CN106897663A - Principal component analysis improves the ultrasonic wave noise-eliminating method of wavelet algorithm - Google Patents

Abstract

Field is extracted the present invention relates to information de-noising, specifically disclose the ultrasonic wave noise-eliminating method that a kind of principal component analysis improves wavelet algorithm, including with empirical mode decomposition algorithm will gather ultrasonic signal X (t) as decomposed signal, resolve into several IMF components；The de-noising threshold value of each IMF component is determined according to wavelet threshold algorithms；The useful signal energy of de-noising threshold calculations each the IMF component according to each IMF component；Useful signal energy according to each IMF component, arrives greatly small according to contribution rate, it is determined that preceding S component is principal component, and then obtains PCA components；Each PCA component is added the IMF components for obtaining de-noising；IMF components after de-noising merge and obtains the steps such as de-noising ultrasonic signal.The present invention can extract purer de-noising ultrasonic signal.The signal to noise ratio of de-noising ultrasonic signal is improve, the reduction degree of de-noising ultrasonic signal is improved.

Description

Principal component analysis improves the ultrasonic wave noise-eliminating method of wavelet algorithm

Technical field

Field is extracted the present invention relates to information de-noising, the ultrasonic wave that particularly a kind of principal component analysis improves wavelet algorithm disappears Method for de-noising.

Background technology

During the ultrasonic signal that noise in ultrasonic wave is eliminated and restored needs in noise circumstance is signal transacting Classical problem；Many solutions, such as wavelet noise, medium filtering etc. have been proposed for this problem.Small echo disappears Make an uproar and algorithm blends (DEL) to empirical mode decomposition (empirical mode decomposition, EMD) is conventional in recent years One of method, but but there is apparent defect in DEL algorithms, by the ultrasonic wave noise cancellation signal variance yields obtained after denoising It is larger with ultrasonic wave purified signal variance yields difference so that noise cancellation signal is larger with purified signal characteristic difference, and signal to noise ratio compared with It is low.

The content of the invention

Present invention seek to address that the problem that signal to noise ratio present in existing method is relatively low, signal characteristic difference is larger, proposes A kind of ultrasonic wave noise-eliminating method that wavelet algorithm is improved based on principal component analysis.

The Principal Component Analysis Algorithm for wherein using is first to be decomposed ultrasonic signal, then extracts the spy of each component The ratio between value indicative, characteristic value are the contribution rates of each component, and the contribution rate then according to these components is chosen, due to contribution rate It is relevant information content to be carried with component signal --- contribution rate is bigger, and correlation is stronger, and information content is bigger；Therefore when extraction is decomposed The small noise signal of correlation can be eliminated, retention relationship is big and the useful signal that contains much information, so as to reach more The purpose of accurate de-noising, and then improve ultrasonic wave noise cancellation signal and the larger defect of ultrasonic wave purified signal different from those, and Due to more accurate noise-eliminating method so that it is more clean thorough that noise is eliminated, and disappears such that it is able to improve ultrasonic wave well The signal to noise ratio of noise cancellation signal.

The technical solution adopted by the present invention is to achieve these goals：Principal component analysis improves the ultrasonic wave of wavelet algorithm Noise-eliminating method, comprises the following steps：

S1, with empirical mode decomposition algorithm will gather ultrasonic signal X (t) as decomposed signal, resolve into several IMF components.

S2, the de-noising threshold value of each IMF component is determined according to wavelet threshold algorithms.

S3, the useful signal energy of de-noising threshold calculations each the IMF component according to each IMF component.

S4, the useful signal energy according to each IMF component arrives greatly small according to contribution rate, it is determined that based on preceding S component into Point, and then obtain PCA components.

S5, each PCA component is added the IMF components for obtaining de-noising.

S6, the IMF components after de-noising merge obtains de-noising ultrasonic signal, and the de-noising ultrasonic signal is represented For：

WhereinIt is the IMF components of de-noising, X^dT () is de-noising ultrasonic signal, n is represented and obtained by after EMD decomposition N-th component.

According to such scheme, further illustrating the process that decomposed signal is resolved into several IMF components is：

Ultrasonic signal is X (t) as decomposed signal by S11, constructs the coenvelope line X of decomposed signal_up(t) and decompose letter Number lower envelope line X_downT (), then calculates the average line H of upper and lower envelope₁(t)=(X_up(t)+X_down(t))/2。

S12 calculates X (t) and H₁The difference of (t), m₁(t)=X (t)-H₁(t), m₁T () is envelope difference.

