CN106405504A - Combined shear wave transformation and singular value decomposition ground penetrating radar data denoising method - Google Patents
Combined shear wave transformation and singular value decomposition ground penetrating radar data denoising method Download PDFInfo
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- CN106405504A CN106405504A CN201610739103.9A CN201610739103A CN106405504A CN 106405504 A CN106405504 A CN 106405504A CN 201610739103 A CN201610739103 A CN 201610739103A CN 106405504 A CN106405504 A CN 106405504A
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- 238000000354 decomposition reaction Methods 0.000 title claims abstract description 35
- 238000000034 method Methods 0.000 title claims abstract description 28
- 230000009466 transformation Effects 0.000 title claims abstract description 15
- 230000000149 penetrating effect Effects 0.000 title abstract description 6
- 239000011159 matrix material Substances 0.000 claims abstract description 96
- 238000010008 shearing Methods 0.000 claims description 28
- 239000000203 mixture Substances 0.000 claims description 14
- 238000006243 chemical reaction Methods 0.000 claims description 13
- 230000001427 coherent effect Effects 0.000 claims description 8
- 230000015572 biosynthetic process Effects 0.000 claims description 6
- 238000003786 synthesis reaction Methods 0.000 claims description 6
- 238000005070 sampling Methods 0.000 claims description 4
- 238000005728 strengthening Methods 0.000 claims description 2
- 230000008569 process Effects 0.000 abstract description 8
- 238000001914 filtration Methods 0.000 abstract description 5
- 238000000926 separation method Methods 0.000 abstract 1
- 238000001514 detection method Methods 0.000 description 6
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- 238000004458 analytical method Methods 0.000 description 1
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/021—Auxiliary means for detecting or identifying radar signals or the like, e.g. radar jamming signals
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/023—Interference mitigation, e.g. reducing or avoiding non-intentional interference with other HF-transmitters, base station transmitters for mobile communication or other radar systems, e.g. using electro-magnetic interference [EMI] reduction techniques
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- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Radar Systems Or Details Thereof (AREA)
- Geophysics And Detection Of Objects (AREA)
Abstract
The invention discloses a ground penetrating radar data denoising method and aims to utilize shear wave transformation and singular value decomposition to realize noise filtering to enhance effective echo signals. According to the method, firstly, singular value decomposition is utilized to realize separation and filtering of direct waves, secondly, shear wave transformation is utilized to process the ground penetrating radar data to acquire a coefficient matrix of a transformation domain, and singular value decomposition is carried out for the coefficient matrix. If the data contains effective signals, a sparse degree is relatively high, a characteristic matrix after decomposition contains a value having a relatively large integral contribution rate; if the data only has noise, characteristic values of a characteristic value matrix are relatively average, and the characteristic values of the characteristic value matrix after decomposition are relatively uniformly dispersed for the integral contribution rate. According to the method, filtering processing on the data is carried out, shear wave inverse transformation for the data after processing is carried out, and the ground penetrating radar data after denoising is acquired.
Description
Technical field
The present invention proposes a kind of Coherent Noise in GPR Record denoising method, by using shearing wave conversion and singular value decomposition, real
Now the compacting to noise filters, and reaches the purpose strengthening effective echo-signal.
Background technology
With the development of electronic technology and computer level, the instrument data processing method of GPR is all continuous
Progressive, there is high detection efficient and high detection accuracy.This technology is continuously available application in engineering and promotes, in ore deposit
Produce resource exploration, Geologic Hazard Prospecting, geotechnical study and the various fields such as City Buried Pipeline and underground disease survey to send out
Wave important function.The signal to noise ratio carrying out useful signal during underground objects detection using ground penetrating radar exploration is higher, to underground mesh
Target detection is also higher with Position location accuracy.
Between the past few decades, wavelet transformation obtains in the data de-noising process field such as image, earthquake and GPR
Extensive application, but the direction of wavelet transformation detection is limited, the effect on driving birds is not good when curve with hyperbolic feature is detected.
In order to solve this problem, scholars propose multi-scale geometric analysis method, including warp wavelet, profile wave convert and shearing
Wave conversion etc..Wherein, shearing wave conversion is proposed by Demetrio Labate and Guo etc., than warp wavelet and profile wave convert
Directivity and openness more preferably, be successfully applied in every field through the development of last decade.
When application shearing wave conversion carries out noise reduction process to data, the selection of threshold value is larger on denoising effect impact.In order to
Improve denoising effect, the problems such as solving threshold value during real data and select the big filter effect of difficulty good, the present invention proposes a kind of knot
Close the filtering algorithm of shearing wave conversion and singular value decomposition, the random noise in compacting Coherent Noise in GPR Record, strengthen buried target
Caused effective reflected signal.
