CN107480619B - Noise-reduction method and system based on EEMD and the Ground Penetrating Radar B-scan image for arranging entropy - Google Patents
Noise-reduction method and system based on EEMD and the Ground Penetrating Radar B-scan image for arranging entropy Download PDFInfo
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Abstract
The invention discloses the noise-reduction methods and system of a kind of Ground Penetrating Radar B-scan image based on EEMD and arrangement entropy, Ground Penetrating Radar two dimension B-scan picture signal is obtained first, then every one of B-scan picture signal of acquisition is denoised, to obtain the signal after the road B-scan picture signal inhibits noise, finally the signal after the denoising of each road is reconfigured, the two-dimentional B-scan picture signal after the noise that is inhibited；Wherein, it include: that EEMD decomposition is carried out for the road B-scan picture signal for the method that any one of B-scan picture signal is denoised, obtain the K IMF component arranged from high frequency to low frequency, calculate the arrangement entropy of each IMF component, selection arrangement entropy is reconstructed no more than the IMF component of preset value, the signal after being denoised.The present invention solves signal mode Aliasing Problem present in EMD decomposition, can be effectively reduced noise.
Description
Technical field
The present invention relates to digital processing field is belonged to, it is related specifically to the B-scan image procossing of Ground Penetrating Radar, specifically
Noise-reduction method and system based on EEMD and the Ground Penetrating Radar B-scan image for arranging entropy.
Background technique
Ground Penetrating Radar is a kind of discontinuity using underground medium come effective detection method of Underground target, extensively
Be applied to the fields such as geology, resource, environment, engineering and military affairs.During actual detection, since underground medium structure is multiple
The presence of miscellaneous, physical parameter difference and noise jamming, the echo of Ground Penetrating Radar is unavoidably by noise pollution, so that echo is believed
Number have non-stationary, nonlinear feature.Noise pollution causes certain difficulty to subsequent object detection and recognition, therefore visits
The noise suppressed of ground radar is particularly important for subsequent data processing.
Hilbert-Huang transform (Hilbert-Huang transform, HHT) is a kind of analysis non-linear, non-stationary letter
Number new method, be suitable for handling the B-scan image of Ground Penetrating Radar.B-scan is to show the echo-signal scanned
In two-dimensional surface, abscissa represents the horizontal displacement direction of scanning, and ordinate represents the depth direction of scanning.This method handles B
When scan image, by empirical mode decomposition (Empirical mode decomposition, EMD) by signal decomposition be it is intrinsic
Mode function (Intrinsic mode function, IMF) can obtain preferable when handling non-stationary, nonlinear signal
Effect.Although EMD method has many advantages, but there are problems that modal overlap in decomposition, cause include in some IMF component
The signal of different scale or similar magnitude signal are present in different IMF components, affect noise to a certain extent
Inhibitory effect causes to cause inhibitory effect poor.
Summary of the invention
The technical problem to be solved in the present invention is that pressing down for above-mentioned EMD transformation when handling Ground Penetrating Radar B-scan image
The technological deficiency of effect difference processed, provide it is a kind of based on EEMD and arrange entropy Ground Penetrating Radar B-scan image noise-reduction method and
System.
