CN104484557A - Multiple-frequency signal denoising method based on sparse autoregressive model modeling - Google Patents

Abstract

The invention discloses a multiple-frequency signal denoising method based on sparse autoregressive model modeling. The method includes on the basis of a sparse autoregressive model, creating an adaptive overcomplete sparse base of a multiple-frequency signal according to sampling values of the multiple-frequency signal; extracting multiple discontinuous rows from the adaptive overcomplete sparse base optionally to form a plurality of redundant dictionaries; acquiring sparse mapping coefficient vectors of vectors, corresponding to the redundant dictionaries, on the corresponding redundant dictionaries by a orthogonal matching pursuit algorithm; averaging the sparse mapping coefficient vectors and taking an average vector as a coefficient needing to be used during signal restoration; combining a denoising result of the original multiple-frequency signal with a denoising result of an inverted signal of the original multiple-frequency signal to acquire a denoised restored signal. The multiple-frequency signal denoising method has the advantages of low calculation complexity, good denoising effect, and stable denoising effect under the condition of processing of signals with different signal to noise ratios.

Description

A kind of multiple-frequency signal denoising method based on sparse autoregressive model modeling

Technical field

The present invention relates to a kind of signal antinoise method, especially relate to a kind of multiple-frequency signal denoising method based on sparse autoregressive model (AR) modeling.

Background technology

Now, the health examination for heavy construction is all generally by gathering architectural vibration signal, studies the health status of heavy construction by analyzing vibration signal.But, due to the impact of external environment and the limitation of collecting device, the vibration signal collected can be caused to contain noise, therefore first will carry out noise reduction process to the vibration signal collected.

At present, signal de-noising disposal route mainly contain Wavelet-denoising Method, least square Denoising Algorithm, based on EMD (EmpiricalMode Decomposition, empirical mode decomposition) threshold deniosing method, based on FFT (Fast Fourier Transform (FFT)) Method of Noise, medium filtering Method of Noise, sparse Method of Noise etc.In these noise-reduction methods above-mentioned, Wavelet-denoising Method is current the most frequently used denoising method, but in Wavelet Denoising Method process, the selection of threshold value can affect the quality of Wavelet Denoising Method result, and also there will be Gibbs phenomenon at signal discontinuity zone.In addition, there is common defect in these noise-reduction methods above-mentioned, and namely denoising effect is general, and can cause the instability of denoising effect when processing signals is different.

Summary of the invention

Technical matters to be solved by this invention is to provide a kind of multiple-frequency signal denoising method based on sparse autoregressive model modeling, and its computation complexity is low, and denoising effect is good, and stable denoising effect when process signal to noise ratio (S/N ratio) different signal.

The present invention solves the problems of the technologies described above adopted technical scheme: a kind of multiple-frequency signal denoising method based on sparse autoregressive model modeling, is characterized in that comprising the following steps:

1. pending multiple-frequency signal is expressed as in the form of vectors $\stackrel{\→}{x}={\left(\begin{array}{cccc}{x}_1& x_2& ...& x_n\end{array}\right)}^T,$ Wherein, (x ₁x ₂x _n) ^tfor (x ₁x ₂x _n) transposed vector, n represents the sampling number of multiple-frequency signal, n>=500, x ₁represent the 1st sampled value of multiple-frequency signal, x ₂represent the 2nd sampled value of multiple-frequency signal, x _nrepresent the n-th sampled value of multiple-frequency signal;

2. based on sparse autoregressive model, structure self-adaptation cross complete sparse base, be designated as Z, $Z=\left(\begin{array}{cccc}{x}_1& x_2& ...& x_p\\ x_2& x_3& ...& x_{p+1}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{n-p}& x_{n-p+1}& ...& x_{n-1}\end{array}\right),$ Then construct vector corresponding to Z according to Z, be designated as ${\stackrel{\→}{b}}_Z=\left(\begin{array}{c}{x}_{p+1}\\ x_{p+2}\\ .\\ .\\ .\\ x_n\end{array}\right),$ Make j represent calculation times again, and make the initial value of j be 1, wherein, the dimension of Z is (n-p) × p, dimension be the exponent number that (n-p) × 1, p represents sparse autoregressive model, x ₃, x _p, x _p+1, x _p+2, x _n-p, x _n-p+1and x _n-1corresponding the 3rd sampled value, a p sampled value, a p+1 sampled value, a p+2 sampled value, the individual sampled value of the n-th-p, the individual sampled value of the n-th-p+1 and (n-1)th sampled value representing multiple-frequency signal, 1≤j≤N, N represents the calculating total degree of setting;

3. in jth time computation process, from Z, randomly draw that discontinuous m is capable forms a jth redundant dictionary according to the order of sequence, be designated as Φ ^j, ${\mathrm{\&Phi;}}^j=\left(\begin{array}{cccc}{x}_{i1}& x_{i1+1}& ...& x_{i1+p-1}\\ x_{i2}& x_{i2+1}& ...& x_{i2+p-1}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{\mathrm{im}}& x_{\mathrm{im}+1}& ...& x_{\mathrm{im}+p-1}\end{array}\right),$ Then according to Φ ^jstructure Φ ^jcorresponding vector, is designated as ${\stackrel{\&RightArrow;}{b}}_{{\mathrm{\&Phi;}}^j}=\left(\begin{array}{c}{x}_{i1+p}\\ x_{i2+p}\\ .\\ .\\ .\\ x_{\mathrm{im}+p}\end{array}\right),$ Wherein, 15<m<p, Φ ^jdimension be m × p, dimension be m × 1, i1, i2, im correspondence represent the m that randomly draws out from Z capable in the 1st row, the 2nd row, the capable line order number in Z of m, and 1≤i1<i2< ... <im≤n-p, x _i1, x _i1+1, x _i1+p-1, x _i2, x _i2+1, x _i2+p-1, x _im, x _im+1, x _im+p-1, x _i1+p, x _i2+p, x _im+pcorresponding represent multiple-frequency signal the i-th 1 sampled values, the i-th 1+1 sampled value, the i-th 1+p-1 sampled value, the i-th 2 sampled values, the i-th 2+1 sampled value, the i-th 2+p-1 sampled value, the i-th m sampled value, the i-th m+1 sampled value, the i-th m+p-1 sampled value, the i-th 1+p sampled value, the i-th 2+p sampled value, the i-th m+p sampled value;