Content of the invention
The purpose of the present invention is by combined shearing wave conversion and singular value decomposition, suppresses random in Coherent Noise in GPR Record
Noise, realizes the filtering and noise reduction to Coherent Noise in GPR Record.
The present invention substantially to realize step as follows：
Step one：To GPR gathered data X0Do singular value decomposition, and by first maximum singular value zero setting, to point
Signal after solution is synthesized, and obtains data X eliminating direct wave, wherein X and X0It is all the array of N row M row, M represents and adopts
Sample road number, N represents the sampling number of each track data；
Step 2：Total Decomposition order K during setting shearing wave conversion, and variable k is set, k is the current decomposition number of plies；
Step 3：During k=1, using Laplacian pyramid method, X is decomposed, after obtaining ground floor decomposition
Low frequency coefficient matrixWith high frequency coefficient matrixOtherwise utilize the low frequency coefficient to -1 layer of kth for the Laplacian-pyramid method
MatrixDecomposed, obtained the low frequency coefficient matrix of kth layerWith high frequency coefficient matrix
Step 4：The high frequency coefficient matrix to kth layer on pseudo- pole is to latticeCarry out Fourier transformation, thus obtaining Fu
In matrix after leaf transformation
Step 5：Using band filter to the matrix in step 3Processed, redefined cartesian coordinate
The sample value of system, and obtain shearing factor matrix using two-dimentional inverse Fourier transform
Step 6：To the shearing factor matrix after decomposingUsing singular value decomposition, to all-round in keeping characteristics value matrix
Measure the larger composition of contribution rate, remove the little composition of contribution rate by zero setting, obtain new eigenvalue matrixCarry out unusual
The synthesis that value is decomposed, obtains new matrix
Step 7：Judge whether k=K sets up, set up and then stop decomposing, to low frequency coefficient matrixDivided using singular value
Solution, to measuring the larger composition of contribution rate, remove the little composition of contribution rate by zero setting in keeping characteristics value matrix, obtains newly
Eigenvalue matrixCarry out the synthesis of singular value decomposition, obtain new matrixOtherwise redirect execution step three；
Step 8：Shearing wave inverse transformation is carried out to the data after processing, obtains the data after final process
Further, in described step one, the concrete formula of singular value decomposition is：
X0=U Ω VH
Represent X0For U, Ω, VHThe multiplication of three matrixes is it is assumed that X0It is the data matrix that a size is N × M, Ω is a N row M
The non-negative diagonal matrix of row, U=[u0,u1,u2,....uN-1] it is the unitary matrice that a N row N arranges, uiIt is left singular vector, wherein
0≤i≤N-1；V=[v0,v1,v2,...,vM-1] it is the unitary matrice that a M row M arranges, vjIt is right singular vector, 0≤j≤N-1, VH
It is the associate matrix of unitary matrice, N is the number of samples of a track data, M represents road to be processed number.Assume N>M then non-negative
Diagonal matrix then can be expressed as：
λ in above formula0,λ1,λ2,...,λMThe singular value of representing matrix X, they be in matrix mathematical characteristic characterization value.Logical
Often we when using ground penetrating radar detection, as air direct wave etc. these interference ripples can be considered direct current signal, in the spatial domain
Can be represented using first right singular value vector, corresponding first eigenvalue λ0, first eigenvalue is separated, Ji Jiangzhi
Reach the background signals such as ripple to separate from radar data：
Wherein XgFor direct wave data matrix, X is the data matrix eliminating direct wave, Ω1、Ω2It is respectively the backgrounds such as direct wave
Signal data and the singular value diagonal matrix eliminating direct wave data, specific as follows：
X synthesizes, after being first eigenvalue of maximum zero setting, the data matrix eliminating direct wave obtaining.
Further, in described step 6, described singular value decomposition is For the shearing of kth layer
Coefficient matrix,ForThe multiplication of three matrixes,It is respectively a corresponding left side unusual
Matrix, eigenvalue matrix and right singular matrix, by eigenvalue matrixProcessed, to complete in keeping characteristics value matrix
The larger composition of energy contribution rate, the little composition of contribution rate is removed by zero setting, obtain new eigenvalue matrixCalculateObtain new matrixBeing calculated as of contribution rateλiIt is characterized value matrixOn middle diagonal
I value, P is characterized value matrixEigenvalue number.
Further, in described step 7, described calculating process is the same with step 6, but the number of input singular value decomposition
According to replacing with low frequency coefficient matrix.
