CN112904334B - Ground penetrating radar backward projection rapid imaging method based on cross correlation - Google Patents
Ground penetrating radar backward projection rapid imaging method based on cross correlation Download PDFInfo
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Abstract
The invention provides a ground penetrating radar backward projection rapid imaging method based on cross correlation, which comprises the steps of firstly, calculating a propagation path of electromagnetic waves at an interface; then, a time delay matrix is established, and the propagation time delay between the imaging area and the transmitting antenna is stored; when calculating the time delay, translational invariance and symmetrical invariance are used, so that the calculation time is further shortened; finally, a three-step imaging method is adopted to image the underground target. The method can greatly reduce the calculated amount, realize quick imaging and well inhibit false targets.
Description
Technical Field
The invention belongs to the technical field of ground penetrating radar imaging, and particularly relates to a cross-correlation-based ground penetrating radar backward projection rapid imaging method.
Background
The ground penetrating radar emits high-frequency broadband electromagnetic waves, receives reflected echo signals of the buried targets, and analyzes the echo signals to infer distribution conditions such as positions, quantity and the like of the underground targets.
The efficiency of the use of ground penetrating radar depends not only on the performance of the radar hardware, but also on the imaging algorithm used by the radar. The imaging algorithm is directly related to the positioning precision, detection and identification capability and imaging speed of the whole radar system on the underground target.
The back projection imaging algorithm BP is widely applied to ground penetrating radar imaging due to the advantages of clear physical concept, accurate compensation, easiness in implementation and the like. The BP algorithm is a coherent imaging algorithm, and coherent superposition of scattered echoes is mainly realized through delay-addition. When calculating the round trip time delay from the transmitting source to the pixel point and then to the receiving antenna, the refraction point of the electric wave at the air ground needs to be solved, and each refraction point is a solution quadratic equation. The back projection imaging algorithm BP consumes a lot of computation time on the time delay between the pixel point and the antenna. These result in longer imaging times, which are detrimental to real-time processing. In addition, due to the coupling between the targets, multipath clutter can occur between the targets and the ground, which can lead to "ghosting" during imaging, which can adversely affect interpretation of the imaged targets.
Therefore, it is necessary to design a ground penetrating radar back projection rapid imaging method.
Disclosure of Invention
The invention aims to provide a simple and practical ground penetrating radar backward projection rapid imaging method based on cross correlation, which solves the problems, and therefore, on the basis of backward projection, the phenomenon of 'ghosts' generated by BP imaging is restrained by adding cross correlation calculation; by adopting the strategies of linear approximation, time delay matrix establishment according to symmetry and translational invariance, coarse-to-fine three-step imaging and the like, the imaging speed is greatly improved.
In order to achieve the above object, the present invention provides the following solutions:
a ground penetrating radar backward projection rapid imaging method based on cross correlation comprises the following steps:
s1, collecting echo data S on a measurement line above the ground l (t);
S2, establishing a matrix for calculating time delay according to echo data;
s3, slave echo signal S l Removing the ground direct wave in (t), and setting the obtained signal as S l ′(t);
S4, from the obtained signal S l Uniformly selecting echo data of partial receiving positions in the' (t), and setting the selected data as { S } l I=1, 2,..l '}, where L' is the total number of received position echo data from the pick-up, using a selected dataset S with a cross-correlation based backprojection algorithm l Imaging at "(t), denoted as I A (X,Z);
S5, performing cross-correlation back projection on the obtained image I A (X, Z) normalized to obtain image I' A (X,Z);
S6, the image I' A (X, Z) performing binary segmentation by using a maximum inter-class variance method to obtain an image
S7, for all possible target pixels (x, z), so thatThen the pixel is considered to be a possible target pixel, imaged using the full dataset data S (n, t); for non-target pixels +.>Is not imaged; the final imaging result is: />
Preferably, the step S1 includes:
s1.1, the measuring line is parallel to the ground, the receiving and transmitting antenna completes one-time measurement, after an echo is obtained, the measuring line is uniformly moved to the next measuring position until all echo data are collected;
s1.2, the ground penetrating radar sequentially detects real apertures at all positions of the measuring line, and the appointed transmitting signals are ultra-wideband pulse signals, so that echo data received at all positions of the measuring line are respectively expressed as { S } l (t), l=1, 2,..l }, where L is the total number of ground penetrating radar transceiver antennas.
