CN107480619A - The noise-reduction method and system of GPR B-scan image based on EEMD and arrangement entropy - Google Patents
The noise-reduction method and system of GPR B-scan image based on EEMD and arrangement entropy Download PDFInfo
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Abstract
The invention discloses a kind of noise-reduction method and system of the GPR B-scan image based on EEMD and arrangement entropy, GPR two dimension B-scan picture signal is obtained first, then denoising is carried out to every one of B-scan picture signal of acquisition, to obtain the signal after the road B-scan picture signal suppresses noise, finally the signal after each road denoising is reconfigured, the two-dimentional B-scan picture signal after the noise that is inhibited；Wherein, the method for denoising is carried out for any one of B-scan picture signal to be included：EEMD decomposition is carried out for the road B-scan picture signal, the K IMF component arranged from high frequency to low frequency is obtained, calculates the arrangement entropy of each IMF components, choose arrangement entropy no more than the IMF components of preset value to reconstruct, obtain the signal after denoising.The present invention solves signal mode Aliasing Problem present in EMD decomposition, can effectively reduce noise.
Description
Technical field
The present invention relates to digital processing field is belonged to, the B-scan image procossing of GPR is related specifically to, specifically
The noise-reduction method and system of GPR B-scan image based on EEMD and arrangement entropy.
Background technology
GPR is a kind of discontinuity using underground medium come effective detection method of Underground target, extensively
Be applied to the field such as geology, resource, environment, engineering and military affairs.During actual detection, because underground medium structure is answered
Miscellaneous, physical parameter difference and the presence of noise jamming, the echo of GPR is unavoidably by noise pollution so that echo is believed
Number have non-stationary, nonlinear feature.Noise pollution causes certain difficulty to follow-up object detection and recognition, therefore visits
The noise suppressed of ground radar is particularly important for follow-up data processing.
Hilbert-Huang transform (Hilbert-Huang transform, HHT) is that one kind analyzes non-linear, non-stationary letter
Number new method, be suitable for handling the B-scan image of GPR.B-scan is to include the echo-signal of scanning
In two dimensional surface, abscissa represents the horizontal displacement direction of scanning, and ordinate represents the depth direction of scanning.This method handles B
During scan image, by empirical mode decomposition (Empirical mode decomposition, EMD) by signal decomposition to be intrinsic
Mode function (Intrinsic mode function, IMF), it can be obtained preferably when handling non-stationary, nonlinear signal
Effect.Although EMD methods have many advantages, but modal overlap in decomposition be present, cause to include in some IMF component
The signal of different scale, or similar magnitude signal are present in different IMF components, have impact on noise to a certain extent
Inhibition, cause to cause inhibition poor.
The content of the invention
The technical problem to be solved in the present invention is, presses down for above-mentioned EMD conversion when handling GPR B-scan image
The technological deficiency of effect processed difference, there is provided a kind of noise-reduction method of GPR B-scan image based on EEMD and arrangement entropy and
System.
