is complementary with pulse ultrasonic wave that signal is handled is a new technology that just grew up in recent years.Some scholars have carried out some pilot study work of this respect both at home and abroad.Such as, people (Agostino Abbate such as Agostino Abbate, Jeff Koay, et al.Signal detection and noisesuppression using a wavelet transform signal processor:application to ultrasonic flawdetection, IEEE TUFF, Vol.44, No.1,1997, pp.14-26) propose directly to utilize the impulse ultrasound echo, utilize the pass band filter characteristic of wavelet transformation, obtain a series of band pass filters by generating function is carried out stretching as wavelet mother function, go to cover the frequency band that detects pulse ultrasonic wave with these filters, can reach reasonable filter effect.In their research, adopt 29 such filters to remove noises in the ultrasonic signal, this technology can handle-signal of 15dB, this is that general filtering technique is difficult to reach.But the used filter number of this method is more, calculates consuming timely, and does not also mention the specific algorithm that how to obtain so many filters in the document.Afterwards, people (Guang-Ming Zhang a such as domestic scholars Guang-Ming Zhang, Ceng-Gang Hou, Yu-Wen Wang, Shu-Yi Zhang, OptimalUltrasonics, Vol.39,2001, pp.13-17) propose to utilize optimal frequency and bandwidth ratio to design matched filter, this method can realize the processing of paired pulses ultrasonic echo with less filter, and filter effect is preferably also arranged, and the author has provided the optimal ratio algorithm that utilizes Gauss wavelet and have the pulsed ultrasonic wave of Gaussian envelope.But, know that by wavelet theory wavelet mother function is in case selected, its centre frequency and bandwidth are that certain restriction relation is arranged, promptly the ratio of wavelet center frequency and bandwidth is constant.So the selection of optimal ratio is subjected to certain restriction.Also have some scholars to analyze the feasibility study of ultrasonic wave as wavelet mother function.

Summary of the invention:

The objective of the invention is at the deficiencies in the prior art, a kind of denoising method that is applicable to time frequency compactly supported signal based on small echo is provided.Easy, the quick and good characteristics of denoising effect that this method has.

The present invention includes following concrete steps:

1) with time frequency compactly supported signal as primary signal, this signal as the reference signal, is determined the centre frequency and the bandwidth of its useful composition;

2) select to have the wavelet mother function of close frequency domain distribution according to the frequency-domain waveform of reference signal, and extract the centre frequency and the bandwidth of this wavelet mother function;

3) match reference signal and selected wavelet mother function, at first expand wavelet mother function, obtain the wavelet basis of different scale, make wavelet basis function consistent with the centre frequency of reference signal, obtain a wavelet scale value, under this yardstick, find the solution the bandwidth of this basic function, and mate with reference signal, promptly examine or check its bandwidth and whether contain the reference signal bandwidth; If contain, then choose this wavelet basis as band pass filter; If do not contain, then respectively get the wavelet basis of an adjacent yardstick again in the yardstick left and right sides of this wavelet basis function correspondence, the bandwidth of coming the match reference signal jointly with the original hase small echo, if coupling, then by three wavelet basiss jointly as the band pass filter group; If still do not match, then expand range scale again, respectively get a yardstick again in its both sides, reach five yardsticks, if coupling then constitutes the band pass filter group by five wavelet basiss; If still do not match, then by that analogy, till containing;

4) will adopt wavelet basis that said method obtains as the band pass filter group, will contain time frequency compactly supported signal projection one by one on each base of noise, synthetic then, just can obtain the signal after the denoising.

Description of drawings:

Fig. 1 is the flow chart of the invention process process

Fig. 2 is the time frequency distribution map of the impulse ultrasound signal used among the present invention and selected Gauss wavelet generating function

Fig. 3 is wavelet basis function and the echo signal frequency domain matching effect figure that tries to achieve

Fig. 4 for actual signal handle example (before handling signal to noise ratio be-0.4dB)

Fig. 5 for actual signal handle example (before handling noise be-18dB)

Fig. 6 is under the white Gaussian noise situation, this method performance curve

Fig. 7 is the treatment effect example of random noise

Fig. 8 is the treatment effect example of multiplicative noise

Embodiment:

Below in conjunction with drawings and Examples technical scheme of the present invention is further described.

1) denoising aim of the present invention

A desirable filter requires its amplitude-frequency characteristic to remain unchanged on the frequency range of being analyzed, and the amplitude perseverance is 1, and its phase-frequency characteristic is wanted the retention wire sexual intercourse.But to be physics can not realize for this.In the application of reality, Filter Design is often relevant with the purpose of handling.In general, a good filter should be able to remain with to greatest extent with on the basis of signal component, and remove noise most possibly.For the ultrasonic signal of being studied, requirement can keep interested frequency content as much as possible, and in the design of the basic enterprising line filter of following three principles: the centre frequency of (1) filter and the centre frequency of ultrasonic signal are consistent; (2) bandwidth of filter should cover hyperacoustic frequency band as much as possible; (3),, raise the efficiency so that save computing time with minimum wavelet transformation number of times.