Preferably, the method for establishing the calculated time delay matrix in step S2 is as follows:
s2.1, calculating a refraction point between the antenna and a specified pixel on the ground according to the position of the antenna, wherein the calculation formula of the refraction point is as follows:
wherein: (x) 0 ,z 0 ) Is a coordinate point of the imaging region, (x) k -h) is the position coordinates of the antenna, (x) 1 0) is (x) 0 ,z 0 ) And antenna (x) k -sitting at the intersection of the straight line connecting between h) and the groundMark, epsilon r Is the relative dielectric constant of ground, (x) r 0) is the coordinates of the ground refraction point;
s2.2, calculating time delay between the pixel point and the antenna:
wherein: τ A,k For electromagnetic waves from the kth antenna position (x k H) passing the ground refractive point to imaging region point A (x) 0 ,z 0 ) Propagation time, c, is the propagation speed of electromagnetic waves in vacuum;
traversing all the receiving and transmitting antenna positions and target area pixel points, and constructing a time delay dictionary matrix tau:
wherein Δx, Δz represent distances between adjacent pixels of the imaging region in the x-direction and the z-direction, respectively; n (N) 1 ,N 2 The number of pixels of the imaging region in the x direction and the z direction are respectively represented; m, n denote the m-th row and n-th column of the matrix, respectively.
Preferably, the method for calculating the back projection of the cross correlation in step S4 is as follows:
s4.1, finding out the k transmitting antenna from the time delay dictionary matrixTo the target pixel point A (x, z), and then to the kth receiving antenna +.>Is (are) a double pass delay tau A,k :
t=|x t -x|/Δx,r=|x r -x|/Δx,j=|z|/Δz
Wherein t represents the number of pixel units of the transmitting antenna position in the x direction relative to the target point a; r represents the number of pixel units of the receiving antenna position in the x direction with respect to the target point a; j represents the number of pixel units of the transmitting-receiving antenna position in the z direction relative to the target point a;
s4.2, receiving data S from a position l of the selected antenna data according to the position l l Finding the measurement data u corresponding to the target pixel point A (x, z) by the (t) sequence A,l :
S4.3, calculating pixel values of the selected points according to the measurement data and the cross-correlation back projection algorithm:
s4.4, traversing each pixel point (x, y) in the imaging area, and repeating the steps S4.1, S4.2 and S4.3 to obtain a final image I A (X,Z)。
Preferably, the method for normalizing the image in step S5 is as follows:
wherein min (I) A (X, Z)) is image I A Minimum pixel value in (X, Z), max (I A (X, Z)) is image I A (X, Z) the maximum pixel value.
Preferably, in the step S6, the matlab command of the maximum inter-class variance method is level=graythresh (I), the image segmentation threshold level is obtained, and the binary segmentation image is:
If it isThe point is considered likely to be targeted and the steps S4, S5 are repeated using all the measurement data to obtain the final image.
The beneficial effects of the invention are as follows:
1. the method fully utilizes the characteristic that the backward operation of multiplication cross-correlation can inhibit clutter and multipath, and can well reduce the interference of 'ghosts' generated by clutter on interpretation of imaging targets during imaging;
2. when calculating time delay to calculate a refraction point, piecewise linear approximation is used for replacing quadratic equation solution, so that the calculation speed is increased;
3. when calculating the time delay, the invention establishes a time delay matrix, and according to the translational invariance and the symmetrical invariance of the relative positions among the antenna and the pixel points, the redundant calculation of the time delay is greatly reduced, and the calculated amount is further reduced by writing the multiplication cross correlation into a summation form;
4. the invention adopts a three-step imaging method from coarse to fine: firstly, a small part of antenna observation data is used, a cross-correlation BP imaging algorithm is adopted to carry out coarse imaging on all pixels, then, the image is segmented through maximum inter-class variance binary segmentation, the pixels which are possibly at target positions are screened out, and the cross-correlation BP imaging algorithm is carried out on all the antenna observation data of the part of pixels to carry out fine imaging.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of object detection in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a target simulation in an embodiment of the present invention;
FIG. 4 is a schematic diagram of time delay translation invariance in an embodiment of the present invention;
FIG. 5 is a diagram showing time delay symmetry invariance in an embodiment of the present invention;
FIG. 6 is a schematic diagram of simulation data in an embodiment of the present invention;
FIG. 7 is a schematic view of partial data imaging in accordance with an embodiment of the present invention;
FIG. 8 is a diagram illustrating two-value segmentation according to an embodiment of the present invention;
FIG. 9 is a final imaging schematic diagram of a cross-correlation back projection rapid imaging algorithm in an embodiment of the invention;
FIG. 10 is a schematic image of a back projection imaging algorithm of the present invention;
fig. 11 is a schematic diagram of a rear projection imaging algorithm of the cross-correlation ground penetrating radar of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The method aims at the problem of 'ghost' interference target interpretation, adopts a back projection imaging algorithm of multiplication cross-correlation, aims at the problem of long calculation time, firstly solves refractive points by using linear approximation to replace a quadratic equation, then establishes a time delay matrix according to translational invariance and symmetrical invariance, and stores the time delay between an antenna and each pixel; the object is then imaged in a three-step method based on the fact that the object only occupies the viewing area.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
The flow chart of the invention is shown in fig. 1, and fig. 2 is a schematic diagram of target detection.