Wherein one side according to the present invention, the present invention are to solve its technical problem, are provided a kind of based on EEMD and row
The noise-reduction method of the Ground Penetrating Radar B-scan image of column entropy, comprising the following steps:
S1, Ground Penetrating Radar two dimension B-scan picture signal X ∈ R is obtainedM×N, wherein M is road number, and N is the sampling of every track data
Points；
S2, every one of B-scan picture signal of acquisition is denoised, to obtain road B-scan picture signal inhibition
Signal after noise；Wherein, the method denoised for any one of B-scan picture signal includes:
S21, for the road B-scan picture signal { x (t), t=1,2 ..., N } carry out EEMD decomposition, obtain from high frequency to
K IMF component c of low frequency arrangement1(t)、c2(t)、…、cK(t)；
S22, the arrangement entropy for calculating each IMF component in step S21；
S23, selection arrangement entropy are reconstructed no more than the IMF component of preset value, the signal x ' (t) after being denoised,
X ' (t) is the sum of the IMF component for arranging entropy and being not more than preset value；
S3, the signal after the denoising of each road is reconfigured, the two-dimentional B-scan picture signal X' after the noise that is inhibited
∈RM×N。
Further, in the S21 of noise-reduction method of the invention, specific step is as follows:
S211, it is separately added into preset T noise signal into x (t), obtains T signals and associated noises, wherein
xi(t)=x (t)+ni(t),
In formula, i=1,2 ..., T, xiIt (t) is i-th of signals and associated noises, ni(t) it makes an uproar for what is be added in i-th of signals and associated noises
Sound, ni(t) be mean value be 0, standard deviation be constant white Gaussian noise；
S212, EMD decomposition is carried out to each signals and associated noises respectively, obtains the IMF component of each signals and associated noises；
S213, it is averaged using following formula to the correspondence IMF component that T signals and associated noises decompose, obtains EEMD
The IMF component of decomposition；
In formula, cp(t) pass through p-th of IMF component that EEMD is decomposed, c for x (t)i,p(t) i-th of signals and associated noises warp
Cross p-th of IMF component that EMD is decomposed, p=1,2,3 ..., K.
Further, in the step S22 of noise-reduction method of the invention, for any one x (t), the row of each IMF component
Column entropy calculation method is as follows:
S221, phase space reconfiguration is carried out for each IMF component of decomposition arrived, obtains matrix:
Wherein, i=1,2 ... Q, m and λ are respectively Embedded dimensions and delay time, and Q is to reconstruct vector in phase space reconstruction
Number, Q=N- (m-1) λ；
S222, component (c will be reconstructedp(i),cp(i+λ),…,cp[i+ (m-1) λ]) it is arranged according to ascending order, as follows:
cp[i+(j1-1)λ]≤cp[i+(j2-1)λ]≤…≤cp[i+(jm-1)λ]
In formula, j1,j2,…,jmIndicate the index of each element column in reconstruct component；
For reconstruct vector c each in phase space reconstructionp(i), one group of symbol for reflecting its element size sequence is obtained respectively
Number sequence S (g)=(j1,j2,…,jm), wherein g=1,2 ..., q, q≤m！；
S223, the Probability p for calculating the appearance of each symbol sebolic addressing1,p2,…,pq, and according to the following formula sequence of calculation { cp
(i), i=1,2 ..., K arrangement entropy Hp(m):
Further, after the step S223 of noise-reduction method of the invention further include:
S224, by arrangement entropy H calculated in S223p(m) new arrangement entropy is updated to after being normalized, new
Arrange the normalized formula of entropy are as follows:
Hp=Hp(m)/ln(m！).
Further, in noise-reduction method of the invention, c in step S211(t)、c2(t)、…、cK(t) for according to from height
Frequency is arranged to low frequency, is specifically included the following steps in step S23:
The preset value is successively compared with the arrangement entropy of each IMF component, when the arrangement entropy of k-th of IMF component
When value is less than or equal to the preset value, it is not more than preset value for each IMF component after k and k as the arrangement entropy
IMF component.
In order to solve the above technical problems, the present invention also provides a kind of based on EEMD and arranges the Ground Penetrating Radar B-scan of entropy
The noise reduction system of image, comprising:
Signal acquisition module, for obtaining Ground Penetrating Radar two dimension B-scan picture signal X ∈ RM×N, wherein M is road number, and N is
The sampling number of every track data；
Signal denoising module is swept for denoising to every one of B-scan picture signal of acquisition with obtaining road B
It retouches picture signal and inhibits the signal after noise；
Signals revivification module, for being reconfigured to the signal after the denoising of each road, the two-dimentional B after the noise that is inhibited
Scan image signal X' ∈ RM×N；
Wherein, signal denoising module is handled any one of B-scan picture signal using following submodules:
EEMD decomposes submodule, for carrying out EEMD points for one of B-scan picture signal { x (t), t=1,2 ..., N }
Solution obtains the K IMF component c arranged from high frequency to low frequency1(t)、c2(t)、…、cK(t)；
Entropy computational submodule is arranged, the arrangement entropy of each IMF component in submodule is decomposed for calculating step EEMD；
Signal reconstruction submodule is reconstructed for choosing arrangement entropy no more than the IMF component of preset value, after obtaining denoising
Signal x ' (t), x ' (t) be arrange entropy be not more than preset value the sum of IMF component.