2) centre frequency and bandwidth are determined

At first will be clear that the spectrum structure characteristic of noise in the signal of processing, selected female small echo and the processing signals.With the impulse ultrasound is example, and it is one is the modulated narrow-band impulse of centre frequency with the sonac centre frequency, and its frequency band is limited.Fig. 2 is the relatively lower ultrasonic signal of a noise level.Wherein, (a) be time domain waveform; (b) be its spectrum structure.As can be seen, it is a band-limited signal.And the noise in the signal generally is a broadband signal, and its spectrum distribution is on whole frequency band.By the characteristic of small echo as can be known, small echo the time, frequency domain all is tight.Among Fig. 2 (c) and (d) listed the time-frequency figure of Gauss wavelet respectively.When utilizing matched Wavelet to carry out filtering, the general Gauss wavelet of selecting is as female small echo of analyzing, this mainly is because it has similar frequency domain distribution to ultrasonic signal, and this point has also been verified in a large amount of test simultaneously, selects the female small echo of Gauss as analysis wavelet here.But, can find that from Fig. 2 (b) and contrast (d) although the two has similar frequency domain envelope, its centre frequency and bandwidth all do not match, so can not be directly with its filter as signal processing.By processing that female small echo is stretched, change the frequency domain distribution of small echo, thereby make small echo have identical centre frequency with the ultrasonic signal of detection as filter, and can form one group of band pass filter by the wavelet basis of different yardsticks, make its frequency band can cover the whole ultrasonic signal.

If

Be a wavelet mother function, its centre frequency w then ₀Can obtain by following formula with bandwidth deltaf w:

${\mathrm{<figure-callout\; id="0"\; label="w"\; filenames="C2006100405400009H2.png,C2006100405400010H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_0=\frac{{\&Integral;}_{-\&infin;}^{\&infin;}w|\mathrm{\&psi;}\left(w\right){|}^2\mathrm{dw}}{{\&Integral;}_{-\&infin;}^{\&infin;}|\mathrm{\&psi;}\left(w\right){|}^2\mathrm{dw}}---\left(1\right)$

$\mathrm{\&Delta;w}=(\frac{{\&Integral;}_{-\&infin;}^{\&infin;}(w-w_0{)}^2|\mathrm{\&psi;}\left(w\right){|}^2\mathrm{dw}}{{\&Integral;}_{-\&infin;}^{\&infin;}|\mathrm{\&psi;}\left(w\right){|}^2\mathrm{dw}}{)}^{\frac{1}{2}}---\left(2\right)$

In the formula, ψ (w) is

Fourier transform; W=2 π f is an angular frequency.

Then can define a frequency window: [w ₀-Δ w/2, w ₀+ Δ w/2].

If it is right

A stretches by yardstick, carries out translation by time shift b again, then can obtain wavelet basis function:

Its Fourier transform is:

${\mathrm{\&psi;}}_{a,b}\left(w\right)=\sqrt{a}{e}^{-\mathrm{jwb}}\mathrm{\&psi;}\left(\mathrm{aw}\right)---\left(4\right)$

Then the frequency window of wavelet basis function correspondence becomes: $\&lsqb;\frac{w_0}{a}-\frac{\mathrm{\&Delta;w}}{2a},\frac{w_0}{a}+\frac{\mathrm{\&Delta;w}}{2a}\&rsqb;.$

Can be by the actual measurement ultrasonic signal be carried out fast fourier transform and obtain if detect hyperacoustic frequency domain distribution, and its centre frequency and bandwidth are respectively w _U0With Δ w _u, if the centre frequency of wavelet basis function and ultrasonic signal is complementary, will suitablely choose the flexible yardstick of small echo, obtain the yardstick of small echo by following formula:

a ₀＝w ₀/w _u0 (5)

At this moment, the frequency domain bandwidth of small echo correspondence becomes Δ w/a ₀Be calculated as follows the bandwidth ratio

$r=\frac{\frac{\mathrm{\&Delta;w}}{a_0}}{{\mathrm{\&Delta;w}}_u}---\left(6\right)$

If r 〉=1 illustrates that then centre frequency is mated mutually on selected yardstick, and the bandwidth of small echo also can cover the frequency band of ultrasonic signal, at this moment, only needs wavelet transformation just can reach the purpose of effective filtering.If r＜1 illustrates that then selected small echo can not cover the effective bandwidth of ultrasonic signal on this yardstick, this moment can be at yardstick a ₀Near select two adjacent yardstick a again _0-1And a ₀₊₁, compare with the bandwidth of three filters and the bandwidth of ultrasonic signal, if following formula is met, illustrate that then three wavelet transformations are just passable.If following formula still can not satisfy, then repeat above-mentioned steps, meet the demands up to bandwidth.