4. adopt orthogonal matching pursuit algorithm, calculate at Φ ^jon sparse mapping coefficient vector, be designated as wherein, dimension be p × 1;

5. judge whether j=N sets up, if set up, then directly perform step 6., if be false, then make j=j+1, then return step and 3. continue to perform, wherein, "=" in j=j+1 is assignment;

6. the N number of sparse mapping coefficient vector obtained is done sums on average, obtain average vector, be designated as will as the sparse mapping coefficient vector needed for signal restoring, wherein, represent the 1st redundant dictionary Φ ¹corresponding vector at the 1st redundant dictionary Φ ¹on sparse mapping coefficient vector, represent the 2nd redundant dictionary Φ ²corresponding vector at the 2nd redundant dictionary Φ ²on sparse mapping coefficient vector, represent N number of redundant dictionary Φ ⁿcorresponding vector at N number of redundant dictionary Φ ⁿon sparse mapping coefficient vector;

7. according to Z and calculate the column vector that rear n-p sampled value after denoising recovery is formed, be designated as ${\stackrel{\&RightArrow;}{y}}_1=Z\stackrel{\&RightArrow;}{\hat{a}}=\left(\begin{array}{c}{y}_{p+1}\\ y_{p+2}\\ .\\ .\\ .\\ y_n\end{array}\right),$ Wherein, y _p+1represent the sampled value of p+1 after denoising recovery, y _p+2represent the sampled value of p+2 after denoising recovery, y _nrepresent the sampled value of n-th after denoising recovery;

8. right be inverted, obtain inversion vector, be designated as ${\stackrel{\&RightArrow;}{x}}^{\&prime;}={\left(\begin{array}{cccc}{x}_n& x_{n-1}& ...& x_1\end{array}\right)}^T,$ Then according to step 2. to step operating process 6., obtain in an identical manner self-adaptation cross complete sparse base and average vector, correspondence be designated as Z' and again according to Z' and calculate the inversion vector of the column vector that front n-p sampled value after denoising recovery is formed, be designated as ${{\stackrel{\&RightArrow;}{y}}_1}^{\text{\&prime;}}=Z^{\&prime;}{\stackrel{\&RightArrow;}{\hat{a}}}^{\&prime;}=\left(\begin{array}{c}{y}_{n-p}\\ y_{n-p-1}\\ .\\ .\\ .\\ y_{11}\end{array}\right),$ Wherein, (x _nx _n-1x ₁) ^tfor (x _nx _n-1x ₁) transposed vector, y _n-prepresent the n-th-p sampled value after denoising recovery, y _n-p-1represent the n-th-p-1 sampled value after denoising recovery, y ₁represent the 1st sampled value after denoising recovery;

9. right be inverted, obtain inversion vector, be designated as ${{\stackrel{\&RightArrow;}{y}}_1}^{\&prime;\&prime;}=\left(\begin{array}{c}{y}_1\\ y_2\\ .\\ .\\ .\\ y_{n-p}\end{array}\right),$ Then will in front p sampled value and in all sampled values form according to the order of sequence denoising release signal, be designated as $\stackrel{\&RightArrow;}{y}=\left(\begin{array}{c}{y}_1\\ y_2\\ .\\ .\\ .\\ y_p\\ y_{p+1}\\ y_{p+2}\\ .\\ .\\ .\\ y_n\end{array}\right),$ So far the denoising process of multiple-frequency signal is completed.

Described step is middle N ∈ [20,40] 2..

Described step detailed process is 4.:

-1 4., make t represent the number of times of iteration, make r _trepresent the residual error of the t time iteration, make Λ _trepresent the indexed set of the t time iteration, make K represent at Φ ^jon the degree of rarefication of sparse mapping coefficient vector, the value of K is used for representative at Φ ^jon sparse mapping coefficient vector in total number of nonzero element, wherein, the initial value of t is 1, K>=1;

4. the residual error r of the t-1 time iteration-2, is calculated _t-1with Φ ^jin the inner product often arranged, then from p the inner product value calculated, select maximal value, then by Φ ^jin the footnote that arrange corresponding with this maximal value be designated as λ _t, wherein, r _t-1represent the residual error of the t-1 time iteration, the r as t=1 _t-1value be λ _t∈ [1, p];

4.-3, Λ is made _t=Λ _t-1∪ { λ _t, wherein, Λ _t-1represent the indexed set of the t-1 time iteration, the Λ as t=1 _t-1value be empty set, symbol " ∪ " is union operation symbol, this symbol " { } " represent set symbol;

4.-4, basis and Φ ^j, when calculating the t time iteration at Φ ^jon sparse mapping coefficient vector, be designated as ${\stackrel{\&RightArrow;}{a}}_t^j=\mathrm{atg}\min {\left|\right|{\stackrel{\&RightArrow;}{b}}_{{\mathrm{\&Phi;}}^j}-{\mathrm{\&Phi;}}^{j}a\left|\right|}_2,$ Wherein, symbol " || || ₂" for asking L2 norm sign, represent to get and make the minimum a of value, a represents sparse mapping coefficient vector;

4.-5, order $r_t=r_{t-1}-{\mathrm{\&Phi;}}^j{\stackrel{\&RightArrow;}{a}}_t^j;$

-6 4., judge whether t=K sets up, if set up, then finishing iteration process, will as at Φ ^jon sparse mapping coefficient vector, be again designated as if be false, then make t=t+1, then return step 4.-2 continuation iteration, wherein, "=" in t=t+1 is assignment.