According to the wherein one side of the present invention, the present invention is its technical problem of solution, there is provided one kind is based on EEMD and row
The noise-reduction method of the GPR B-scan image of row entropy, comprises the following steps：
S1, obtain GPR two dimension B-scan picture signal X ∈ RM×N, wherein M is road number, and N is the sampling per track data
Points；
S2, every one of B-scan picture signal to acquisition carry out denoising, are suppressed with obtaining the road B-scan picture signal
Signal after noise；Wherein, the method for denoising is carried out for any one of B-scan picture signal to be included：
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 components c of low frequency arrangement1(t)、c2(t)、…、cK(t)；
The arrangement entropy of each IMF components in S22, calculation procedure S21；
S23, selection arrangement entropy are reconstructed no more than the IMF components of preset value, obtain the signal x ' (t) after denoising,
X ' (t) is the IMF component sums that arrangement entropy is not more than preset value；
S3, the signal after each road denoising is reconfigured, the two-dimentional B-scan picture signal X' after the noise that is inhibited
∈RM×N。
Further, comprised the following steps that in the S21 of the noise-reduction method of the present invention：
S211, default T noise signal is separately added into x (t), obtains T signals and associated noises, wherein
xi(t)=x (t)+ni(t),
In formula, i=1,2 ..., T, xi(t) it is i-th of signals and associated noises, ni(t) made an uproar for what is added in i-th of signals and associated noises
Sound, ni(t) it is that average is 0, standard deviation is the white Gaussian noise of constant；
S212, EMD decomposition is carried out respectively to each signals and associated noises, obtain the IMF components of each signals and associated noises；
S213, the corresponding IMF components for decomposing to obtain to T signals and associated noises using following formula are averaged, and obtain EEMD
The IMF components of decomposition；
In formula, cp(t) p-th of IMF component for decomposing to obtain by EEMD for x (t), ci,p(t) i-th of signals and associated noises warp
Cross p-th of IMF component that EMD decomposes to obtain, p=1,2,3 ..., K.
Further, in the step S22 of the noise-reduction method of the present invention, for any one x (t), the row of each IMF components
Row entropy computational methods are as follows：
S221, each IMF components arrived for decomposition carry out phase space reconfiguration, obtain matrix：
Wherein, i=1,2 ... Q, m and λ are respectively Embedded dimensions and time delay, and Q is that vector is reconstructed 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]) arranged according to ascending order, it is as follows：
cp[i+(j1-1)λ]≤cp[i+(j2-1)λ]≤…≤cp[i+(jm-1)λ]
In formula, j1,j2,…,jmRepresent the index of each element column in reconstruct component；
For each vectorial c of reconstruct in phase space reconstructionp(i) one group of symbol for reflecting its element size order, 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, also include after the step S223 of the noise-reduction method of the present invention：
S224, the arrangement entropy H that will be calculated in S223p(m) new arrangement entropy is updated to after being normalized, new
Arrangement entropy normalized formula be：
Hp=Hp(m)/ln(m！).
Further, in the noise-reduction method of the present invention, c in step S211(t)、c2(t)、…、cK(t) it is according to from height
Frequency arranges to low frequency, is specifically comprised the following steps in step S23：
By the preset value successively compared with the arrangement entropy of each IMF components, 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 using each IMF components after k and k as the arrangement entropy
IMF components.
In order to solve the above technical problems, present invention also offers a kind of GPR B-scan based on EEMD and arrangement entropy
The noise reduction system of image, including：
Signal acquisition module, for obtaining GPR two dimension B-scan picture signal X ∈ RM×N, wherein M is road number, and N is
Sampling number per track data；
Signal denoising module, for carrying out denoising to every one of B-scan picture signal of acquisition, swept with obtaining road B
Retouch picture signal and suppress the signal after noise；
Signals revivification module, for being reconfigured to the signal after each road denoising, 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, obtain the K IMF components c arranged from high frequency to low frequency1(t)、c2(t)、…、cK(t)；
Entropy calculating sub module is arranged, the arrangement entropy of each IMF components in submodule is decomposed for calculation procedure EEMD；
Signal reconstruction submodule, reconstructed for choosing arrangement entropy no more than the IMF components of preset value, after obtaining denoising
Signal x ' (t), x ' (t) be arrangement entropy be not more than preset value IMF component sums.
Further, in the noise reduction system of the present invention, EEMD decomposes submodule and specifically included：
Noise adding device, for being separately added into default T noise signal into x (t), T signals and associated noises are obtained, its
In
xi(t)=x (t)+ni(t),
In formula, i=1,2 ..., T, xi(t) it is i-th of signals and associated noises, ni(t) made an uproar for what is added in i-th of signals and associated noises
Sound, ni(t) it is that average is 0, standard deviation is the white Gaussian noise of constant；
EMD resolving cells, for carrying out EMD decomposition respectively to each signals and associated noises, obtain the IMF of each signals and associated noises
Component；
IMF converter units, the corresponding IMF components for decomposing to obtain to T signals and associated noises using following formula are put down
, the IMF components of EEMD decomposition are obtained；
In formula, cp(t) p-th of IMF component for decomposing to obtain by EEMD for x (t), ci,p(t) i-th of signals and associated noises warp
Cross p-th of IMF component that EMD decomposes to obtain, p=1,2,3 ..., K.