Further, in described step 8, the concretely comprising the following steps of shearing wave inverse transformation：
Step1：Shearing wave coefficient to kth layerCarry out pseudo- pole to discrete Fourier transform, obtain
Step2：Result to Step1 gainedCarry out liftering process, obtain
Step3：RightCarry out inverse puppet pole to discrete Fourier transform, obtain the high frequency coefficient matrix of kth layer
Step4：Using Laplacian Pyramid Reconstruction algorithm, to the kth floor height frequency coefficient matrix after processingWith low frequency system
Matrix number utilizes Laplacian pyramid reconstruction algorithm, obtains the low frequency coefficient matrix of -1 layer of kth；K=k-1 is made to repeat Step1
To Step4, stop when k=0, obtain the data matrix reconstructingBy calculating the cutting kth layer of Step1 to Step3
Cut wave system matrix number to change for the high frequency coefficient matrix of kth layer, Step4 is then by the high frequency coefficient matrix of kth layer and low frequency system
Matrix number utilizes Laplacian pyramid reconstruction algorithm, obtains the low frequency coefficient matrix of -1 layer of kth；As k=K, low frequency coefficient
Matrix is the matrix after processing in step 7Otherwise the low frequency coefficient matrix of -1 layer of kth is by shearing wave coefficient during kth layer
Matrix and low frequency coefficient matrix pass through being calculated of Step1 to Step4.
Brief description
Fig. 1 is the FB(flow block) of the inventive method；
Pretreated Gpr Data figure is processed after Fig. 2 is plus makes an uproar and through step one singular value decomposition；
Fig. 3 is the comparison diagram after the inventive method and conventional shearing wave hard-threshold denoising method denoising.
Specific embodiment
Below in conjunction with concrete grammar implementation process, the present invention is described in further detail, example is served only for explaining this
Bright, it is not intended to limit the scope of the present invention.
Calculated using simulation software and produce a Gpr Data containing underground utilities target, and it is carried out plus makes an uproar, obtain
To plus the Gpr Data figure after making an uproar, as shown in Figure 2 A.Afterwards the data matrix of this section is located in accordance with the following steps
Reason：
Step one：To data X in temporal-spatial field0Do singular value decomposition, and by first eigenvalue of maximum zero setting, to point
Signal after solution is synthesized, and obtains data X eliminating direct wave, wherein X and X0It is all the array of N row M row, M represents and adopts
Sample road number, N represents the sampling number of each track data, M=100, N=512 in current data, the data display after being processed
In the Gpr Data of Fig. 2 B；
Step 2：Total Decomposition order K during setting shearing wave conversion, and variable k is set, k is the current decomposition number of plies, currently processed
Middle K=3；
Step 3：During k=1, using Laplacian pyramid method, X is decomposed, obtain low after ground floor decomposes
Frequency coefficient matrixWith high frequency coefficient matrixOtherwise utilize the low frequency coefficient to -1 layer of kth for the Laplacian-pyramid method
MatrixDecomposed, obtained the low frequency coefficient matrix of kth layerWith high frequency coefficient matrix
Step 4：The high frequency coefficient matrix to kth layer on pseudo- pole is to latticeCarry out Fourier transformation, thus obtaining Fourier
Matrix after conversion
Step 5：Using band filter to the matrix in step 3Processed, redefined cartesian coordinate system
Sample value, and obtain shearing factor matrix using two-dimentional inverse Fourier transform
Step 6：To the shearing factor matrix after decomposingUsing singular value decomposition, to tribute all can be measured in keeping characteristics value matrix
The larger composition of rate of offering, the little composition of contribution rate is removed by zero setting, obtain new eigenvalue matrixCarry out singular value to divide
The synthesis of solution, the shearing factor matrix after being processed
Step 7：Judge whether k=K sets up, set up and then stop decomposing, to low frequency coefficient matrixUsing singular value decomposition, protect
Stay in eigenvalue matrix to the larger composition of contribution rate all can be measured, the little composition of contribution rate removed by zero setting, obtain new spy
Value indicative matrixCarry out the synthesis of singular value decomposition, obtain new matrixOtherwise redirect execution step three, contribution rate η is adopted
WithCalculate, λiIt is characterized value matrixI-th value on middle diagonal, P is characterized value matrixEigenvalue
Number, currently processed in think that the value more than 10% for the contribution rate is the larger value of contribution rate, retain this part λiValue, remaining λi's
Value zero setting；
Step 8：Shearing wave inverse transformation is carried out to the data after processing, obtains the data after final process
Using the buried target effective signal enhancing method above illustrating, to Fig. 2 B process, obtain Fig. 3 A, permissible from Fig. 3 A
Find out that background signal is separated, noise is effectively neutralized, originally faint hyperbolic reflectance signature is strengthened.Fig. 3 B is employing
The Gpr Data figure that traditional hard thresholding method obtains after corresponding data matrix carries out denoising to Fig. 2 B, by contrast
Fig. 3 A and Fig. 3 B can be seen that the inventive method denoising effect preferably, and useful signal is strengthened, and buried target becomes apparent from.