Compared with prior art, the invention has the advantages that:

1) the inventive method is based on sparse autoregressive model, and the self-adaptation utilizing the sampled value of multiple-frequency signal self to build multiple-frequency signal crosses complete sparse base, make have the self-adaptation of oneself to cross complete sparse base for different multiple-frequency signals, effectively improve the practicality of the inventive method.

2) redundant dictionary in the inventive method crosses the capable formation of discontinuous m in complete sparse base by randomly drawing self-adaptation, therefore redundant dictionary is also adaptive, like this along with the change redundant dictionary of multiple-frequency signal also can change, compared with the fixing redundant dictionary of use, the redundant dictionary of the inventive method structure has more dirigibility, practicality, more well can catch the architectural feature of multiple-frequency signal, thus effectively improve denoising effect, make the inventive method stable denoising effect when the signal that process signal to noise ratio (S/N ratio) is different simultaneously; In addition, because redundant dictionary crosses the capable formation of discontinuous m in complete sparse base by randomly drawing self-adaptation, therefore computation complexity is low.

3) by repeatedly randomly drawing self-adaptation, the inventive method to cross in complete sparse base that discontinuous m is capable builds multiple redundant dictionary, try to achieve the sparse mapping coefficient vector of multiple correspondence, then arithmetic mean is asked to these sparse mapping coefficient vectors, using the average vector obtained as the coefficient that will use during signal restoring, This effectively reduces the instability randomly drawing the denoising brought.

4) the inventive method is by carrying out denoising to the former multiple-frequency signal collected and the signal after former multiple-frequency signal being inverted, and finally merges twice denoising result, to overcome before in a denoising p signal well not by shortcoming that denoising is restored.

Accompanying drawing explanation

Fig. 1 is the FB(flow block) of the inventive method;

Fig. 2 is original signal in experiment simulation figure;

Fig. 3 is original noise-free signal it is the signal of the noise of SNR0=10dB containing signal to noise ratio (S/N ratio) utilize the inventive method pair the denoising release signal obtained after carrying out denoising comparison of wave shape figure;

Fig. 4 is original noise-free signal be SNR containing signal to noise ratio (S/N ratio) ₀the signal of the noise of=10dB utilize existing Wavelet noise-eliminating method pair the denoising release signal obtained after carrying out denoising comparison of wave shape figure;

Fig. 5 is to original noise-free signal add the signal that different size noise obtains signal to noise ratio snr ₀, utilize the inventive method to noise-free signal the signal obtained after adding different size noise signal ( signal to noise ratio (S/N ratio) be original signal to noise ratio snr ₀) signal to noise ratio snr of denoising release signal that obtains after denoising ₁with utilize existing Wavelet noise-eliminating method to noise-free signal the signal obtained after adding different size noise signal ( signal to noise ratio (S/N ratio) be original signal to noise ratio snr ₀) obtain after denoising denoising release signal signal to noise ratio snr _wvalue comparison diagram.

Embodiment

Below in conjunction with accompanying drawing embodiment, the present invention is described in further detail.

The one that the present invention proposes is based on the multiple-frequency signal denoising method of sparse autoregression (AR) model modeling, and as shown in Figure 1, it comprises the following steps its FB(flow block):

1. pending multiple-frequency signal is expressed as in the form of vectors $\stackrel{\&RightArrow;}{x}={\left(\begin{array}{cccc}{x}_1& x_2& ...& x_n\end{array}\right)}^T,$ Wherein, (x ₁x ₂x _n) ^tfor (x ₁x ₂x _n) transposed vector, n represents the sampling number of multiple-frequency signal, n>=500, x ₁represent the 1st sampled value of multiple-frequency signal, x ₂represent the 2nd sampled value of multiple-frequency signal, x _nrepresent the n-th sampled value of multiple-frequency signal.

At this, the value of n is preferably and is more than or equal to 500 and is less than or equal to 2000, as got n=1000, this is because: if the value of n is too small, then the self-adaptation of subsequent construction crosses the architectural feature comprising multiple-frequency signal that complete sparse base may not be very complete, finally affects the denoising result of multiple-frequency signal; If the value of n is excessive, then crosses complete sparse base by constructing very large self-adaptation, the computing velocity of follow-up denoising can be affected like this.

2. based on sparse autoregressive model, structure self-adaptation cross complete sparse base, be designated as Z, $Z=\left(\begin{array}{cccc}{x}_1& x_2& ...& x_p\\ x_2& x_3& ...& x_{p+1}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{n-p}& x_{n-p+1}& ...& x_{n-1}\end{array}\right),$ Then construct vector corresponding to Z according to Z, be designated as ${\stackrel{\&RightArrow;}{b}}_Z=\left(\begin{array}{c}{x}_{p+1}\\ x_{p+2}\\ .\\ .\\ .\\ x_n\end{array}\right),$ Make j represent calculation times again, and make the initial value of j be 1, wherein, the dimension of Z is (n-p) × p, dimension be the exponent number that (n-p) × 1, p represents sparse autoregressive model, the occurrence of p be best value is selected by experiment, as got p=300, x as n=1000 in scope ₃, x _p, x _p+1, x _p+2, x _n-p, x _n-p+1and x _n-1corresponding the 3rd sampled value, a p sampled value, a p+1 sampled value, a p+2 sampled value, the individual sampled value of the n-th-p, the individual sampled value of the n-th-p+1 and (n-1)th sampled value representing multiple-frequency signal, 1≤j≤N, N represents the calculating total degree of setting, N ∈ [20,40], in the present embodiment, this multiple-frequency signal denoising method is emulated through many experiments, finds that N is in [20,40] value within the scope of this, denoising effect can reach best, when concrete operations if the value of desirable N is 30.