Further, in noise reduction system of the invention, EEMD decomposes submodule and specifically includes:
Noise adding unit is used to be separately added into preset T noise signal into x (t), obtains T signals and associated noises,
In
xi(t)=x (t)+ni(t),
In formula, i=1,2 ..., T, xiIt (t) is i-th of signals and associated noises, ni(t) it makes an uproar for what is be added in i-th of signals and associated noises
Sound, ni(t) be mean value be 0, standard deviation be constant white Gaussian noise；
EMD decomposition unit obtains the IMF of each signals and associated noises for carrying out EMD decomposition respectively to each signals and associated noises
Component；
IMF converter unit is flat for being carried out using following formula to the correspondence IMF component that T signals and associated noises decompose
, the IMF component of EEMD decomposition is obtained；
In formula, cp(t) pass through p-th of IMF component that EEMD is decomposed, c for x (t)i,p(t) i-th of signals and associated noises warp
Cross p-th of IMF component that EMD is decomposed, p=1,2,3 ..., K.
Further, it in noise reduction system of the invention, for any one x (t), arranges under the utilization of entropy computational submodule
State the arrangement entropy that unit calculates each IMF component:
Phase space reconfiguration unit carries out phase space reconfiguration for each IMF component arrived for decomposition, obtains matrix:
Wherein, i=1,2 ... Q, m and λ are respectively Embedded dimensions and delay time, and Q is to reconstruct vector in phase space reconstruction
Number, Q=N- (m-1) λ；
Symbol sebolic addressing acquiring unit, for component (c will to be reconstructedp(i),cp(i+λ),…,cp[i+ (m-1) λ]) according to ascending order
Arrangement, as follows:
cp[i+(j1-1)λ]≤cp[i+(j2-1)λ]≤…≤cp[i+(jm-1)λ]
In formula, j1,j2,…,jmIndicate the index of each element column in reconstruct component；
For reconstruct vector c each in phase space reconstructionp(i), one group of symbol for reflecting its element size sequence is obtained respectively
Number sequence S (g)=(j1,j2,…,jm), wherein g=1,2 ..., q, q≤m！；
Entropy computing unit is arranged, for calculating the Probability p of each symbol sebolic addressing appearance1,p2,…,pq, and according to following
The formula sequence of calculation { cp(i), i=1,2 ..., K arrangement entropy Hp(m):
Further, in noise reduction system of the invention, entropy computational submodule is arranged further include:
Entropy updating unit is arranged, for calculated arrangement entropy H in entropy computing unit will to be arrangedp(m) place is normalized
New arrangement entropy is updated to after reason, the normalized formula of new arrangement entropy are as follows:
Hp=Hp(m)/ln(m！).
Further, specifically include following module in signal reconstruction submodule in noise reduction system of the invention:
The preset value is successively compared with the arrangement entropy of each IMF component, when the arrangement entropy of k-th of IMF component
When value is less than or equal to the preset value, it is not more than preset value for each IMF component after k and k as the arrangement entropy
IMF component.