S13 judges m₁Whether t () meet the property of intrinsic mode functions component, by m if meeting₁T () is used as first IMF components k₁(t), if be unsatisfactory for, by m₁T () repeats to process above, until obtaining first as new decomposed signal IMF components k₁T (), then calculates remainder r₁(t)=X (t)-k₁(t)。

S14 judges first remainder r₁Whether t () meet the characteristic of monotonic function, by r if being unsatisfactory for₁T () is used as new Decomposed signal, repeat more than process, second IMF components k is obtained again₂(t) and second remainder r₂(t), until being expired N-th remainder r of sufficient monotonic function characteristic_nT (), terminates to decompose.

In such scheme, the computing formula of the de-noising threshold value isy_niFor wavelet coefficient square, T_{n_rigrsure}It is de-noising threshold value, σ represents noise variance.

Further, the useful signal energy method for determination of amount of the IMF components is：

S31 carries out the extraction of detailed information to every layer of IMF component：

k'_nI () is the new IMF components by being obtained after detail extraction, k_nI () represents that the absolute value of IMF signal amplitudes is big In the component of threshold value, [k_n(i)] represent IMF component of signal amplitudes absolute value.

S32 calculates the noise energy of IMF components as follows： W_nIt is noise energy；

S33 further calculates useful signal energy：

W'_nIt is useful signal energy.

S described in step S4 is determined by the ratio of useful ultrasonic energy signal and raw ultrasound signals energy.It is useful The ratio of ultrasonic energy signal and raw ultrasound signals energy is：

W_n' represent useful signal energy, ε (k_n(t))=∑_I=1k_n(i)²Represent collection Raw ultrasound signals actual energy.

For the basis that two problems that DEL is present, the present invention are blended in wavelet noise and empirical mode decomposition algorithm On the threshold function table of DEL algorithms is improved, main method is by DEL algorithms and principal component analysis (principal Component analysis, PCA) after algorithm merged, original threshold function table is substituted for Principal Component Analysis Algorithm, so De-noising is carried out by useful signal energy proportion afterwards, such that it is able to improve the effect of ultrasonic wave de-noising, is improved ultrasonic signal and is disappeared The performance made an uproar, has very important significance to ultrasonic signal de-noising tool.

In sum, by adopting the above-described technical solution, the beneficial effects of the invention are as follows：Improve de-noising ultrasonic wave letter Number signal to noise ratio, the reduction degree of de-noising ultrasonic signal is improved, so as to obtain purer and reduction degree ultrasound higher Ripple noise cancellation signal.

Brief description of the drawings

Fig. 1 is schematic flow sheet of the invention.

Specific embodiment

Embodiments of the invention are described in detail below, the example of the embodiment is shown in the drawings, wherein from start to finish Same or similar label is represented with same or like function.Embodiment below with reference to Description of Drawings is exemplary , it is only used for explaining the present invention, and be not considered as limiting the invention.

Referring to Fig. 1, the invention provides a kind of ultrasonic wave noise-eliminating method that wavelet algorithm is improved based on principal component analysis, bag Include following steps：

S1, the ultrasonic signal of input is X (t), as decomposed signal, constructs the coenvelope line X of primary signal_up(t) and The lower envelope line X of primary signal_downT (), then calculates the average line of upper and lower envelope：

H₁(t)=(X_up(t)+X_down(t))/2

Then X (t) and H is calculated₁T the difference of (), is denoted as m₁(t)：

m₁(t)=X (t)-H₁(t)

Then m is judged₁Whether t () meet intrinsic mode functions component (Intrinsic Mode Function, IMF) component Property, by m if meeting₁T () is used as first IMF components k₁(t), if be unsatisfactory for, by m₁T () is denoted as X (t) so Above formula is repeated afterwards, until obtaining first IMF components k₁(t)；Then remainder is calculated：

r₁(t)=X (t)-k₁(t)

Then judge whether this remainder meets the feature of monotonic function, by r if being unsatisfactory for₁T () divides as new Solution signal, repeats above step, and second IMF components k is obtained again₂(t) and second remainder r₂T (), repeats down always, N-th remainder r until being met monotonic function characteristic_n(t), leave it at that decomposition, can now obtain n IMF component, These components can be designated as k₁(t),k₂(t),k₃(t)……k_nT (), r is designated as by remainder_n(t), therefore, primary signal X (t) can It is denoted as：

S2, the threshold value selection of each IMF component is carried out according to fixed Stein unbiased esti-mators：

Wherein y_niFor wavelet coefficient square, σ represents noise variance.