3., in jth time computation process, from Z, randomly draw a discontinuous m capable formation jth redundant dictionary, be designated as Φ ^j, ${\mathrm{\&Phi;}}^j=\left(\begin{array}{cccc}{x}_{i1}& x_{i1+1}& ...& x_{i1+p-1}\\ x_{i2}& x_{i2+1}& ...& x_{i2+p-1}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{\mathrm{im}}& x_{\mathrm{im}+1}& ...& x_{\mathrm{im}+p-1}\end{array}\right),$ Then according to Φ ^jstructure Φ ^jcorresponding vector, is designated as ${\stackrel{\&RightArrow;}{b}}_{{\mathrm{\&Phi;}}^j}=\left(\begin{array}{c}{x}_{i1+p}\\ x_{i2+p}\\ .\\ .\\ .\\ x_{\mathrm{im}+p}\end{array}\right),$ Wherein, 15<m<p, Φ ^jdimension be m × p, dimension be m × 1, i1, i2, im correspondence represent the m that randomly draws out from Z capable in the 1st row, the 2nd row, the capable line order number in Z of m, and 1≤i1<i2< ... <im≤n-p, x _i1, x _i1+1, x _i1+p-1, x _i2, x _i2+1, x _i2+p-1, x _im, x _im+1, x _im+p-1, x _i1+p, x _i2+p, x _im+pcorresponding represent multiple-frequency signal the i-th 1 sampled values, the i-th 1+1 sampled value, the i-th 1+p-1 sampled value, the i-th 2 sampled values, the i-th 2+1 sampled value, the i-th 2+p-1 sampled value, the i-th m sampled value, the i-th m+1 sampled value, the i-th m+p-1 sampled value, the i-th 1+p sampled value, the i-th 2+p sampled value, the i-th m+p sampled value.

4. adopt existing orthogonal matching pursuit (OMP) algorithm, calculate at Φ ^jon sparse mapping coefficient vector, be designated as wherein, dimension be p × 1.

In this particular embodiment, step detailed process is 4.:

-1 4., make t represent the number of times of iteration, make r _trepresent the residual error of the t time iteration, make Λ _trepresent the indexed set of the t time iteration, make K represent at Φ ^jon the degree of rarefication of sparse mapping coefficient vector, namely the value of K is used for representative at Φ ^jon sparse mapping coefficient vector in total number of nonzero element, wherein, the initial value of t is 1, K>=1.

4. the residual error r of the t-1 time iteration-2, is calculated _t-1with Φ ^jin the inner product often arranged, then from p the inner product value calculated, select maximal value, then by Φ ^jin the footnote that arrange corresponding with this maximal value be designated as λ _t, wherein, r _t-1represent the residual error of the t-1 time iteration, the r as t=1 _t-1value be λ _t∈ [1, p].

4.-3, Λ is made _t=Λ _t-1∪ { λ _t, wherein, Λ _t-1represent the indexed set of the t-1 time iteration, the Λ as t=1 _t-1value be empty set, symbol " ∪ " is union operation symbol, this symbol " { } " represent set symbol.

4.-4, basis and Φ ^j, when calculating the t time iteration at Φ ^jon sparse mapping coefficient vector, be designated as ${\stackrel{\&RightArrow;}{a}}_t^j=\mathrm{atg}\min {\left|\right|{\stackrel{\&RightArrow;}{b}}_{{\mathrm{\&Phi;}}^j}-{\mathrm{\&Phi;}}^{j}a\left|\right|}_2,$ Wherein, symbol " || || ₂" for asking L2 norm sign, represent to get and make the minimum a of value, a represents sparse mapping coefficient vector.

4.-5, order $r_t=r_{t-1}-{\mathrm{\&Phi;}}^j{\stackrel{\&RightArrow;}{a}}_t^j.$

-6 4., judge whether t=K sets up, if set up, then finishing iteration process, will as at Φ ^jon sparse mapping coefficient vector, be again designated as if be false, then make t=t+1, then return step 4.-2 continuation iteration, wherein, "=" in t=t+1 is assignment.

5. judge whether j=N sets up, if set up, then directly perform step 6., if be false, then make j=j+1, then return step and 3. continue to perform, wherein, "=" in j=j+1 is assignment.

6. the N number of sparse mapping coefficient vector obtained is done sums on average, obtain average vector, be designated as will as the sparse mapping coefficient vector needed for signal restoring, wherein, represent the 1st redundant dictionary Φ ¹corresponding vector at the 1st redundant dictionary Φ ¹on sparse mapping coefficient vector, represent the 2nd redundant dictionary Φ ²corresponding vector at the 2nd redundant dictionary Φ ²on sparse mapping coefficient vector, represent N number of redundant dictionary Φ ⁿcorresponding vector at N number of redundant dictionary Φ ⁿon sparse mapping coefficient vector.

7. according to Z and calculate the column vector that rear n-p sampled value after denoising recovery is formed, be designated as ${\stackrel{\&RightArrow;}{y}}_1=Z\stackrel{\&RightArrow;}{\hat{a}}=\left(\begin{array}{c}{y}_{p+1}\\ y_{p+2}\\ .\\ .\\ .\\ y_n\end{array}\right),$ Wherein, y _p+1represent the sampled value of p+1 after denoising recovery, y _p+2represent the sampled value of p+2 after denoising recovery, y _nrepresent the sampled value of n-th after denoising recovery.