Implement the noise-reduction method and system of the invention based on EEMD and the Ground Penetrating Radar B-scan image for arranging entropy, has
Below the utility model has the advantages that the present invention decomposes Gpr Signal using EEMD method, the arrangement from high frequency to low frequency is obtained
IMF solves signal mode Aliasing Problem present in EMD decomposition, can be effectively reduced noise.And it is further, it is calculating
When the arrangement entropy of each IMF component, determine that noise signal corresponds to the separation of IMF IMF corresponding with echo signal by preset value, into
And the corresponding IMF of echo signal is reconstructed, noise can be effectively suppressed, more retain target information.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing:
Fig. 1 is an embodiment of the noise-reduction method of the Ground Penetrating Radar B-scan image of the invention based on EEMD and arrangement entropy
Flow chart；
Fig. 2 is the original B-scan picture signal of Ground Penetrating Radar；
Fig. 3 is to add the image after making an uproar to original B-scan image；
Fig. 4 is the 40th signal and its EEMD exploded view added after making an uproar；
Fig. 5 is the signal after the 40th signals and associated noises and inhibition noise；
Fig. 6 is the image for reconfigure after denoising to all road signals in Fig. 3；
Fig. 7 is an embodiment of the noise reduction system of the Ground Penetrating Radar B-scan image of the invention based on EEMD and arrangement entropy
Functional block diagram.
Specific embodiment
For a clearer understanding of the technical characteristics, objects and effects of the present invention, now control attached drawing is described in detail
A specific embodiment of the invention.
As shown in Figure 1, it is the noise-reduction method of the invention based on EEMD and the Ground Penetrating Radar B-scan image for arranging entropy
The flow chart of one embodiment.In the noise-reduction method of the present embodiment, include following steps:
S1, Ground Penetrating Radar two dimension B-scan picture signal X ∈ R is obtainedM×N, wherein M is road number, and N is the sampling of every track data
Points.
S2, every one of B-scan picture signal of acquisition is denoised, to obtain road B-scan picture signal inhibition
Signal after noise.Wherein, the method any one of B-scan picture signal being reconstructed includes:
S21, EEMD decomposition is carried out for one B-scan picture signal { x (t), t=1,2 ..., N }, obtain from high frequency to
K IMF component c of low frequency arrangement1(t)、c2(t)、…、cK(t).Wherein,
Wherein K is the number for the IMF component that the number decomposed namely EEMD are decomposed, c1(t)、c2(t)、…、cKIt (t) is point
The IMF component arranged slave high frequency to low frequency that solution obtains, r (t) are to decompose the survival function finally obtained.
S22, the arrangement entropy for calculating each IMF component in step 2.Since frequency is higher, arrangement entropy is bigger, therefore arranges
The descending arrangement of entropy.
S23, according to the arrangement entropy of each IMF component, selected threshold Th determines that noise signal corresponds to IMF and echo signal pair
Answer separation k, 1≤k≤K of IMF, the separation k obtained according to step, using k-th and k-th later IMF component into
Row reconstruct, the signal x ' (t) after being denoised.K-th and k-th later IMF component be and echo signal (non-noise letter
Number) corresponding IMF component, the IMF component before k-th is IMF component corresponding with noise signal.Wherein,
Wherein x ' (t) is to inhibit the road noise Hou Gai B-scan picture signal.
Specifically, the preset value successively can be compared with the arrangement entropy of each IMF component, when k-th of IMF component
Arrangement entropy be less than or equal to the preset value when, each IMF component after k and k is little as the arrangement entropy
In the IMF component of preset value.
S3, the signal after the denoising of each road is reconfigured, the two-dimentional B-scan picture signal X' after the noise that is inhibited
∈RM×N。
In the step S21 of the present embodiment, one of Gpr Signal EEMD decomposition method is as follows:
S211, for one of original signal x (t), be separately added into preset T noise signal, obtain T signals and associated noises,
Wherein:
xi(t)=x (t)+ni(t) i=1,2 ..., T
Wherein xiIt (t) is i-th of signals and associated noises, ni(t) it is the noise being added in i-th signals and associated noises, be mean value is 0,
Standard deviation is the white Gaussian noise of constant.
S212, to xi(t) EMD decomposition is carried out, a series of IMF components are obtained, in which:
Wherein K is the quantity of IMF component, ci,p(t) p-th of IMF component of i-th of signals and associated noises, ri(t) contain for i-th
The survival function of noise cancellation signal.
