CN109799499B - Wall parameter estimation method of through-wall radar - Google Patents
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Abstract
A wall parameter estimation method of a through-wall radar mainly solves the problem that the deviation of wall parameter estimation results is large due to the fact that the accuracy of time delay estimation results is poor in the conventional method. The method comprises the steps of estimating the time delay difference of the reflected waves of the front surface and the rear surface of the wall body through a seven-step orthogonal matching pursuit sparse reconstruction algorithm, constructing the time delay difference estimated values and the time delay difference theoretical values of M observation positions into an objective function, accurately estimating the thickness and the relative dielectric constant of the wall body through minimizing the objective function, and accurately estimating the conductivity of the wall body by combining the amplitude ratio of the reflected waves of the rear surface and the front surface of the wall body under the condition of single-base transceiving. In the wall parameter estimation process, an orthogonal matching pursuit sparse reconstruction algorithm is adopted to estimate the double-pass transmission delay difference of the front surface and the rear surface of the wall, so that the resolution and the accuracy of the delay difference estimation result under the condition of low signal-to-noise ratio are improved, and the accuracy of wall parameter estimation is ensured. The method is particularly suitable for parameter estimation of the thin-layer wall body under the condition of low signal-to-noise ratio.
Description
Technical Field
The invention relates to the technical field of through-wall radars, in particular to a through-wall radar wall parameter estimation method which is mainly applied to the fields of urban law enforcement, disaster relief, military operations and the like and is particularly suitable for parameter estimation of a thin-layer wall under the condition of low signal to noise ratio.
Background
The through-wall radar is a perspective imaging technology for detecting hidden targets behind a wall by utilizing the low-frequency penetration characteristic of electromagnetic waves, and in the detection process of the through-wall radar, if wall parameters (dielectric constant, conductivity and wall thickness) are known, a plurality of imaging algorithms (such as a back projection algorithm and the like) easily eliminate the position offset effect caused by the wall. However, in practical application, the wall parameters cannot be known in advance, and the estimation accuracy of the wall parameters can cause problems of reduced imaging quality, deviation of target position positioning, false targets and the like. Therefore, how to effectively and accurately estimate the wall parameters is one of the problems faced by the current through-wall radar.
For wall parameter estimation of through-wall radar, several students have studied it and proposed a series of methods. From the aspect of echo utilization, two types of information are classified, wherein one type of information comprises wall parameters extracted from echoes of the front surface and the rear surface of a wall, and the wall parameters are calculated and determined through a correlation function formula; and the other is to collect the echo data of the target behind the wall and image and position the echo data, and seek the optimal wall parameters through multiple image quality evaluation and positioning correction.
At present, wall parameters can be estimated by a method for measuring the difference of the reflection echo time delay of the front surface and the back surface of the wall, and the existing time delay estimation method generally adopts a method based on fast Fourier transform and subspace super-resolution, but the methods are limited by the thickness of the wall and the signal-to-noise ratio of measured data, and the accuracy of the time delay estimation result of the reflection echo of the front surface and the back surface of the wall is poor, so that the estimation result of the wall parameters has great deviation.
Disclosure of Invention
The invention aims to solve the technical problem of providing a wall parameter estimation method of a through-wall radar for realizing accurate estimation of wall parameters in the detection process of the through-wall radar. And estimating the time delay difference of the reflected waves of the front surface and the rear surface of the wall body by using an orthogonal matching pursuit sparse reconstruction algorithm, constructing an objective function based on the time delay difference estimated values and the time delay difference theoretical values of M observation positions, accurately estimating the thickness and the relative dielectric constant of the wall body by minimizing the objective function, and accurately estimating the conductivity of the wall body by combining the amplitude comparison of the reflected waves of the rear surface and the front surface of the wall body under the condition of single-base transceiving.
