CN113433546A - Ground penetrating radar data enhancement method based on singular value scaling - Google Patents
Ground penetrating radar data enhancement method based on singular value scaling Download PDFInfo
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- CN113433546A CN113433546A CN202110754944.8A CN202110754944A CN113433546A CN 113433546 A CN113433546 A CN 113433546A CN 202110754944 A CN202110754944 A CN 202110754944A CN 113433546 A CN113433546 A CN 113433546A
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- 230000000149 penetrating effect Effects 0.000 title claims abstract description 65
- 238000000034 method Methods 0.000 title claims abstract description 15
- 238000000354 decomposition reaction Methods 0.000 claims abstract description 16
- 239000011159 matrix material Substances 0.000 claims description 14
- 230000008878 coupling Effects 0.000 description 3
- 238000010168 coupling process Methods 0.000 description 3
- 238000005859 coupling reaction Methods 0.000 description 3
- 238000005457 optimization Methods 0.000 description 1
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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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/885—Radar or analogous systems specially adapted for specific applications for ground probing
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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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
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Abstract
According to the method, a zero-offset mode ground penetrating radar is adopted, ground penetrating radar data obtained by B scanning is used as a basis, singular value decomposition is adopted to decompose original data, then a singular value scaling function is used to change the size of a singular value, and finally enhanced ground penetrating radar data are obtained through calculation, so that weak signals in the ground penetrating radar data are enhanced, and strong interference is weakened.
Description
Technical Field
The invention belongs to the field of computer digital image processing, and an algorithm is based on singular value decomposition, and adopts a singular value scaling function to change the size of a singular value so as to realize the data enhancement of a ground penetrating radar.
Background
The ground penetrating radar sends pulse-form high-frequency broadband electromagnetic waves to the underground, and one part of the high-frequency broadband electromagnetic waves directly reaches a receiving antenna through a transmitting antenna to form coupled waves; the coupling wave and the direct wave are often called as direct coupling waves and are often used for judging a time zero point and used as a judgment reference for the depth of an underground target body, the other part of electromagnetic waves enter the underground and are transmitted in an underground medium, when the coupling wave and the direct wave meet the underground target body with electrical difference (such as a cavity, a water bag, a loose medium and the like) or the interface of different media, the electromagnetic waves are reflected, and the reflected electromagnetic waves are received by the receiving antenna when returning to the ground. The received signals are acquired, processed and stored to form ground penetrating radar data containing underground medium information.
The ground penetrating radar data is seriously interfered by shallow direct waves and needs to be filtered. Meanwhile, the deep ground penetrating radar signal is weak, and needs to be effectively enhanced. Therefore, it is necessary to research a ground penetrating radar data enhancement method, which is to filter out shallow direct waves and enhance deep signals. In order to realize the goal, the ground penetrating radar data is decomposed into an orthogonal matrix and a singular value matrix by adopting a singular value decomposition method, and the size of a singular value is changed according to a singular value scaling function, so that the ground penetrating radar data is enhanced. Singular value decomposition is an important matrix decomposition in linear algebra, and singular value decomposition is popularization of eigenvalue decomposition on any matrix. Singular value decomposition has important application in the fields of signal processing, statistics and the like.
Disclosure of Invention
The invention aims to decompose ground penetrating radar data into an orthogonal matrix and a singular value matrix by adopting a singular value decomposition method according to the characteristics of the ground penetrating radar data, and change the size of a singular value according to a singular value scaling function to realize the enhancement of the ground penetrating radar data. The method separates effective signals from the ground penetrating radar data according to the following steps:
step (a 1): performing singular value decomposition on ground penetrating radar data D (i, j), wherein i is 1,2, …, n, j is 1,2, …, m, to obtain D is USV, wherein n is the number of lines of the ground penetrating radar data, m is the number of columns of the ground penetrating radar data, and S is [ diag (σ)1,σ2,...,σn)]Is a matrix of singular values, U, V are both orthogonal matrices, σ1,σ2,...,σnSingular values of the ground penetrating radar data D;
step (a 2): in order to enhance weak signals and weaken strong interference in ground penetrating radar data, the size of singular values is changed through a singular value scaling function, and the scaled singular values
Satisfy the requirement of
Wherein n is the number of rows of radar data, C is the wave velocity of electromagnetic waves in vacuum, epsilon is a condition threshold, beta and C are constants;
step (a 3): the singular value matrix after scaling by the singular value scaling function is
The enhanced ground penetrating radar data is obtained as D '═ US' V.
The invention has the following advantages:
1. the singular value scaling function provided by the invention can weaken the direct wave intensity interference and simultaneously strengthen the weak signal, thereby realizing the enhancement of the ground penetrating radar data.
2. The singular value decomposition method does not need parameter solving and iterative optimization processes, and the ground penetrating radar data can be rapidly enhanced.
Drawings
FIG. 1 is a detailed view of a data enhancement process of a ground penetrating radar according to the present invention
FIG. 2 is a flow chart of the ground penetrating radar data enhancement of the present invention
Detailed Description
Aiming at the problems of strong direct wave interference and serious deep signal attenuation of ground penetrating radar B scanning data in a zero offset mode, the method changes the size of a singular value according to a singular value scaling function on the basis of singular value decomposition, converts a larger singular value into a smaller singular value through nonlinearity, converts the smaller singular value into a larger singular value through nonlinearity, and realizes the data enhancement of the ground penetrating radar.