To sum up, the present invention proposes a kind of denoising of Coherent Noise in GPR Record by combined shearing wave conversion and singular value decomposition
New method, filters the noise in data and strengthens useful signal.
The foregoing is only the preferred embodiments realizing the present invention, not in order to limit the present invention, all spirit in the present invention and former
Within then, any modification, equivalent substitution and improvement made etc., should be included within the scope of the present invention.
Claims (1)
1. a kind of Coherent Noise in GPR Record denoising method, for wavelet transform it is characterised in that by using shearing wave
Conversion and singular value decomposition, realize the compacting to noise in Coherent Noise in GPR Record, reach the purpose strengthening useful signal, including such as
Lower step：
Step one：To GPR gathered data X0Do singular value decomposition, and by first eigenvalue of maximum zero setting, after decomposing
Signal synthesized, obtain data X eliminating direct wave, wherein X and X0It is all the array of N row M row, M represents sampling channel
Number, N represents the sampling number of each track data；
Step 2：Total Decomposition order K during setting shearing wave conversion, and variable k is set, k is the current decomposition number of plies；
Step 3：During k=1, using Laplacian pyramid method, X is decomposed, obtain the low frequency after ground floor decomposes
Coefficient matrixWith high frequency coefficient matrixOtherwise utilize the low frequency coefficient matrix to -1 layer of kth for the Laplacian-pyramid methodDecomposed, obtained the low frequency coefficient matrix of kth layerWith high frequency coefficient matrix
Step 4：The high frequency coefficient matrix to kth layer on pseudo- pole is to latticeCarry out Fourier transformation, thus obtain Fourier becoming
Matrix after changing
Step 5：Using band filter to the matrix in step 3Processed, redefined taking out of cartesian coordinate system
Sample value, and obtain shearing factor matrix using two-dimentional inverse Fourier transform
Step 6：To the shearing factor matrix after decomposingUsing singular value decomposition, to tribute all can be measured in keeping characteristics value matrix
The larger composition of rate of offering, the little composition of contribution rate is removed by zero setting, obtain new eigenvalue matrixCarry out singular value decomposition
Synthesis, the shearing factor matrix after being processed
Step 7：Judge whether k=K sets up, set up and then stop decomposing, to low frequency coefficient matrixUsing singular value decomposition, protect
Stay in eigenvalue matrix to the larger composition of contribution rate all can be measured, the little composition of contribution rate removed by zero setting, obtain new spy
Value indicative matrixCarry out the synthesis of singular value decomposition, obtain new matrixOtherwise redirect execution step three；
Step 8：Shearing wave inverse transformation is carried out to the data after processing, obtains the data after final denoising
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109345592A (en) * | 2018-11-01 | 2019-02-15 | 中国矿业大学(北京) | Underground cavity three-dimensional coordinate extraction algorithm based on Ground Penetrating Radar |
| CN110673138A (en) * | 2019-10-09 | 2020-01-10 | 国家电网有限公司 | Ground penetrating radar image processing method based on singular value decomposition and fuzzy C mean value method |
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| EP2017647A1 (en) * | 2007-07-19 | 2009-01-21 | Consiglio Nazionale delle Ricerche | Method for processing data sensed by a synthetic aperture radar (SAR) and related remote sensing system |
| CN103399348A (en) * | 2013-08-15 | 2013-11-20 | 电子科技大学 | Denoising method for seismic signal based on Shearlet transform |
| CN105319593A (en) * | 2014-07-04 | 2016-02-10 | 中国石油化工股份有限公司 | Combined denoising method based on curvelet transform and singular value decomposition |
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| EP2017647A1 (en) * | 2007-07-19 | 2009-01-21 | Consiglio Nazionale delle Ricerche | Method for processing data sensed by a synthetic aperture radar (SAR) and related remote sensing system |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109345592A (en) * | 2018-11-01 | 2019-02-15 | 中国矿业大学(北京) | Underground cavity three-dimensional coordinate extraction algorithm based on Ground Penetrating Radar |
| CN109345592B (en) * | 2018-11-01 | 2021-09-21 | 中国矿业大学(北京) | Underground cavity three-dimensional coordinate extraction algorithm based on ground penetrating radar |
| CN110673138A (en) * | 2019-10-09 | 2020-01-10 | 国家电网有限公司 | Ground penetrating radar image processing method based on singular value decomposition and fuzzy C mean value method |
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