3) noise reduction l-G simulation test and analysis

In order to verify the effect of top filtering method, carried out l-G simulation test.Test is to carry out on the composite signal.Composite signal is superposeed by ultrasonic signal, and the white Gaussian noise of different magnitudes forms.Wherein, ultrasonic wave is to be produced by the impulse ultrasound of 5MHz probe, in the test with signal to noise ratio (snr) as measurement index, wherein SNR is that formula below adopting calculates:

$\mathrm{SNR}=10\log (\underset{i=1}{\overset{N_s}{\mathrm{\&Sigma;}}}\left(\frac{s_i^2}{N_s}\right)/\underset{i=1}{\overset{N_n}{\mathrm{\&Sigma;}}}\left(\frac{n_i^2}{N_n}\right))---\left(7\right)$

In the formula, s _iIt is the amplitude of ultrasonic signal; N _sBe counting of the ultrasonic signal analyzed; n _iIt is the amplitude of noise signal; N _nBe counting of the noise signal analyzed.

In order to determine required wavelet transform dimension and number of filter, calculate yardstick a by top method ₀≈ 7, and under this yardstick, the frequency band of Gauss wavelet can cover the frequency band of whole ultrasonic ripple fully, as shown in Figure 3, so, only need a filter just passable.

Find in the test that this method can reach good filter effect, particularly also has the ability of good differentiation signal and noise for the situation of low signal-to-noise ratio.Fig. 4 and Fig. 5 have listed the filter effect figure under two kinds of low signal-to-noise ratios.Wherein, the signal to noise ratio of primary signal is-0.4dB among Fig. 4, and the amplitude of the amplitude of noise and signal on same magnitude, is difficult to distinguish ultrasonic echo substantially from signals and associated noises (a) at this moment, can find out echo-signal significantly after handling.Signal to noise ratio is-18dB among Fig. 5, and this moment, the amplitude of noise will be much larger than the amplitude of signal, and almost do not see that echo-signal is arranged this moment from signals and associated noises (a), but in this way after the filtering, also can accomplish effective differentiation.In order to weigh its filter capacity when the different signal to noise ratio, the signal to noise ratio change curve before and after handling of having drawn among Fig. 6, each point among the figure are all by on average obtaining behind 100 sample statistics.

As can be seen from Figure 6, this filtering method is in the signal to noise ratio scope of being analyzed, and signal to noise ratio all is significantly improved.This method biggest advantage is that amount of calculation is little, saves time very much.

Fig. 7 is listed as the denoising effect of this method to random noise.Fig. 8 has listed in this way the denoising effect to multiplicative noise.Therefrom as can be seen, this method also has certain denoising effect to these two kinds of noises, but the stability of its denoising effect and performance is not so good as the effective of white Gaussian noise.

Claims (1)

1, a kind of Wavelet noise-eliminating method of time frequency compactly supported signal is characterized in that comprising following concrete steps:

1) with time frequency compactly supported signal as primary signal, this signal as the reference signal, is determined the centre frequency and the bandwidth of its useful composition;

2) select to have the wavelet mother function of close frequency domain distribution according to the frequency-domain waveform of reference signal, and extract the centre frequency and the bandwidth of this wavelet mother function;

3) match reference signal and selected wavelet mother function, at first expand wavelet mother function, obtain the wavelet basis of different scale, make wavelet basis function consistent with the centre frequency of reference signal, obtain a wavelet scale value, under this yardstick, find the solution the bandwidth of this basic function, and mate with reference signal, promptly examine or check its bandwidth and whether contain the reference signal bandwidth; If contain, then choose this wavelet basis as band pass filter; If do not contain, then respectively get the wavelet basis of an adjacent yardstick again in the yardstick left and right sides of this wavelet basis function correspondence, the bandwidth of coming the match reference signal jointly with the original hase small echo, if coupling, then by three wavelet basiss jointly as the band pass filter group; If still do not match, then expand range scale again, respectively get a yardstick again in its both sides, reach five yardsticks, if coupling then constitutes the band pass filter group by five wavelet basiss; If still do not match, then by that analogy, till containing;

4) will adopt wavelet basis that said method obtains as the band pass filter group, will contain time frequency compactly supported signal projection one by one on each base of noise, synthetic then, just can obtain the signal after the denoising.

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