8. right be inverted, obtain inversion vector, be designated as ${\stackrel{\&RightArrow;}{x}}^{\&prime;}={\left(\begin{array}{cccc}{x}_n& x_{n-1}& ...& x_1\end{array}\right)}^T,$ Then according to step 2. to step operating process 6., obtain in an identical manner self-adaptation cross complete sparse base and average vector, correspondence be designated as Z' and 8.-1 namely detailed process is:, based on sparse autoregressive model, structure self-adaptation cross complete sparse base, be designated as Z', $Z^{\&prime;}=\left(\begin{array}{cccc}{x}_n& x_{n-1}& ...& x_{n-p+1}\\ x_{n-1}& x_{n-1}& ...& x_{n-p}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{p+1}& x_p& ...& x_2\end{array}\right),$ Then construct vector corresponding to Z' according to Z', be designated as ${\stackrel{\&RightArrow;}{b}}_{Z^{\&prime;}}=\left(\begin{array}{c}{x}_{n-p}\\ x_{n-p-1}\\ .\\ .\\ .\\ x_1\end{array}\right),$ Make j represent calculation times again, and make the initial value of j be 1; Wherein, x _nand x _n-2corresponding the n-th sampled value and the n-th-2 sampled values representing multiple-frequency signal.-2 8., in jth time computation process, from Z', randomly draw that discontinuous m is capable forms a jth redundant dictionary according to the order of sequence, be designated as Φ ^j', ${\mathrm{\&Phi;}}^{j\&prime;}=\left(\begin{array}{cccc}{x}_{i1}& x_{i1-1}& ...& x_{i1-p+1}\\ x_{i2}& x_{i2-1}& ...& x_{i2-p+1}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{\mathrm{im}}& x_{\mathrm{im}-1}& ...& x_{\mathrm{im}-p+1}\end{array}\right),$ Then according to Φ ^j' structure Φ ^j' corresponding vector, be designated as ${\stackrel{\&RightArrow;}{b}}_{{\mathrm{\&Phi;}}^{j\&prime;}}=\left(\begin{array}{c}{x}_{i1-p}\\ x_{i2-p}\\ .\\ .\\ .\\ x_{\mathrm{im}-p}\end{array}\right);$ Wherein, n >=i1>i2> ... >im >=p+1.-3 8., adopt existing orthogonal matching pursuit (OMP) algorithm, calculate at Φ ^j' on sparse mapping coefficient vector, be designated as -4 8., judge whether j=N sets up, if set up, then directly perform step 8.-5, if be false, then make j=j+1, then return step and 8.-2 continue to perform;-5 8., the N number of sparse mapping coefficient vector obtained is done sums on average, obtain average vector, be designated as will as the sparse mapping coefficient vector needed for signal restoring, wherein, represent the 1st redundant dictionary Φ ¹' corresponding vector at the 1st redundant dictionary Φ ¹' on sparse mapping coefficient vector, represent the 2nd redundant dictionary Φ ²' corresponding vector at the 2nd redundant dictionary Φ ²' on sparse mapping coefficient vector, represent N number of redundant dictionary Φ ⁿ' corresponding vector at N number of redundant dictionary Φ ⁿ' on sparse mapping coefficient vector; Again according to Z' and calculate the inversion vector of the column vector that front n-p sampled value after denoising recovery is formed, be designated as ${{\stackrel{\&RightArrow;}{y}}_1}^{\text{\&prime;}}=Z^{\&prime;}{\stackrel{\&RightArrow;}{\hat{a}}}^{\&prime;}=\left(\begin{array}{c}{y}_{n-p}\\ y_{n-p-1}\\ .\\ .\\ .\\ y_{11}\end{array}\right),$ Wherein, (x _nx _n-1x ₁) ^tfor (x _nx _n-1x ₁) transposed vector, y _n-prepresent the n-th-p sampled value after denoising recovery, y _n-p-1represent the n-th-p-1 sampled value after denoising recovery, y ₁represent the 1st sampled value after denoising recovery.

9. right be inverted, obtain inversion vector, be designated as ${{\stackrel{\&RightArrow;}{y}}_1}^{\&prime;\&prime;}=\left(\begin{array}{c}{y}_1\\ y_2\\ .\\ .\\ .\\ y_{n-p}\end{array}\right),$ Then will in front p sampled value and in all sampled values form according to the order of sequence denoising release signal, be designated as $\stackrel{\&RightArrow;}{y}=\left(\begin{array}{c}{y}_1\\ y_2\\ .\\ .\\ .\\ y_p\\ y_{p+1}\\ y_{p+2}\\ .\\ .\\ .\\ y_n\end{array}\right),$ So far the denoising process of multiple-frequency signal is completed.

For the feasibility of the inventive method is described, carry out denoising for the concrete multiple-frequency signal being added with white Gaussian noise.

1) suppose that pending multiple-frequency signal is x ₁(t), x ₁(t)=x ₀(t)+n (t), wherein, x ₀(t)=sin (2 π × 100t+0.1)+3cos (2 π × 130t+0.9)+0.7sin (2 π × 170t+1.5)+1.2cos (2 π × 70t), n (t) is white Gaussian noise, is time variable at this t; Then x is set ₁the signal to noise ratio snr of (t) ₀=10dB; Again to x ₁t () carries out Nyquist uniform sampling, sample frequency F _s=1000Hz, sampling x ₁t signal that () obtains is write as vector form ${\stackrel{\&RightArrow;}{x}}_1={\left(\begin{array}{ccccc}{x}_1& x_2& ...& x_{999}& x_{1000}\end{array}\right)}^T,$ Sampling x ₀t signal vector that () obtains is ${\stackrel{\&RightArrow;}{x}}_0={\left(\begin{array}{ccccc}{x}_{1_0}& x_{2_0}& ...& x_{{999}_0}& x_{{1000}_0}\end{array}\right)}^T,$ As shown in Figure 2.