Further, in the noise reduction system of the present invention, for any one x (t), under arrangement entropy calculating sub module utilizes
State the arrangement entropy that unit calculates each IMF components：
Phase space reconfiguration unit, phase space reconfiguration is carried out for each IMF components arrived for decomposition, obtains matrix：
Wherein, i=1,2 ... Q, m and λ are respectively Embedded dimensions and time delay, and Q is that vector is reconstructed 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, it is as follows：
cp[i+(j1-1)λ]≤cp[i+(j2-1)λ]≤…≤cp[i+(jm-1)λ]
In formula, j1,j2,…,jmRepresent the index of each element column in reconstruct component；
For each vectorial c of reconstruct in phase space reconstructionp(i) one group of symbol for reflecting its element size order, 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 the noise reduction system of the present invention, arrangement entropy calculating sub module also includes：
Entropy updating block is arranged, for the arrangement entropy H calculated 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 is：
Hp=Hp(m)/ln(m！).
Further, in the noise reduction system of the present invention, specifically following module is included in signal reconstruction submodule：
By the preset value successively compared with the arrangement entropy of each IMF components, 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 using each IMF components after k and k as the arrangement entropy
IMF components.
Implement the noise-reduction method and system of the GPR B-scan image based on EEMD and arrangement entropy of the present invention, have
Following beneficial effect：The present invention is decomposed using EEMD methods to Gpr Signal, obtains what is arranged from high frequency to low frequency
IMF, solve signal mode Aliasing Problem present in EMD decomposition, can effectively reduce noise.And it is further, calculating
During the arrangement entropy of each IMF components, determine that noise signal corresponds to IMF IMFs corresponding with echo signal separation by preset value, enter
And IMF corresponding to echo signal is reconstructed, it can effectively suppress noise, more retain target information.
Brief description of the drawings
Below in conjunction with drawings and Examples, the invention will be further described, in accompanying drawing：
Fig. 1 is an embodiment of the noise-reduction method of the GPR B-scan image based on EEMD and arrangement entropy of the present invention
Flow chart；
Fig. 2 is the original B-scan picture signal of GPR；
Fig. 3 is to add the image after making an uproar to original B-scan image；
Fig. 4 is to add the 40th signal and its EEMD exploded views after making an uproar；
Fig. 5 is the 40th signals and associated noises and suppresses the signal after noise；
Fig. 6 is the image to being reconfigured after all road signals progress denoising in Fig. 3；
Fig. 7 is an embodiment of the noise reduction system of the GPR B-scan image based on EEMD and arrangement entropy of the present invention
Theory diagram.
Embodiment
In order to which technical characteristic, purpose and the effect of the present invention is more clearly understood, now compares accompanying drawing and describe in detail
The embodiment of the present invention.
As shown in figure 1, it is the noise-reduction method based on EEMD and the GPR B-scan image for arranging entropy of the invention
The flow chart of one embodiment.In the noise-reduction method of the present embodiment, following steps is included：
S1, obtain GPR two dimension B-scan picture signal X ∈ RM×N, wherein M is road number, and N is the sampling per track data
Points.
S2, every one of B-scan picture signal to acquisition carry out denoising, are suppressed with obtaining the road B-scan picture signal
Signal after noise.Wherein, the method being reconstructed for any one of B-scan picture signal includes：
S21, carry out EEMD decomposition for one B-scan picture signal { x (t), t=1,2 ..., N }, obtain from high frequency to
K IMF components c of low frequency arrangement1(t)、c2(t)、…、cK(t).Wherein,
Wherein K be decompose number, namely EEMD decompose IMF components number, c1(t)、c2(t)、…、cK(t) it is point
The IMF components arranged from high frequency to low frequency that solution obtains, r (t) are to decompose the survival function finally obtained.