S3, because every layer after EMD is decomposed of noise content is different, so threshold value is also different, noise energy is not yet Equally, but the noise characteristic of each IMF component after being decomposed due to EMD will not change, it is possible to a kind of identical side Method calculates the noise energy of every layer signal component with reference to different threshold values；Details is carried out to every layer of IMF signal according to threshold value The extraction of information：

Then according to extract detailed information can calculate every layer of IMF contained by noise energy：

It is possible thereby to calculate the energy of useful signal：

W'_n=∑_I=1k_n(i)²-∑_I=1[k_n(i)-k'_n(i)]²

Wherein k'_nI () is the new IMF components by being obtained after detail extraction, W_nIt is the energy of noise signal, W'_nIt is have With the energy of signal.

S4, after each IMF component determines by useful signal energy, then to carry out principal component to each IMF component true It is fixed, it is assumed that each IMF component is resolved into a data matrixCan be obtained by deformationWith corresponding characteristic vector MatrixAnd corresponding Component MatricesMay finally determine preceding S component according to contribution rate size in Component Matrices It is principal component；Can be expressed as after IMF component de-noisings：

M represents that each IMF has M rows by the matrix formed after conversion in formula.S is represented to be needed from each IMF Component Matrices The principal component component number to be extracted.

The noise being now deleted is：

The energy of raw ultrasound signals and the energy of institute's Noise are respectively：

N represents the component of signal total number that each IMF component is obtained when detail extraction is carried out by digital quantization.

Then the energy of effective ultrasonic signal can be expressed as：

The ratio of useful signal energy and original energy can now be obtained：

The useful ultrasonic signal and the energy meter of raw ultrasound signals now finally tried to achieve according to S3 steps calculate energy Amount ratio, then calculates the main content into composition according to this ratio：

The numerical value for only needing to calculate S can just extract preceding S useful principal component in each IMF component.Wherein Represent that each IMF component resolves into a data matrix,ForMathematic expectaion matrix,It is corresponding characteristic vector Matrix,PCA Component Matrices after being decomposed for each IMF,The data matrix after de-noising is represented,Expression is eliminated Noise data matrix,Represent original energy,Represent noise energy,Represent useful signal Energy, λ_iIt is data matrixCharacteristic value, ε (k_n(t))=∑_I=1k_n(i)²Represent the reality of the raw ultrasound signals of collection Border energy.

S5, the noise in each IMF component just can be filtered according to above procedure, in then obtaining each IMF component Useful signal：

WhereinIt is main PCA components,It is the IMF components of de-noising.

S6, de-noising ultrasonic signal is restored finally according to each de-noising IMF components obtained in S5：

X^dT () is the de-noising ultrasonic signal for finally giving.

It is as shown in table 1 according to the available contrast effect of above specific implementation step：

Table 1 respectively tests signal to noise ratio (SNR) data

Table 2 each experimental variance (D) deviation data

Can just be found out from two above form, improve the SNR empirical values of denoising algorithm than conventional denoising algorithm SNR empirical values it is bigger, improve denoising algorithm D deviations empirical value than the D deviation empirical values of conventional denoising algorithm It is smaller, it can be seen that the wavelet Based on Denoising Algorithm after improvement has preferably performance on Signal-to-Noise and signals revivification degree, because This proves that improved wavelet Based on Denoising Algorithm can usefully improve conventional denoising algorithm and make the reduction of noise cancellation signal signal to noise ratio and go back The relatively low defect of former degree.

In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show The description of example " or " some examples " etc. means to combine specific features, structure, material or spy that the embodiment or example are described Point is contained at least one embodiment of the invention or example.In this manual, to the schematic representation of above-mentioned term not Necessarily refer to identical embodiment or example.And, the specific features of description, structure, material or feature can be any One or more embodiments or example in combine in an appropriate manner.

Although an embodiment of the present invention has been shown and described, it will be understood by those skilled in the art that：Not Can these embodiments be carried out with various changes, modification, replacement and modification in the case of departing from principle of the invention and objective, this The scope of invention is limited by claim and its equivalent.