S213, it is averaged to the correspondence IMF component that T signals and associated noises decompose, obtains the IMF component of EEMD decomposition
Are as follows:
Wherein cp(t) pass through p-th of IMF component that EEMD is decomposed for original signal.
Original signal x (t) may finally be indicated by what EEMD was decomposed are as follows:
Wherein r (t) is final survival function, represents the average tendency of original signal.
In the step S22 of the present embodiment, the arrangement entropy calculation method of each IMF component is as follows:
S221, the IMF component { c arrived for decompositionp(i), i=1,2 ..., K } phase space reconfiguration is carried out, obtain square
Battle array:
Wherein, i=1,2 ... Q, m and λ are respectively Embedded dimensions and delay time, and Q is to reconstruct vector in phase space reconstruction
Number, Q=N- (m-1) λ；
S222, component (c will be reconstructedp(i),cp(i+λ),…,cp[i+ (m-1) λ]) it is arranged according to ascending order, as follows:
cp[i+(j1-1)λ]≤cp[i+(j2-1)λ]≤…≤cp[i+(jm-1)λ]
In formula, j1,j2,…,jmIndicate the index of each element column in reconstruct component.
Accordingly, for reconstruct vector c any in phase space reconstructionp(i), available to reflect the one of its element size sequence
Group code sequence S (g)=(j1,j2,…,jm), wherein g=1,2 ..., q, q≤m！.M different symbol j1,j2,…,jmAltogether
There is m！The different symbol sebolic addressing of kind, S (g) is m！Different one of the symbol sebolic addressing of kind；
S223, the Probability p for calculating the appearance of each symbol sebolic addressing1,p2,…,pq, and according to the following formula sequence of calculation { cp
(i), i=1,2 ..., K arrangement entropy Hp(m):
In actual treatment, those skilled in the art are accustomed to Hp(m) normalized is done, using normalized arrangement entropy as row
The end value of column entropy.Wherein, work as pg=1/m！When, Hp(m) reach maximum value ln (m！), Hp(m) use is normalized
Following formula carry out:
Hp=Hp(m)/ln(m！).
The B-scan image for generating Ground Penetrating Radar is emulated using FDTD method, as shown in Figure 2.Simulation parameters are as follows:
(1) underground medium is concrete, and relative dielectric constant 6.0, center of antenna frequency is 900MHz；
(2) simulating area width is 3m, depth 2m；Three targets are ideal cylindrical conductor, radius 0.2m, water
Prosposition sets respectively 0.9m, 1.5m and 2.1m, and depth is 0.6m；There is an a length of 1m at depth 1.5m, width is the air of 0.4m
The rectangular area of filling；
(3) B-scan image shares 80, and per pass has 2036 sampled points；
Processing of making an uproar is added to the Ground Penetrating Radar B-scan image of emulation, obtains noisy image, signal-to-noise ratio 0.985dB such as schemes
Shown in 3.
EEMD decomposition, each IMF component such as Fig. 4 institute that original signal and decomposition obtain are carried out to the 40th signals and associated noises
Show.
The arrangement entropy for calculating each IMF component determines that noise corresponds to the separation of IMF IMF corresponding with echo signal, step
It is as follows:
(1) the arrangement entropy for each IMF component that EEMD is decomposed is calculated；
(2) setting threshold value Th is 0.4, is successively compared the arrangement entropy of each IMF component with threshold value, obtains noise signal
IMF separation k with echo signal is 5；
(3) the separation k=5 obtained according to step (2) is reconstructed the 5th and its subsequent IMF component, obtains
Signal after denoising, as shown in Figure 5.
To adding all road signals after making an uproar to handle, the ground penetrating radar image after the noise that is inhibited, signal-to-noise ratio is
15.385dB as shown in Figure 6.
It is the one of the noise reduction system of the Ground Penetrating Radar B-scan image of the invention based on EEMD and arrangement entropy with reference to Fig. 7
The functional block diagram of embodiment, the noise reduction system of the present embodiment include signal acquisition module 71, signal denoising module 72 and signal also
Former module 73.