The arrangement entropy of each IMF components in S22, calculation procedure 2.Because frequency is higher, arrangement entropy is bigger, therefore arranges
The descending arrangement of entropy.
S23, the arrangement entropy according to each IMF components, selected threshold Th determine that noise signal corresponds to IMF and echo signal pair
IMF separation k, 1≤k≤K, the separation k obtained according to step are answered, is entered using k-th and k-th later IMF component
Row reconstruct, obtains the signal x ' (t) after denoising.K-th and k-th later IMF component be and echo signal (non-noise letter
Number) corresponding to IMF components, the IMF components before k-th are IMF components corresponding with noise signal.Wherein,
Wherein x ' (t) is suppression noise Hou Gai roads B-scan picture signal.
Specifically, can be by the preset value successively compared with the arrangement entropy of each IMF components, when k-th of IMF component
Arrangement entropy when being less than or equal to the preset value, each IMF components after k and k is little as the arrangement entropy
In the IMF components of preset value.
S3, the signal after each road denoising 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 primary signal x (t), be separately added into default T noise signal, obtain T signals and associated noises,
Wherein：
xi(t)=x (t)+ni(t) i=1,2 ..., T
Wherein xi(t) it is i-th of signals and associated noises, ni(t) it is the noise added in i-th of signals and associated noises, it is that average is 0,
Standard deviation is the white Gaussian noise of constant.
S212, to xi(t) EMD decomposition is carried out, obtains a series of IMF components, wherein：
Wherein K be IMF components quantity, 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, the corresponding IMF components for decomposing to obtain to T signals and associated noises are averaged, and obtain the IMF components of EEMD decomposition
For：
Wherein cp(t) p-th of IMF component for decomposing to obtain by EEMD for primary signal.
Primary signal x (t) may finally be expressed as by what EEMD was decomposed：
Wherein r (t) is final survival function, represents the average tendency of primary signal.
In the step S22 of the present embodiment, the arrangement entropy computational methods of each IMF components are as follows：
S221, the IMF components { 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 time delay, and Q is that vector is reconstructed 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]) arranged according to ascending order, it is as follows：
cp[i+(j1-1)λ]≤cp[i+(j2-1)λ]≤…≤cp[i+(jm-1)λ]
In formula, j1,j2,…,jmRepresent the index of each element column in reconstruct component.
Accordingly, for any vectorial c of reconstruct in phase space reconstructionp(i), can obtain reflecting the one of its element size order
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！One kind in the different 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 row entropy.Wherein, p is worked asg=1/m！When, Hp(m) maximum ln (m are reached！), Hp(m) use is normalized
Following formula are carried out：
Hp=Hp(m)/ln(m！).
The B-scan image for producing GPR is emulated using FDTD methods, as shown in Figure 2.Simulation parameters are as follows：
(1) underground medium is concrete, and its relative dielectric constant is 6.0, and 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 puts respectively 0.9m, 1.5m and 2.1m, and depth is 0.6m；There are an a length of 1m, a width of 0.4m air at depth 1.5m
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 GPR B-scan image of emulation, obtains noisy image, its signal to noise ratio is 0.985dB, is such as schemed
Shown in 3.
40th signals and associated noises are carried out with EEMD decomposition, primary signal is with decomposing obtained each IMF components such as Fig. 4 institutes
Show.
The arrangement entropy of each IMF components is calculated, determines that noise corresponds to IMF IMFs corresponding with echo signal separation, step
It is as follows：
(1) calculating EEMD decomposes the arrangement entropy of obtained each IMF components；
(2) it is 0.4 to set threshold value Th, and the arrangement entropy of each IMF components is obtained into noise signal compared with threshold value successively
IMF separations k with echo signal is 5；
(3) the separation k=5 obtained according to step (2), IMF components to the 5th and behind are reconstructed, obtained
Signal after denoising, as shown in Figure 5.