2) arrange the self-adaptation that need build to cross complete sparse base and have 300 row, i.e. parameters p=300, with the signal vector obtained of sampling build self-adaptation cross complete sparse base $Z=\left(\begin{array}{ccccc}{x}_1& x_2& ...& x_{299}& x_{300}\\ x_2& x_3& ...& x_{300}& x_{301}\\ .& .& & .& .\\ .& .& & .& .\\ .& .& & .& .\\ x_{699}& x_{700}& ...& x_{997}& x_{998}\\ x_{700}& x_{701}& ...& x_{998}& x_{999}\end{array}\right),$ Vector corresponding to Z is constructed again according to Z ${\stackrel{\&RightArrow;}{b}}_z=\left(\begin{array}{c}{x}_{301}\\ x_{302}\\ .\\ .\\ .\\ x_{999}\\ x_{1000}\end{array}\right).$

3) line number arranging redundant dictionary is 100, i.e. parameters m=100, randomly draws discontinuous 100 row and form a jth redundant dictionary according to the order of sequence from Z ${\mathrm{\&Phi;}}^j=\left(\begin{array}{cccc}{x}_{i1}& x_{i1+1}& ...& x_{i1+299}\\ x_{i2}& x_{i2+1}& ...& x_{i2+299}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{i100}& x_{i100+1}& ...& x_{i100+299}\end{array}\right),$ Then according to Φ ^jstructure Φ ^jcorresponding vector ${\stackrel{\&RightArrow;}{\mathrm{\&Phi;}}}_{{\mathrm{\&Phi;}}^j}=\left(\begin{array}{c}{x}_{i1+300}\\ x_{i2+300}\\ .\\ .\\ .\\ x_{i100+300}\end{array}\right),$ Wherein, 1≤i1<i2< ... <im≤700, as Φ ^jin the 1st row be the 5th row, i.e. i1=5 in the Z randomly drawed out.

4) calculate at Φ ^jon sparse mapping coefficient vector adopt OMP Algorithm for Solving sparse coefficient vector suppose K=15, then obtain ${\stackrel{\&RightArrow;}{a}}^j=\left(\begin{array}{c}{a}_1\\ a_2\\ .\\ .\\ .\\ a_{300}\end{array}\right),$ A ₁, a ₂..., a ₃₀₀represent respectively in the 1st value, the 2nd value ..., the 300th value.

5) double counting times N=25 are set, repeated execution of steps 3) and 4) totally 25 times, 25 redundant dictionary, 25 corresponding vectors and 25 sparse mapping coefficient vectors can be obtained.

6) 25 sparse mapping coefficient vectors of trying to achieve are done sums on average obtain average vector $\stackrel{\&RightArrow;}{\hat{a}}=\frac{1}{25}({\stackrel{\&RightArrow;}{a}}^1+{\stackrel{\&RightArrow;}{a}}^2+...+{\stackrel{\&RightArrow;}{a}}^{25}).$

7) according to Z and calculate the column vector that rear 700 sampled values after denoising recovery are formed ${\stackrel{\&RightArrow;}{y}}_1=Z\stackrel{\&RightArrow;}{\hat{a}}\left(\begin{array}{c}{y}_{301}\\ y_{302}\\ .\\ .\\ .\\ y_{1000}\end{array}\right),$ Wherein, y ₃₀₁, y ₃₀₂..., y ₁₀₀₀be respectively the 301st value of release signal after denoising, the 302nd value ..., the 1000th value.

8) right carry out inversion operation, obtain a new signal vector ${\stackrel{\&RightArrow;}{x}}_1^{\&prime;}=\left(\begin{array}{ccccc}{x}_{1000}& x_{999}& ...& x_2& x_1\end{array}\right),$ Then according to step 2) to step 6) operating process, obtain in an identical manner self-adaptation cross complete sparse base $Z^{\&prime;}=\left(\begin{array}{ccccc}{x}_{1000}& x_{999}& ...& x_{702}& x_{701}\\ x_{999}& x_{998}& ...& x_{701}& x_{700}\\ .& .& & .& .\\ .& .& & .& .\\ .& .& & .& .\\ x_{302}& x_{301}& ...& x_4& x_3\\ x_{301}& x_{300}& ...& x_3& x_2\end{array}\right),$ Corresponding vector ${\stackrel{\&RightArrow;}{b}}_{Z^{\&prime;}}=\left(\begin{array}{c}{x}_{700}\\ x_{699}\\ .\\ .\\ .\\ x_2\\ x_1\end{array}\right),$ Average vector again according to Z' and calculate the inversion vector of the column vector that front 700 sampled values after denoising recovery are formed ${{\stackrel{\&RightArrow;}{y}}_1}^{\&prime;}\left(\begin{array}{c}{y}_{700}\\ y_{699}\\ .\\ .\\ .\\ y_2\\ y_1\end{array}\right).$

9) right carry out inversion to obtain ${\stackrel{\&RightArrow;}{y}}_1^{\&prime;\&prime;}=\left(\begin{array}{c}{y}_1\\ y_2\\ .\\ .\\ .\\ y_{699}\\ y_{700}\end{array}\right),$ Wherein, y ₁, y ₂..., y ₆₉₉, y ₇₀₀be the 1st value of release signal after final denoising, the 2nd value ..., the 699th value, the 700th value; Then the number of winning the confidence front 300 signaling points with all signaling points merge and obtain finally complete denoising release signal $\stackrel{\&RightArrow;}{y}=\left(\begin{array}{ccccc}{y}_1& y_2& ...& y_{999}& y_{1000}\end{array}\right).$

Denoising release signal obtained above $\stackrel{\&RightArrow;}{y}=\left(\begin{array}{ccccc}{y}_1& y_2& ...& y_{999}& y_{1000}\end{array}\right)$ Signal to noise ratio (S/N ratio) be ask for respectively with MATLAB emulation original signal to noise ratio snr ₀with signal to noise ratio snr ₁, SNR ₀=9.54dB, SNR ₁=18.89dB.

Signal containing different signal to noise ratio (S/N ratio) is set the inventive method and existing Wavelet noise-eliminating method is adopted to carry out denoising to these signals respectively, wherein by original signal to noise ratio snr ₀be arranged on (1dB ~ 20dB).The experiment parameter of the inventive method is: F _s=1000Hz, p=300, m=100, N=25.The experiment parameter of existing Wavelet noise-eliminating method (wavelet function wden ()) is: heuristic threshold function table form (heursure), and be set as that Soft Thresholding for Signal threshold value (s) processes, threshold value thresholding is determined automatically by Wavelet Denoising Method function, only according to the sparse estimating noise level of ground floor wavelet decomposition (sln), with sym8 small echo, the denoising that 5 layers have been decomposed pair signals is done to signal.