S1, collecting echo data on a measurement line above the ground;
in the electromagnetic simulation software gprmax2.0, the simulation scene setting is shown in fig. 3. Wherein, the measuring line is located at z=2.3m, the starting point of the transmitting antenna is x=0.0m, the starting point of the receiving antenna is x=0.28m, after completing the a-Scan at each position, the transmitting antenna and the receiving antenna translate to the right according to 0.02m at the same time until the transmitting antenna is located at x=1.72m at the final position, and the receiving antenna is located at x=2.0m and ends for 87 channels of a-Scan data, as shown in fig. 4.
The imaging region is a rectangular region composed of diagonal coordinate points (0 m,0 m) and (2 m,2 m); sandy land with a relative dielectric constant of 4+j0.01; the conductor cylinder object 1 is positioned at (0.8 m,0.95 m) with a radius of 0.1m; the conductor cylinder target 2 is located at (1.2 m,1.05 m) with a radius of 0.1m.
S2, establishing a matrix for calculating time delay;
from the position of the transmitting (receiving) antenna, the refraction point between the antenna and the specified pixel at the ground is calculated.
The refractive index is calculated as:
wherein: (x) 0 ,z 0 ) Is a coordinate point of the imaging region a, (x) k -h) is the position coordinates of the antenna, (x) 1 0) is (x) 0 ,z 0 ) And antenna (x) k -coordinates of the intersection point of the straight line connecting between h) and the ground, ε r Is the relative dielectric constant of ground, (x) r 0) ground refractionCoordinates of the points;
calculating the time delay between the pixel point and the antenna:
wherein: τ A,k C is the propagation time of electromagnetic waves from the antenna to the imaging region point through the ground refraction point, and c is the pixel point of the target region and the position of all transmitting and receiving antennas;
constructing a time delay dictionary matrix:
wherein Δx, Δz represent distances between adjacent pixels of the imaging region in the x-direction and the z-direction, respectively; n (N) 1 ,N 2 The number of pixels of the imaging region in the x direction and the z direction are respectively represented; m, n denote the m-th row and n-th column of the matrix, respectively.
According to the translational invariance and the symmetry invariance, the time delay between all the antenna positions and the pixel points of the target area can find the corresponding delay value in the dictionary matrix, as shown in fig. 5.
S3, outputting a ground direct wave from the obtained echo signal, wherein the obtained signal is S i ′(t);
The simulation experiment adopts a background cancellation method to remove clutter. Namely, the simulation data without the target is subtracted from the simulation data with the target, so that the direct wave is eliminated, and the echo simulation data of the target is obtained. The target echo data is shown in fig. 6.
The imaging region was divided into 200×200 pixels according to 0.01m×0.01 m.
Wherein 4 (10 th, 32 th, 54 th, 76 th) lanes of data are selected for the first imaging.