Pair plus all road signals after making an uproar handle, the ground penetrating radar image after the noise that is inhibited, its signal to noise ratio is
15.385dB as shown in Figure 6.
With reference to figure 7, it is the one of the noise reduction system based on EEMD and the GPR B-scan image for arranging entropy of the invention
The theory 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 GPR two dimension B-scan picture signal X ∈ RM×N, signal denoising module 72, to obtaining
Every one of B-scan picture signal taken carries out denoising, to obtain the signal after the road B-scan picture signal suppresses noise, letter
Number recovery module 73, is reconfigured to the signal after each road denoising, the two-dimentional B-scan image letter after the noise that is inhibited
Number.
Wherein, signal denoising module 72 decomposes submodule, arrangement entropy calculating sub module and signal weight using following EEMD
Every one of B-scan picture signal is reconstructed 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 components c arranged from high frequency to low frequency1(t)、c2(t)、…、cK
(t) the arrangement entropy that entropy calculating sub module calculation procedure EEMD decomposes each IMF components in submodule, signal reconstruction submodule, are arranged
Block chooses arrangement entropy no more than the IMF components of preset value to reconstruct, and obtains the signal x ' (t) after denoising, and x ' (t) is arrangement entropy
IMF component sum of the value no more than preset value.
In the present embodiment, EEMD decomposes submodule specifically comprising noise adding device, EMD resolving cells and IMF conversion
Unit.Noise adding device is separately added into default T noise signal into x (t), obtains T signals and associated noises, and EMD decomposes single
Member carries out EMD decomposition respectively to each signals and associated noises, obtains the IMF components of each signals and associated noises, IMF converter units are to T
The corresponding IMF components that signals and associated noises decompose to obtain are averaged, and obtain the IMF components of EEMD decomposition.
In the present embodiment, calculated using following units each IMF points for any one x (t), arrangement entropy calculating sub module
The arrangement entropy of amount：
Phase space reconfiguration unit, phase space reconfiguration is carried out for each IMF components arrived for decomposition, obtains matrix：
Wherein, i=1,2 ... Q, m and λ are respectively Embedded dimensions and time delay, and Q is that vector is reconstructed 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, it is as follows：
cp[i+(j1-1)λ]≤cp[i+(j2-1)λ]≤…≤cp[i+(jm-1)λ]
In formula, j1,j2,…,jmRepresent the index of each element column in reconstruct component；
For each vectorial c of reconstruct in phase space reconstructionp(i) one group of symbol for reflecting its element size order, 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 block is arranged, for the arrangement entropy H calculated 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 is：
Hp=Hp(m)/ln(m！).
Embodiments of the invention are described above in conjunction with accompanying drawing, but the invention is not limited in above-mentioned specific
Embodiment, above-mentioned embodiment is only schematical, rather than restricted, one of ordinary skill in the art
Under the enlightenment of the present invention, in the case of present inventive concept and scope of the claimed protection is not departed from, it can also make a lot
Form, these are belonged within the protection of the present invention.