Above-mentioned pending signal is a multiple-frequency signal, meets sparse autoregressive model (AR) model, namely has stronger temporal correlation.Fig. 3 gives original noise-free signal be SNR containing signal to noise ratio (S/N ratio) ₀the signal of the noise of=10dB utilize the inventive method pair the denoising release signal obtained after carrying out denoising comparison of wave shape figure, denoising release signal signal to noise ratio snr ₁for 18.89dB; Fig. 4 gives original noise-free signal be SNR containing signal to noise ratio (S/N ratio) ₀the signal of the noise of=10dB utilize existing Wavelet noise-eliminating method pair the denoising release signal obtained after carrying out denoising comparison of wave shape figure, denoising release signal signal to noise ratio snr _wfor 12.86dB.As can be seen from Fig. 3 and Fig. 4, the inventive method is adopted to carry out to signal the denoising release signal that denoising obtains than adopting Wavelet noise-eliminating method, the denoising release signal that denoising obtains is carried out to signal closer to original noise-free signal waveform.By the signal to noise ratio (S/N ratio) of denoising release signal obtained after comparing denoising, the inventive method more objectively can be compared better than the denoising effect of existing Wavelet noise-eliminating method.Fig. 5 gives original noise-free signal add after making an uproar and obtain signal signal to noise ratio snr ₀, adopt the inventive method and existing Wavelet noise-eliminating method respectively to noise-free signal the signal obtained after adding different size noise signal carry out the signal to noise ratio (S/N ratio) comparison diagram of the denoising release signal that denoising obtains.As can be seen from Figure 5 the denoising effect of the inventive method is better than the denoising effect of existing Wavelet noise-eliminating method, and existing Wavelet noise-eliminating method is along with original noise-free signal the increase denoising effect of signal to noise ratio (S/N ratio) relatively weaken, be not namely fine for the signal denoising effect that original Noise signal is relatively little.And the inventive method is to the signal denoising effect stability containing different size signal to noise ratio (S/N ratio), namely the inventive method has good denoising effect to the signal containing different size noise, build this is because the self-adaptation of the inventive method crosses complete sparse base Z by the band noise signal collected, redundant dictionary is the capable structure of m randomly drawing Z, namely self-adaptation crosses complete sparse base and redundant dictionary has adaptivity, can utilize the feature of signal own well; Relate in the inventive method and randomly draw step, if only once extract, simulation result can be unstable, takes the operation repeating to be averaged and carry out stable denoising effect in the inventive method.

Claims (3)

1., based on a multiple-frequency signal denoising method for sparse autoregressive model modeling, it is characterized in that comprising the following steps:

1. pending multiple-frequency signal is expressed as in the form of vectors $\stackrel{\&RightArrow;}{x}={\left(\begin{array}{cccc}{x}_1& x_2& ...& x_n\end{array}\right)}^T,$ Wherein, (x ₁x ₂x _n) ^tfor (x ₁x ₂x _n) transposed vector, n represents the sampling number of multiple-frequency signal, n>=500, x ₁represent the 1st sampled value of multiple-frequency signal, x ₂represent the 2nd sampled value of multiple-frequency signal, x _nrepresent the n-th sampled value of multiple-frequency signal;

2. based on sparse autoregressive model, structure self-adaptation cross complete sparse base, be designated as Z, $Z=\left(\begin{array}{cccc}{x}_1& x_2& ...& x_p\\ x_2& x_3& ...& x_{p+1}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{n-p}& x_{n-p+1}& ...& x_{n-1}\end{array}\right),$ Then construct vector corresponding to Z according to Z, be designated as ${\stackrel{\&RightArrow;}{b}}_Z=\left(\begin{array}{c}{x}_{p+1}\\ x_{p+2}\\ .\\ .\\ .\\ x_n\end{array}\right),$ Make j represent calculation times again, and make the initial value of j be 1, wherein, the dimension of Z is (n-p) × p, dimension be the exponent number that (n-p) × 1, p represents sparse autoregressive model, x ₃, x _p, x _p+1, x _p+2, x _n-p, x _n-p+1and x _n-1corresponding the 3rd sampled value, a p sampled value, a p+1 sampled value, a p+2 sampled value, the individual sampled value of the n-th-p, the individual sampled value of the n-th-p+1 and (n-1)th sampled value representing multiple-frequency signal, 1≤j≤N, N represents the calculating total degree of setting;

3. in jth time computation process, from Z, randomly draw that discontinuous m is capable forms a jth redundant dictionary according to the order of sequence, be designated as Φ ^j, ${\mathrm{\&Phi;}}^j=\left(\begin{array}{cccc}{x}_{i1}& x_{i1+1}& ...& x_{i1+p-1}\\ x_{i2}& x_{i2+1}& ...& x_{i2+p-1}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{\mathrm{im}}& x_{\mathrm{im}+1}& ...& x_{\mathrm{im}+p-1}\end{array}\right),$ Then according to Φ ^jstructure Φ ^jcorresponding vector, is designated as ${\stackrel{\&RightArrow;}{b}}_{{\mathrm{\&Phi;}}^j}=\left(\begin{array}{c}{x}_{i1+p}\\ x_{i2+p}\\ .\\ .\\ .\\ x_{\mathrm{im}+p}\end{array}\right),$ Wherein, 15<m<p, Φ ^jdimension be m × p, dimension be m × 1, i1, i2, im correspondence represent the m that randomly draws out from Z capable in the 1st row, the 2nd row, the capable line order number in Z of m, and 1≤i1<i2< ... <im≤n-p, x _i1, x _i1+1, x _i1+p-1, x _i2, x _i2+1, x _i2+p-1, x _im, x _im+1, x _im+p-1, x _i1+p, x _i2+p, x _im+pcorresponding represent multiple-frequency signal the i-th 1 sampled values, the i-th 1+1 sampled value, the i-th 1+p-1 sampled value, the i-th 2 sampled values, the i-th 2+1 sampled value, the i-th 2+p-1 sampled value, the i-th m sampled value, the i-th m+1 sampled value, the i-th m+p-1 sampled value, the i-th 1+p sampled value, the i-th 2+p sampled value, the i-th m+p sampled value;