Signal acquisition module 71 obtains Ground Penetrating Radar two dimension B-scan picture signal X ∈ RM×N, signal denoising module 72, to obtaining
Every one of B-scan picture signal taken is denoised, to obtain the signal after the road B-scan picture signal inhibits noise, letter
Number recovery module 73 reconfigures the signal after the denoising of each road, the two-dimentional B-scan image letter after the noise that is inhibited
Number.
Wherein, signal denoising module 72 decomposes submodule, arrangement entropy computational submodule and signal weight using following EEMD
Every one of B-scan picture signal is reconstructed in structure submodule.EEMD decomposes submodule to any one of B-scan picture signal { x
(t), t=1,2 ..., N } EEMD decomposition is carried out, obtain the K IMF component c arranged from high frequency to low frequency1(t)、c2(t)、…、cK
(t), arrangement entropy computational submodule calculates the arrangement entropy that step EEMD decomposes each IMF component in submodule, signal reconstruction submodule
Block chooses arrangement entropy no more than the IMF component of preset value to reconstruct, and the signal x ' (t) after being denoised, x ' (t) are arrangement entropy
Value is not more than the sum of the IMF component of preset value.
In the present embodiment, it specifically includes noise adding unit, EMD decomposition unit and IMF transformation that EEMD, which decomposes submodule,
Unit.Noise adding unit is separately added into preset T noise signal into x (t), obtains T signals and associated noises, and EMD decomposes single
Member carries out EMD decomposition to each signals and associated noises respectively, obtains the IMF component of each signals and associated noises, IMF converter unit is to T
The correspondence IMF component that signals and associated noises decompose is averaged, and the IMF component of EEMD decomposition is obtained.
In the present embodiment, for any one x (t), it is IMF points each using the calculating of following units to arrange entropy computational submodule
The arrangement entropy of amount:
Phase space reconfiguration unit carries out phase space reconfiguration for each IMF component arrived for decomposition, obtains matrix:
Wherein, i=1,2 ... Q, m and λ are respectively Embedded dimensions and delay time, and Q is to reconstruct vector in phase space reconstruction
Number, Q=N- (m-1) λ；
Symbol sebolic addressing acquiring unit, for component (c will to be reconstructedp(i),cp(i+λ),…,cp[i+ (m-1) λ]) according to ascending order
Arrangement, as follows:
cp[i+(j1-1)λ]≤cp[i+(j2-1)λ]≤…≤cp[i+(jm-1)λ]
In formula, j1,j2,…,jmIndicate the index of each element column in reconstruct component；
For reconstruct vector c each in phase space reconstructionp(i), one group of symbol for reflecting its element size sequence is obtained respectively
Number sequence S (g)=(j1,j2,…,jm), wherein g=1,2 ..., q, q≤m！；
Entropy computing unit is arranged, for calculating the Probability p of each symbol sebolic addressing appearance1,p2,…,pq, and according to following
The formula sequence of calculation { cp(i), i=1,2 ..., K arrangement entropy Hp(m):
Entropy updating unit is arranged, for calculated arrangement entropy H in entropy computing unit will to be arrangedp(m) place is normalized
New arrangement entropy is updated to after reason, the normalized formula of new arrangement entropy are as follows:
Hp=Hp(m)/ln(m！).
The embodiment of the present invention is described with above attached drawing, but the invention is not limited to above-mentioned specific
Embodiment, the above mentioned embodiment is only schematical, rather than restrictive, those skilled in the art
Under the inspiration of the present invention, without breaking away from the scope protected by the purposes and claims of the present invention, it can also make very much
Form, all of these belong to the protection of the present invention.