In order to achieve the above purpose, the invention adopts the following technical scheme: a wall-penetrating radar wall parameter estimation method comprises the following steps:
step 1: the distance from the transmitting antenna and the receiving antenna of the through-wall radar to the front surface of the wall body is r, the transmitting antenna is kept motionless, the receiving antenna moves for M times along the horizontal line direction according to fixed step length, M observing positions are obtained, measuring data of N uniform frequency points are recorded at each observing position, and the measuring data of the M (m=0, 1, …, M-1) observing positions are expressed as N multiplied by 1 dimensional vector T m ＝[T m (f 0 )，T m (f 1 )，…，T m (f N-1 )] T ，f n ＝f 0 +nΔf is the nth (n=0,1, …, N-1) frequencies of frequency bins, f 0 For the starting frequency of the through-wall radar system, Δf is the frequency step interval;
step 2: the receiving and transmitting antennas are arranged in free space, corresponding to each receiving and transmitting antenna interval same as that in the step 1, the antenna direct wave measurement data of N uniform frequency points are recorded, and the M (m=0, 1, …, M-1) observation position measurement data are expressed as an N multiplied by 1 dimensional vector b m ＝[b m (f 0 )， b m(f 1 )，…，b m (f N-1 )] T ；
Step 3: and (3) removing the antenna direct wave signal in the measurement data obtained in the step (1) by adopting a background cancellation method to obtain wall echo measurement data. The (m=0, 1, …, M-1) th observation position wall echo measurement data is expressed as an n×1-dimensional vector y m ＝T m -b m . Setting maximum double-pass transmission delay tau max The maximum double-pass transmission delay tau is calculated max Evenly dividing the two-way transmission delay vector into Q delay grids, and obtaining a Q multiplied by 1-dimensional two-way transmission delay vector tau= [ tau ] 0 ，τ 1 ，…，τ Q-1 ] T . The M (m=0, 1, …, M-1) th observation position wall echo measurement data is expressed in the form of a matrix vector as shown in formula (1):
y m ＝As m +n m (1)
wherein y is m ＝[y m (f 0 )，y m (f 1 )，…，y m (f N-1 )] T For the Nx1 dimension wall echo measurement data vector s corresponding to the mth observation position m ＝[s m (0)，s m (1)，…，s m (Q-1)] T For Q x 1-dimensional magnitude vector, n m For n×1-dimensional measurement of noise vectors, a= [ a ] 0 ，a 1 ，…，a Q-1 ]For an n×q-dimensional dictionary matrix, the Q (q=0, 1, …, Q-1) column is shown in formula (2):
step 4: in the M (m=0, 1, …, M-1) observation position, adopting an orthogonal matching pursuit sparse reconstruction algorithm to perform time delay estimation on wall echo measurement data at each receiving-transmitting antenna interval to obtain time delay difference estimation values of reflected waves of the front surface and the rear surface of the wall
The method comprises the following specific steps:
(1) initializing residual r m0 ＝y m Support set Ω 0 For an empty set, the number of iterations k=0;
(2) calculating residual r mk Index set corresponding to maximum value in column vector inner product of dictionary matrix, namely lambda k ＝argmax q {u m (q) } wherein the correlation coefficient u m (q)＝|<r mk ，a q >|，q＝0，1，…，Q-1；
(3) Updating support set Ω k+1 ＝Ω k ∪Λ k Calculation of
(4) Updating residual errors
(5) Adding 1 to the iteration times k, returning to the step (2) when k is less than 2, otherwise stopping iteration;
(6) obtaining the estimated value of the double-pass transmission delay difference of the reflected waves of the front surface and the rear surface of the wall body, and marking the estimated value as
Step 5: calculating theoretical time delay difference delta t of reflected waves of front surface and rear surface of wall body through geometric model m (d，ε r ，L m ) At the mth observation position, the theoretical time delay difference of the reflected waves of the front surface and the rear surface of the wall is expressed as follows:
wherein 2L m Is the distance between the transmitting antenna and the receiving antenna at the m observation position, c is the propagation speed of electromagnetic wave in vacuum, d is the thickness of the wall body, epsilon r Is the relative dielectric constant of the wall. X is x m The position of the refraction point P corresponding to the mth observation position can be expressed as
Step 6: constructing an objective function f (d, ε) r ) Obtaining the thickness d of the wall body and the relative dielectric constant epsilon r Is a function of the estimated value of (2);
utilizing the delay difference estimated values of M observation positions obtained in the step 4
And the delay difference theoretical value delta t of M observation positions obtained in the step 5 m (d，ε r ，L m ) The objective function is constructed as follows: />
By solving the minimum value of the objective function shown in the formula (5) for the wall thickness d and the relative dielectric constant epsilon r Is used for the estimation of the estimated value of (a).