Claims (10)
1. a kind of noise-reduction method of the GPR B-scan image based on EEMD and arrangement entropy, it is characterised in that including following step
Suddenly：
S1, obtain GPR two dimension B-scan picture signal X ∈ RM×N, wherein M is road number, and N is the sampling number per track data；
S2, every one of B-scan picture signal to acquisition carry out denoising, suppress noise to obtain the road B-scan picture signal
Signal afterwards；Wherein, the method for denoising is carried out for any one of B-scan picture signal to be included：
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 components c of arrangement1(t)、c2(t)、…、cK(t)；
The arrangement entropy of each IMF components in S22, calculation procedure S21；
S23, selection arrangement entropy are reconstructed no more than the IMF components of preset value, obtain the signal x ' (t) after denoising, x ' (t)
It is not more than the IMF component sums of preset value for arrangement entropy；
S3, the signal after each road denoising is reconfigured, the two-dimentional B-scan picture signal X' ∈ R after the noise that is inhibitedM ×N。
2. noise-reduction method according to claim 1, it is characterised in that the S21's comprises the following steps that：
S211, default T noise signal is separately added into x (t), obtains T signals and associated noises, wherein
xi(t)=x (t)+ni(t),
In formula, i=1,2 ..., T, xi(t) it is i-th of signals and associated noises, ni(t) it is the noise added in i-th of signals and associated noises, ni
(t) it is that average is 0, standard deviation is the white Gaussian noise of constant；
S212, EMD decomposition is carried out respectively to each signals and associated noises, obtain the IMF components of each signals and associated noises；
S213, the corresponding IMF components for decomposing to obtain to T signals and associated noises using following formula are averaged, and obtain EEMD decomposition
IMF components；
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<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>T</mi>
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<mo>&Sigma;</mo>
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In formula, cp(t) p-th of IMF component for decomposing to obtain by EEMD for x (t), ci,p(t) i-th of signals and associated noises passes through EMD
Decompose p-th obtained of IMF components, p=1,2,3 ..., K.
3. noise-reduction method according to claim 1, it is characterised in that in the step S22, for any one x (t),
The arrangement entropy computational methods of each IMF components are as follows：
S221, each IMF components arrived for decomposition carry out phase space reconfiguration, obtain matrix：
<mfenced open = "[" close = "]">
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<mn>...</mn>
</mtd>
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<mi>p</mi>
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<mo>(</mo>
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<mi>m</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
<mi>&lambda;</mi>
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</mrow>
</mtd>
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<mtd>
<mn>...</mn>
</mtd>
<mtd>
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<mi>c</mi>
<mi>p</mi>
</msub>
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<mo>(</mo>
<mi>Q</mi>
<mo>+</mo>
<mo>(</mo>
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<mi>m</mi>
<mo>-</mo>
<mn>1</mn>
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<mo>)</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, i=1,2 ... Q, m and λ are respectively Embedded dimensions and time delay, and Q is to reconstruct vectorial number in phase space reconstruction,
Q=N- (m-1) λ；
S222, component (c will be reconstructedp(i),cp(i+λ),…,cp[i+ (m-1) λ]) arranged according to ascending order, it is as follows：
cp[i+(j1-1)λ]≤cp[i+(j2-1)λ]≤…≤cp[i+(jm-1)λ]
In formula, j1,j2,…,jmRepresent the index of each element column in reconstruct component；
For each vectorial c of reconstruct in phase space reconstructionp(i) the group code sequence for reflecting its element size order, 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)：
<mrow>
<msub>
<mi>H</mi>
<mi>p</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>g</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>q</mi>
</munderover>
<msub>
<mi>p</mi>
<mi>g</mi>
</msub>
<mi>ln</mi>
<mi> </mi>
<msub>
<mi>p</mi>
<mi>g</mi>
</msub>
<mo>.</mo>
</mrow>
4. noise-reduction method according to claim 3, it is characterised in that also include after the step S223：
S224, the arrangement entropy H that will be calculated in S223p(m) new arrangement entropy, new arrangement are updated to after being normalized
The normalized formula of entropy is：
Hp=Hp(m)/ln(m！).
5. noise-reduction method according to claim 1, it is characterised in that c in step S211(t)、c2(t)、…、cK(t) be by
Arrange according to from high frequency to low frequency, specifically comprised the following steps in step S23：
By the preset value successively compared with the arrangement entropy of each IMF components, 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 components after k and k as the arrangement entropy
Component.