Claims (8)
1. a kind of noise-reduction method of the Ground Penetrating Radar B-scan image based on EEMD and arrangement entropy, which is characterized in that including following step
It is rapid:
S1, Ground Penetrating Radar two dimension B-scan picture signal X ∈ R is obtainedM×N, wherein M is road number, and N is the sampling number of every track data；
S2, every one of B-scan picture signal of acquisition is denoised, inhibits noise to obtain the road B-scan picture signal
Signal afterwards；Wherein, the method denoised for any one of B-scan picture signal includes:
S21, EEMD decomposition is carried out for the road B-scan picture signal { x (t), t=1,2 ..., N }, obtained from high frequency to low frequency
K IMF component c of arrangement1(t)、c2(t)、…、cK(t)；
S22, the arrangement entropy for calculating each IMF component in step S21；
S23, selection arrangement entropy are reconstructed no more than the IMF component of preset value, the signal x ' (t) after being denoised, x ' (t)
It is not more than the sum of the IMF component of preset value for arrangement entropy；
S3, the signal after the denoising of each road is reconfigured, the two-dimentional B-scan picture signal X' ∈ R after the noise that is inhibitedM ×N；
In the step S22, for any one x (t), the arrangement entropy calculation method of each IMF component is as follows:
S221, each IMF component obtained for decomposition carry out phase space reconfiguration, obtain matrix:
Wherein, i=1,2 ... Q, m and λ are respectively Embedded dimensions and delay time, and Q is that vector number is reconstructed in phase space reconstruction,
Q=N- (m-1) λ；
S222, component (c will be reconstructedp(i),cp(i+λ),…,cp[i+ (m-1) λ]) it is arranged according to ascending order, as follows:
cp[i+(j1-1)λ]≤cp[i+(j2-1)λ]≤…≤cp[i+(jm-1)λ]
In formula, j1,j2,…,jmIndicate the index of each element column in reconstruct component；
For reconstruct vector c each in phase space reconstructionp(i), the group code sequence for reflecting its element size sequence is obtained respectively
S (g)=(j1,j2,…,jm), wherein g=1,2 ..., q, q≤m！；
S223, the Probability p for calculating the appearance of each symbol sebolic addressing1,p2,…,pq, and according to the following formula sequence of calculation { cp(i),i
=1,2 ..., K arrangement entropy Hp(m):
2. noise-reduction method according to claim 1, which is characterized in that specific step is as follows by the S21:
S211, it is separately added into preset T noise signal into x (t), obtains T signals and associated noises, wherein
xi(t)=x (t)+ni(t),
In formula, i=1,2 ..., T, xiIt (t) is i-th of signals and associated noises, niIt (t) is the noise being added in i-th of signals and associated noises, ni
(t) be mean value be 0, standard deviation be constant white Gaussian noise；
S212, EMD decomposition is carried out to each signals and associated noises respectively, obtains the IMF component of each signals and associated noises；
S213, it is averaged using following formula to the correspondence IMF component that T signals and associated noises decompose, obtains EEMD decomposition
IMF component；
In formula, cp(t) pass through p-th of IMF component that EEMD is decomposed, c for x (t)i,p(t) i-th of signals and associated noises passes through EMD
Decompose p-th obtained of IMF component, p=1,2,3 ..., K.
3. noise-reduction method according to claim 1, which is characterized in that after the step S223 further include:
S224, by arrangement entropy H calculated in S223p(m) new arrangement entropy, new arrangement are updated to after being normalized
The normalized formula of entropy are as follows:
Hp=Hp(m)/ln(m！).
4. noise-reduction method according to claim 1, which is characterized in that c in step S211(t)、c2(t)、…、cK(t) for by
It arranges according to from high frequency to low frequency, is specifically included the following steps in step S23:
The preset value is successively compared with the arrangement entropy of each IMF component, when the arrangement entropy of k-th of IMF component is small
When the preset value, the IMF of preset value is not more than using each IMF component after k and k as the arrangement entropy
Component.