S4, setting the selected data as { S } i "(t), i=1, 2,..m '}, where M' is the total number of echo data from the selection; using a selected dataset S with a cross-correlation based backprojection algorithm i "(t) imagingIs denoted as I A (x,z)。
Finding out the double-pass time delay tau from the transmitting antenna to the target pixel point and then to the receiving antenna from the dictionary matrix A,i :
Wherein τ A,k Representing the two-way delay of an electromagnetic wave from the transmitting antenna at the kth position to the imaged pixel point a and scattering echoes from the point a to the receiving antenna at the kth position.Representing a time delay from the electromagnetic wave emitted from the transmitting antenna at the kth position to the imaged pixel point a; />And (3) scattering the time delay of the echo reaching the receiving antenna at the kth position from the point A. />
According to a cross-correlation back projection algorithm, calculating the pixel value of the point A:
wherein u is A,i For transmitting antenna from kThe transmitted signal is scattered by the target pixel point (x, z) and is received by the kth receiving antenna +.>Receiving the obtained receiving signal; l 'is the total number of received position echo data from the selection, in this embodiment L' =4.
Traversing each pixel point (x, z) in the imaging region, repeating equations (4) (5) (6) to obtain a final image I A (X,Z);
S5, performing cross-correlation back projection on the selected partial echo data to obtain an image I A (x, z) performing image normalization to obtain an image I' A (x, z) (as shown in fig. 7), the normalized expression is:
wherein min (I A (X, Z)) is image I A Minimum pixel value in (X, Z), max (I A (X, Z)) is image I A (X, Z) the maximum pixel value.
S6, the image I' A (X, Z) performing binary segmentation by using a maximum inter-class variance method to obtain an image I A (XZ) (shown in fig. 8);
the maximum inter-class variance matlab command is level=graythresh (I), and the image segmentation threshold level is obtained.
The binary segmentation results in the following images:
a second imaging was performed using the entire data.
For a pair ofThe possible target pixels are imaged using the full dataset data S (n, t), while for non-target pixels, no imaging is performed, resulting in: />If: />The pixel value of point a is: />
If it isRepeating step S4 to obtain->Then pair->Normalizing to obtain a final image I o (x, z) as shown in fig. 9.
Wherein, the liquid crystal display device comprises a liquid crystal display device,for image->A minimum pixel value of (2); />For image->Is the maximum pixel value of (c).
The GprMax2.0 is provided, the transmitting antenna transmits 'ricker' pulse waves, the center frequency is 1GHz, and the 3db bandwidth is as follows: 1.14GHZ.
The simulation experiment uses 4G memory, an Inteli5-4590 processor (3.3 GHz), a win764 bit operating system, matlab2014b software.
As imaging contrast, using the same imaging data, an image using a time domain BP imaging algorithm is shown in fig. 10.
As imaging contrast, using the same imaging data, an image imaged using the cross-correlation BP imaging algorithm is shown in fig. 11.
The invention has the advantages that:
1. the characteristic that the multiplication cross correlation backward operation can inhibit clutter and multipath is fully utilized, and the interference of 'ghosts' generated by clutter on interpretation of an imaging target can be well reduced during imaging;
2. aiming at the problems of large calculated amount and long imaging time of a time domain back projection imaging algorithm: (1) When calculating the time delay to calculate the refraction point, piecewise linear approximation is used for replacing quadratic equation solution, so that the calculation speed is increased; (2) When calculating the time delay, by establishing a time delay matrix and according to the translational invariance and the symmetrical invariance of the relative positions among the pixels of the antenna, redundant calculation of the time delay is greatly reduced; (3) Further reducing the computational effort by writing the multiplicative cross-correlation into a summation form; (4) To further increase the imaging speed, a three-step imaging method from coarse to fine is employed. Firstly, observing data by using a small part of antennas, and performing coarse imaging on all pixels by adopting a cross-correlation BP imaging algorithm; then, the image is segmented through maximum inter-class variance binary segmentation, and pixels which are possibly the target positions are screened out. And carrying out cross-correlation BP imaging algorithm on the part of pixels by adopting data observed by all antennas, and carrying out fine imaging.
3. The cross-correlation BP imaging algorithm has high calculation speed and good ghost inhibition effect, and when the cross-correlation imaging algorithm is performed in the third step, the time delay matrix is calculated in the first step, and the imaging speed is not required to be recalculated, so that the imaging speed can be greatly improved on the basis of ensuring the imaging resolution.
The above embodiments are merely illustrative of the preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, but various modifications and improvements made by those skilled in the art to which the present invention pertains are made without departing from the spirit of the present invention, and all modifications and improvements fall within the scope of the present invention as defined in the appended claims.