Ground penetrating radar data enhancement based on singular value is zoomed has 2 kinds of processing procedures, and 1 st kind of procedure is directly to ground penetrating radar data enhancement, requires that ground penetrating radar data's column number is more than or equal to ground penetrating radar data's line number, and concrete step is as follows:
(1) performing singular value decomposition on the ground penetrating radar data D to obtain D ═ USV, wherein S ═ diag (sigma)1,σ2,...,σn)]Is a singular value matrix of D, U, V are orthogonal matrices of D, sigma1,σ2,...,σnThe singular value of the ground penetrating radar data D is shown, and n is the line number of the radar data.
(2) In order to enhance weak signals and weaken strong interference in ground penetrating radar data, the size of singular values is changed through a singular value scaling function, and the scaled singular values
Satisfy the requirement of
Wherein C is the wave velocity of the electromagnetic wave in vacuum, epsilon is a conditional threshold, beta and C are constants.
(3) The singular value matrix after scaling by the singular value scaling function is
The enhanced ground penetrating radar data is obtained as D '═ US' V.
When the column number of the ground penetrating radar data is smaller than the line number of the ground penetrating radar data, the ground penetrating radar data is enhanced by adopting the 2 nd flow, and the specific steps are as follows:
(1) and performing column continuation on the ground penetrating radar data D to form new ground penetrating radar data T (D D), judging whether the column number of the ground penetrating radar data is less than the line number of the ground penetrating radar data, if the column number of the ground penetrating radar data is still less than the line number of the ground penetrating radar data, continuing the column continuation to obtain new ground penetrating radar data T (DD), and so on until the column number of the ground penetrating radar data is more than or equal to the line number of the ground penetrating radar data.
(2) Performing singular value decomposition on the ground penetrating radar data T after the column extension to obtain T which is POQ, wherein O is [ diag (sigma)1,σ2,...,σn)]Is a singular value matrix of T, P, Q are orthogonal matrices of T, sigma1,σ2,...,σnAre singular values of the ground penetrating radar data T.
(3) In order to enhance weak signals and weaken strong interference in ground penetrating radar data, the size of singular values is changed through a singular value scaling function, and the scaled singular values
Satisfy the requirement of
Wherein n is the number of rows of extended radar data, C is the wave velocity of electromagnetic waves in vacuum, epsilon is a conditional threshold, and beta and C are constants.
(4) The singular value matrix after scaling by the singular value scaling function is
The enhanced ground penetrating radar data is obtained as T ═ PO' Q.
(5) And intercepting the front m columns of the ground penetrating radar data T 'as finally enhanced ground penetrating radar data D' because the column number of the ground penetrating radar data D is m.
Claims (1)
1. A ground penetrating radar data enhancement method based on singular value scaling is based on singular value decomposition, and the singular value is changed through a singular value scaling function, so that weak signals in ground penetrating radar data are enhanced, and strong interference is weakened, and the method specifically comprises the following steps:
step (a 1): performing singular value decomposition on ground penetrating radar data D (i, j), wherein i is 1,2, …, n, j is 1,2, …, m, to obtain D is USV, wherein n is the number of lines of the ground penetrating radar data, m is the number of columns of the ground penetrating radar data, and S is [ diag (σ)1,σ2,...,σn)]Is a matrix of singular values, U, V are both orthogonal matrices, σ1,σ2,...,σnSingular values of the ground penetrating radar data D;
step (a 2): in order to enhance weak signals and weaken strong interference in ground penetrating radar data, the size of singular values is changed through a singular value scaling function, and the scaled singular values
Satisfy the requirement of
Wherein n is the number of rows of radar data, C is the wave velocity of electromagnetic waves in vacuum, epsilon is a condition threshold, beta and C are constants;
step (a 3): the singular value matrix after scaling by the singular value scaling function is
The enhanced ground penetrating radar data is obtained as D '═ US' V.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105527618A (en) * | 2016-02-26 | 2016-04-27 | 中国矿业大学(北京) | Ground penetrating radar buried target effective signal enhancement method |
| 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 |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105527618A (en) * | 2016-02-26 | 2016-04-27 | 中国矿业大学(北京) | Ground penetrating radar buried target effective signal enhancement method |
| 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 |
Non-Patent Citations (4)
| Title |
|---|
| HONGYAN SHEN ET AL.: ""Enhancement of GPR Diffracted Waves Processing: A Case Study from Taiyuan, China"", 《JEEG》 * |
| MAIZA BEKARA1 ET AL.: ""Local singular value decomposition for signal enhancement of seismic data"", 《GEOPHYSICS》 * |
| 冯德山 等: ""基于Hilbert-Huang变换的探地雷达信号增强及复信号分析"", 《物探与化探》 * |
| 郑晶 等: ""基于Shearlet变换的探地雷达数据噪声压制研究"", 《矿业科学学报》 * |
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