5. a kind of noise reduction system of the Ground Penetrating Radar B-scan image based on EEMD and arrangement entropy characterized by comprising
Signal acquisition module, for obtaining Ground Penetrating Radar two dimension B-scan picture signal X ∈ RM×N, wherein M is road number, and N is per pass
The sampling number of data；
Signal denoising module, for being denoised to every one of B-scan picture signal of acquisition, to obtain the road B-scan figure
Signal after inhibiting noise as signal；
Signals revivification module, for being reconfigured to the signal after the denoising of each road, the two-dimentional B-scan after the noise that is inhibited
Picture signal X' ∈ RM×N；
Wherein, signal denoising module is handled any one of B-scan picture signal using following submodules:
EEMD decomposes submodule, for carrying out EEMD decomposition for one of B-scan picture signal { x (t), t=1,2 ..., N }, obtains
To the K IMF component c arranged from high frequency to low frequency1(t)、c2(t)、…、cK(t)；
Entropy computational submodule is arranged, the arrangement entropy of each IMF component in submodule is decomposed for calculating step EEMD；
Signal reconstruction submodule reconstructs, the letter after being denoised for choosing arrangement entropy no more than the IMF component of preset value
Number x ' (t), x ' (t) are the sum of the IMF component for arranging entropy and being not more than preset value；
For any one x (t), the arrangement entropy that entropy computational submodule calculates each IMF component using following units is arranged:
Phase space reconfiguration unit, each IMF component for obtaining for decomposition carry out phase space reconfiguration, obtain matrix:
Wherein, i=1,2 ... Q, m and λ are respectively Embedded dimensions and delay time, and Q is that vector number is reconstructed in phase space reconstruction,
Q=N- (m-1) λ；
Symbol sebolic addressing acquiring unit, for component (c will to be reconstructedp(i),cp(i+λ),…,cp[i+ (m-1) λ]) it is arranged according to ascending order
Column, as follows:
cp[i+(j1-1)λ]≤cp[i+(j2-1)λ]≤…≤cp[i+(jm-1)λ]
In formula, j1,j2,…,jmIndicate the index of each element column in reconstruct component；
For reconstruct vector c each in phase space reconstructionp(i), the group code sequence for reflecting its element size sequence is obtained respectively
S (g)=(j1,j2,…,jm), wherein g=1,2 ..., q, q≤m！；
Entropy computing unit is arranged, for calculating the Probability p of each symbol sebolic addressing appearance1,p2,…,pq, and according to following formula
The sequence of calculation { cp(i), i=1,2 ..., K arrangement entropy Hp(m):
6. noise reduction system according to claim 5, which is characterized in that the EEMD decomposes submodule and specifically includes:
Noise adding unit is used to be separately added into preset T noise signal into x (t), obtains T signals and associated noises, wherein
xi(t)=x (t)+ni(t),
In formula, i=1,2 ..., T, xiIt (t) is i-th of signals and associated noises, niIt (t) is the noise being added in i-th of signals and associated noises, ni
(t) be mean value be 0, standard deviation be constant white Gaussian noise；
EMD decomposition unit obtains IMF points of each signals and associated noises for carrying out EMD decomposition respectively to each signals and associated noises
Amount；
IMF converter unit is obtained for being averaged using following formula to the correspondence IMF component that T signals and associated noises decompose
The IMF component decomposed to EEMD；
In formula, cp(t) pass through p-th of IMF component that EEMD is decomposed, c for x (t)i,p(t) i-th of signals and associated noises passes through EMD
Decompose p-th obtained of IMF component, p=1,2,3 ..., K.
7. noise reduction system according to claim 5, which is characterized in that arrangement entropy computational submodule further include:
Entropy updating unit is arranged, for calculated arrangement entropy H in entropy computing unit will to be arrangedp(m) after being normalized more
It is newly new arrangement entropy, the normalized formula of new arrangement entropy are as follows:
Hp=Hp(m)/ln(m！).
8. noise reduction system according to claim 5, which is characterized in that specifically comprising such as lower die in signal reconstruction submodule
Block:
The preset value is successively compared with the arrangement entropy of each IMF component, when the arrangement entropy of k-th of IMF component is small
When the preset value, the IMF of preset value is not more than using each IMF component after k and k as the arrangement entropy
Component.
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