4. adopt orthogonal matching pursuit algorithm, calculate at Φ ^jon sparse mapping coefficient vector, be designated as wherein, dimension be p × 1;

5. judge whether j=N sets up, if set up, then directly perform step 6., if be false, then make j=j+1, then return step and 3. continue to perform, wherein, "=" in j=j+1 is assignment;

6. the N number of sparse mapping coefficient vector obtained is done sums on average, obtain average vector, be designated as will as the sparse mapping coefficient vector needed for signal restoring, wherein, represent the 1st redundant dictionary Φ ¹corresponding vector at the 1st redundant dictionary Φ ¹on sparse mapping coefficient vector, represent the 2nd redundant dictionary Φ ²corresponding vector at the 2nd redundant dictionary Φ ²on sparse mapping coefficient vector, represent N number of redundant dictionary Φ ⁿcorresponding vector at N number of redundant dictionary Φ ⁿon sparse mapping coefficient vector;

7. according to Z and calculate the column vector that rear n-p sampled value after denoising recovery is formed, be designated as ${\stackrel{\&RightArrow;}{y}}_1=Z\stackrel{\&RightArrow;}{\hat{a}}=\left(\begin{array}{c}{y}_{p+1}\\ y_{p+2}\\ .\\ .\\ .\\ y_n\end{array}\right),$ Wherein, y _p+1represent the sampled value of p+1 after denoising recovery, y _p+2represent the sampled value of p+2 after denoising recovery, y _nrepresent the sampled value of n-th after denoising recovery;

8. right be inverted, obtain inversion vector, be designated as ${\stackrel{\&RightArrow;}{x}}^{\&prime;}={\left(\begin{array}{cccc}{x}_n& x_{n-1}& ...& x_1\end{array}\right)}^T,$ Then according to step 2. to step operating process 6., obtain in an identical manner self-adaptation cross complete sparse base and average vector, correspondence be designated as Z' and again according to Z' and calculate the inversion vector of the column vector that front n-p sampled value after denoising recovery is formed, be designated as ${{\stackrel{\&RightArrow;}{y}}_1}^{\&prime;}=Z^{\&prime;}{\stackrel{\&RightArrow;}{\hat{a}}}^{\&prime;}=\left(\begin{array}{c}{y}_{n-p}\\ y_{n-p-1}\\ .\\ .\\ .\\ y_1\end{array}\right),$ Wherein, (x _nx _n-1x ₁) ^tfor (x _nx _n-1x ₁) transposed vector, y _n-prepresent the n-th-p sampled value after denoising recovery, y _n-p-1represent the n-th-p-1 sampled value after denoising recovery, y ₁represent the 1st sampled value after denoising recovery;

9. right be inverted, obtain inversion vector, be designated as ${{\stackrel{\&RightArrow;}{y}}_1}^{\&prime;\&prime;}=\left(\begin{array}{c}{y}_1\\ y_2\\ .\\ .\\ .\\ y_{n-p}\end{array}\right),$ Then will in front p sampled value and in all sampled values form according to the order of sequence denoising release signal, be designated as $\stackrel{\&RightArrow;}{y}=\left(\begin{array}{c}{y}_1\\ y_2\\ .\\ .\\ .\\ y_p\\ y_{p+1}\\ y_{p+2}\\ .\\ .\\ .\\ y_n\end{array}\right),$ So far the denoising process of multiple-frequency signal is completed.

2. a kind of multiple-frequency signal denoising method based on sparse autoregressive model modeling according to claim 1, is characterized in that described step 2. middle N ∈ [20,40].

3. a kind of multiple-frequency signal denoising method based on sparse autoregressive model modeling according to claim 1 and 2, is characterized in that described step detailed process is 4.:

-1 4., make t represent the number of times of iteration, make r _trepresent the residual error of the t time iteration, make Λ _trepresent the indexed set of the t time iteration, make K represent at Φ ^jon the degree of rarefication of sparse mapping coefficient vector, the value of K is used for representative at Φ ^jon sparse mapping coefficient vector in total number of nonzero element, wherein, the initial value of t is 1, K>=1;

4. the residual error r of the t-1 time iteration-2, is calculated _t-1with Φ ^jin the inner product often arranged, then from p the inner product value calculated, select maximal value, then by Φ ^jin the footnote that arrange corresponding with this maximal value be designated as λ _t, wherein, r _t-1represent the residual error of the t-1 time iteration, the r as t=1 _t-1value be λ _t∈ [1, p];

4.-3, Λ is made _t=Λ _t-1∪ { λ _t, wherein, Λ _t-1represent the indexed set of the t-1 time iteration, the Λ as t=1 _t-1value be empty set, symbol " ∪ " is union operation symbol, this symbol " { } " represent set symbol;

4.-4, basis and Φ ^j, when calculating the t time iteration at Φ ^jon sparse mapping coefficient vector, be designated as ${\stackrel{\&RightArrow;}{a}}_t^j=\arg \min {\left|\right|{\stackrel{\&RightArrow;}{b}}_{{\mathrm{\&Phi;}}^j}-{\mathrm{\&Phi;}}^{j}a\left|\right|}_2,$ Wherein, symbol " || || ₂" for asking L2 norm sign, represent to get and make the minimum a of value, a represents sparse mapping coefficient vector;

4.-5, order $r_t=r_{t-1}-{\mathrm{\&Phi;}}^j{\stackrel{\&RightArrow;}{a}}_t^j;$

-6 4., judge whether t=K sets up, if set up, then finishing iteration process, will as at Φ ^jon sparse mapping coefficient vector, be again designated as if be false, then make t=t+1, then return step 4.-2 continuation iteration, wherein, "=" in t=t+1 is assignment.