Claims (4)
1. A ground penetrating radar backward projection rapid imaging method based on cross correlation is characterized by comprising the following steps:
s1, collecting echo data S on a measurement line above the ground l (t);
S2, establishing a matrix for calculating time delay according to echo data;
s3, slave echo signal S l Removing the ground direct wave in (t), and setting the obtained signal as S' l (t);
S4, from the resulting signal S' l Uniformly selecting echo data of partial receiving positions in (t), and setting the selected data as { S } " l (t), i=1, 2,.. l (t) imaging, designated I A (X,Z);
S5, performing cross-correlation back projection on the obtained image I A (X, Z) normalized to obtain image I' A (X,Z);
S6, the image I' A (X, Z) performing binary segmentation by using a maximum inter-class variance method to obtain an image
S7, for all possible target pixels (x, z), so thatThen the pixel is considered to be a possible target pixel, imaged using the full dataset data S (n, t); for non-target pixels +.>Is not imaged; the final imaging result is: />
The method for establishing the calculation time delay matrix in the S2 comprises the following steps:
s2.1, calculating a refraction point between the antenna and a specified pixel on the ground according to the position of the antenna, wherein the calculation formula of the refraction point is as follows:
wherein: (x) 0 ,z 0 ) Is a coordinate point of the imaging region, (x) k -h) is the position coordinates of the antenna, (x) 1 0) is (x) 0 ,z 0 ) And antenna (x) k -coordinates of the intersection point of the straight line connecting between h) and the ground, ε r Is the relative dielectric constant of ground, (x) r 0) is the coordinates of the ground refraction point;
s2.2, calculating time delay between the pixel point and the antenna:
wherein: τ A,k For electromagnetic waves from the kth antenna position (x k H) passing the ground refractive point to imaging region point A (x) 0 ,z 0 ) Propagation time, c, is the propagation speed of electromagnetic waves in vacuum;
traversing all the receiving and transmitting antenna positions and target area pixel points, and constructing a time delay matrix tau:
wherein Δx, Δz represent distances between adjacent pixels of the imaging region in the x-direction and the z-direction, respectively; n (N) 1 ,N 2 The number of pixels of the imaging region in the x direction and the z direction are respectively represented; m, n represent the m-th row and n-th column of the matrix, respectively;
the method for calculating the back projection of the cross correlation in the S4 comprises the following steps:
s4.1, from the time delay dictionary matrixFind out the transmitting antenna from the kthTo the target pixel point A (x, z), and then to the kth receiving antenna +.>Is (are) a double pass delay tau A,k :
t=|x t -x|/Δx,r=|x r -x|/Δx,j=|z|/Δz
Wherein t represents the number of pixel units of the transmitting antenna position in the x direction relative to the target point a; r represents the number of pixel units of the receiving antenna position in the x direction with respect to the target point a; j represents the number of pixel units of the transmitting-receiving antenna position in the z direction relative to the target point a;
s4.2, receiving data S from a position l of the selected antenna data according to the position l l Finding the measurement data u corresponding to the target pixel point A (x, z) by the (t) sequence A,l :
S4.3, calculating pixel values of the selected points according to the measurement data and the cross-correlation back projection algorithm:
s4.4, traversing each pixel point (x, y) in the imaging area, and repeating the steps S4.1, S4.2 and S4.3 to obtain a final image I A (X,Z)。
2. The method for rapid imaging of rear projection of a ground penetrating radar based on cross-correlation according to claim 1, wherein the step S1 comprises:
s1.1, the measuring line is parallel to the ground, the receiving and transmitting antenna completes one-time measurement, after an echo is obtained, the measuring line is uniformly moved to the next measuring position until all echo data are collected;
s1.2, the ground penetrating radar sequentially detects real apertures at all positions of the measuring line, and the appointed transmitting signals are ultra-wideband pulse signals, so that echo data received at all positions of the measuring line are respectively expressed as { S } l (t), l=1, 2,..l }, where L is the total number of ground penetrating radar transceiver antennas.
3. The method for back projection rapid imaging of ground penetrating radar based on cross correlation according to claim 1, wherein the method for normalizing the image in step S5 is as follows:
wherein min (I) A (X, Z)) is image I A Minimum pixel value in (X, Z), max (I A (X, Z)) is image I A (X, Z) the maximum pixel value.
4. The method for rapid imaging of rear projection of ground penetrating radar based on cross correlation according to claim 1, wherein the matlab command of the maximum inter-class variance method in step S6 is level=graythresh (I), the image segmentation threshold level is obtained, and the image obtained by binary segmentation is:
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