Claims (7)

1. principal component analysis improves the ultrasonic wave noise-eliminating method of wavelet algorithm, comprises the following steps：

S1, ultrasonic signal X (t) that will be gathered with empirical mode decomposition algorithm resolves into several IMF point as decomposed signal Amount；

S2, the de-noising threshold value of each IMF component is determined according to wavelet threshold algorithms；

S3, the useful signal energy of de-noising threshold calculations each the IMF component according to each IMF component；

S4, the useful signal energy according to each IMF component arrives greatly small according to contribution rate, it is determined that preceding S component is principal component, And then obtain PCA components；

S5, each PCA component is added the IMF components for obtaining de-noising；

S6, the IMF components after de-noising merge obtains de-noising ultrasonic signal.

2. principal component analysis improves the ultrasonic wave noise-eliminating method of wavelet algorithm according to claim 1, it is characterised in that：It is described It is by the process that decomposed signal resolves into several IMF components：

Ultrasonic signal is X (t) as decomposed signal by S11, constructs the coenvelope line X of decomposed signal_up(t) and decomposed signal Lower envelope line X_downT (), then calculates the average line H of upper and lower envelope₁(t)=(X_up(t)+X_down(t))/2：

S12 calculates X (t) and H₁The difference of (t), m₁(t)=X (t)-H₁(t), m₁T () is envelope difference；

S13 judges m₁Whether t () meet the property of intrinsic mode functions component, by m if meeting₁T () is used as first IMF points Amount k₁(t), if be unsatisfactory for, by m₁T () repeats to process above, until obtaining first IMF points as new decomposed signal Amount k₁T (), then calculates remainder r₁(t)=X (t)-k₁(t)；

S14 judges first remainder r₁Whether t () meet the characteristic of monotonic function, by r if being unsatisfactory for₁T () divides as new Solution signal, is repeated to process above, and second IMF components k is obtained again₂(t) and second remainder r₂(t), until being met list Adjust n-th remainder r of function characteristic_nT (), terminates to decompose.

3. principal component analysis improves the ultrasonic wave noise-eliminating method of wavelet algorithm according to claim 1, it is characterised in that：It is described The computing formula of de-noising threshold value isy_niFor wavelet coefficient square, T_{n_rigrsure}It is de-noising threshold value, σ is represented Noise variance.

4. principal component analysis improves the ultrasonic wave noise-eliminating method of wavelet algorithm according to claim 3, it is characterised in that：It is described The useful signal energy method for determination of amount of IMF components is：

S31 carries out the extraction of detailed information to every layer of IMF component：

$k_n^{\&prime;}\left(i\right)=\left\{\begin{array}{cc}{k}_n\left(i\right)& \&lsqb;k_n\left(i\right)\&rsqb;\&GreaterEqual;T_{n\_rigrsure}\\ 0& \&lsqb;k_n\left(i\right)\&rsqb;<T_{n\_rigrsure}\end{array}\right.$

k'_nI () is the new IMF components by being obtained after detail extraction, k_nI () represents that the absolute value of IMF signal amplitudes is more than threshold The component of value, [k_n(i)] represent that IMF signal amplitudes obtain absolute value.

S32 calculates the noise energy of IMF components as follows：W_nIt is Noise energy；

S33 further calculates useful signal energy：

W'_nIt is useful signal energy.

5. principal component analysis improves the ultrasonic wave noise-eliminating method of wavelet algorithm according to claim 1, it is characterised in that：Step S described in S4 is determined by the ratio of useful ultrasonic energy signal and raw ultrasound signals energy.

6. principal component analysis improves the ultrasonic wave noise-eliminating method of wavelet algorithm according to claim 5, it is characterised in that：It is described The ratio of useful ultrasonic energy signal and raw ultrasound signals energy is：

W_n' represent useful signal energy, ε (k_n(t))=∑_I=1k_n(i)²Represent the original of collection The actual energy of beginning ultrasonic signal.

7. principal component analysis improves the ultrasonic wave noise-eliminating method of wavelet algorithm according to claim 1, it is characterised in that：It is described De-noising ultrasonic signal is expressed as

$X^d\left(t\right)=\underset{m=1}{\overset{n}{\&Sigma;}}{\tilde{k}}_m\left(t\right)$

WhereinIt is the IMF components of de-noising, X^dT () is de-noising ultrasonic signal, n represents that each IMF component is carried carrying out details N-th component obtained by digital quantization when taking.