A kind of 6. noise reduction system of the GPR B-scan image based on EEMD and arrangement entropy, it is characterised in that including：
Signal acquisition module, for obtaining GPR 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 carrying out denoising to every one of B-scan picture signal of acquisition, to obtain the road B-scan figure
Suppress the signal after noise as signal；
Signals revivification module, for being reconfigured to the signal after each road denoising, 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 components c arranged from high frequency to low frequency1(t)、c2(t)、…、cK(t)；
Entropy calculating sub module is arranged, the arrangement entropy of each IMF components in submodule is decomposed for calculation procedure EEMD；
Signal reconstruction submodule, reconstructed for choosing arrangement entropy no more than the IMF components of preset value, obtain the letter after denoising
Number x ' (t), x ' (t) are the IMF component sums that arrangement entropy is not more than preset value.
7. noise reduction system according to claim 6, it is characterised in that the EEMD decomposes submodule and specifically included：
Noise adding device, for being separately added into default T noise signal into x (t), T signals and associated noises are obtained, wherein
xi(t)=x (t)+ni(t),
In formula, i=1,2 ..., T, xi(t) it is i-th of signals and associated noises, ni(t) it is the noise added in i-th of signals and associated noises, ni
(t) it is that average is 0, standard deviation is the white Gaussian noise of constant；
EMD resolving cells, for carrying out EMD decomposition respectively to each signals and associated noises, obtain IMF points of each signals and associated noises
Amount；
IMF converter units, the corresponding IMF components for decomposing to obtain to T signals and associated noises using following formula are averaged, obtained
The IMF components decomposed to EEMD；
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<msub>
<mi>c</mi>
<mi>p</mi>
</msub>
<mrow>
<mo>(</mo>
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<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>T</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</munderover>
<msub>
<mi>c</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>p</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
In formula, cp(t) p-th of IMF component for decomposing to obtain by EEMD for x (t), ci,p(t) i-th of signals and associated noises passes through EMD
Decompose p-th obtained of IMF component, p=1,2,3 ..., K.
8. noise reduction system according to claim 6, it is characterised in that for any one x (t), arrangement entropy calculates submodule
Block calculates the arrangement entropy of each IMF components using following units：
Phase space reconfiguration unit, phase space reconfiguration is carried out for each IMF components arrived for decomposition, obtains matrix：
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mi>p</mi>
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<mi>c</mi>
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</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mn>...</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mi>p</mi>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
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<mo>(</mo>
<mrow>
<mi>m</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
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</mtd>
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</mrow>
</mrow>
</mtd>
<mtd>
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</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mi>p</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>Q</mi>
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<mo>(</mo>
<mrow>
<mi>m</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, i=1,2 ... Q, m and λ are respectively Embedded dimensions and time delay, and Q is to reconstruct vectorial number 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]) arranged according to ascending order
Row, it is as follows：
cp[i+(j1-1)λ]≤cp[i+(j2-1)λ]≤…≤cp[i+(jm-1)λ]
In formula, j1,j2,…,jmRepresent the index of each element column in reconstruct component；
For each vectorial c of reconstruct in phase space reconstructionp(i) the group code sequence for reflecting its element size order, 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)：
<mrow>
<msub>
<mi>H</mi>
<mi>p</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>-</mo>
<munderover>
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<mrow>
<mi>g</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>q</mi>
</munderover>
<msub>
<mi>p</mi>
<mi>g</mi>
</msub>
<mi>ln</mi>
<mi> </mi>
<msub>
<mi>p</mi>
<mi>g</mi>
</msub>
<mo>.</mo>
</mrow>
9. noise reduction system according to claim 8, it is characterised in that arrangement entropy calculating sub module also includes：
Entropy updating block is arranged, for the arrangement entropy H calculated 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 is：
Hp=Hp(m)/ln(m！).
10. noise reduction system according to claim 6, it is characterised in that following mould is specifically included in signal reconstruction submodule
Block：
By the preset value successively compared with the arrangement entropy of each IMF components, 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 components after k and k as the arrangement entropy
Component.
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| CN113822235A (en) * | 2021-11-22 | 2021-12-21 | 中南大学 | CEEMD denoising and signal reconstructing method and device based on permutation entropy standard measurement |
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