Step 7: and (3) estimating the conductivity sigma of the wall body by using the solving result in the step (6), wherein the specific method is as follows:
the transmitting and receiving co-located antenna is placed at a position R away from the front surface of the wall body to obtain the amplitude R of reflected waves of the front surface and the rear surface of the wall body 1 And R is 2 Therefore, the amplitude ratio of the reflected waves of the rear surface and the front surface of the wall is
Solving the formula (6) to obtain the wall loss attenuation rate expression as
The wall thickness d and the relative dielectric constant epsilon estimated in the step 6 are calculated r And (5) carrying out the formula (8) to obtain the wall loss attenuation rate alpha. Aiming at the wall body with lower electromagnetic wave loss, the conductivity sigma of the wall body can be accurately calculated by using the following formula
Wherein the free space wave impedance η 0 ＝120π。
The beneficial effects of adopting above-mentioned technical scheme to produce lie in: in the wall parameter estimation process, an orthogonal matching pursuit sparse reconstruction algorithm is adopted to estimate the double-pass transmission delay difference of the reflected waves of the front surface and the rear surface of the wall, the resolution and the accuracy of the delay difference estimation result under the low signal-to-noise ratio are obviously improved, and the accuracy of the wall parameter estimation is ensured. The through-wall radar wall parameter estimation method provided by the invention is particularly suitable for parameter estimation of a thin-layer wall under the condition of low signal-to-noise ratio.
Drawings
FIG. 1 is a flowchart of a wall parameter estimation method of a through-wall radar according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a wall parameter inversion scenario provided by an embodiment of the present invention;
fig. 3 is a diagram of a result of wall parameter estimation performed by using the wall parameter estimation method of the through-wall radar according to the embodiment of the present invention.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
Examples
As shown in fig. 1, a wall parameter estimation method of a through-wall radar is realized by the following steps:
step 1: the distance from the transmitting antenna and the receiving antenna of the through-wall radar to the front surface of the wall body is r, the transmitting antenna is kept motionless, the receiving antenna moves for M times along the horizontal line direction according to fixed step length, M observing positions are obtained, measuring data of N uniform frequency points are recorded at each observing position, and the measuring data of the M (m=0, 1, …, M-1) observing positions are expressed as N multiplied by 1 dimensional vector T m ＝[T m (f 0 )，T m (f 1 )，…，T m (f N-1 )] T ，f n ＝f 0 +nΔf is the frequency of the nth (n=0, 1, …, N-1) frequency point, f 0 For the starting frequency of the through-wall radar system, Δf is the frequency step interval;
step 2: the receiving and transmitting antennas are arranged in free space, corresponding to each receiving and transmitting antenna interval same as that in the step 1, the antenna direct wave measurement data of N uniform frequency points are recorded, and the M (m=0, 1, …, M-1) observation position measurement data are expressed as an N multiplied by 1 dimensional vector b m ＝[b m (f 0 )，b m (f 1 )，…，b m (f N-1 )] T ；
Step 3: and (3) removing the antenna direct wave signal in the measurement data obtained in the step (1) by adopting a background cancellation method to obtain wall echo measurement data. The (m=0, 1, …, M-1) th observation position wall echo measurement data is expressed as an n×1-dimensional vector y m ＝T m -b m . Setting maximum double-pass transmission delay tau max The maximum double-pass transmission delay tau is calculated max Evenly dividing the two-way transmission delay vector into Q delay grids, and obtaining a Q multiplied by 1-dimensional two-way transmission delay vector tau= [ tau ] 0 ，τ 1 ，…，τ Q-1 ] T . The M (m=0, 1, …, M-1) th observation position wall echo measurement data is expressed in the form of a matrix vector as shown in formula (1):
y m ＝As m +n m (9)
wherein y is m ＝[y m (f 0 )，y m (f 1 )，…，y m (f N-1 )] T For the Nx1 dimension wall echo measurement data vector s corresponding to the mth observation position m ＝[s m (0)，s m (1)，…，s m (Q-1)] T For Q x 1-dimensional magnitude vector, n m For n×1-dimensional measurement of noise vectors, a= [ a ] 0 ，a 1 ，…，a Q-1 ]For an n×q-dimensional dictionary matrix, the Q (q=0, 1, …, Q-1) column is shown in formula (2):
step 4: in the M (m=0, 1, …, M-1) observation position, adopting an orthogonal matching pursuit sparse reconstruction algorithm to perform time delay estimation on wall echo measurement data at each receiving-transmitting antenna interval to obtain time delay difference estimation values of reflected waves of the front surface and the rear surface of the wall
The method comprises the following specific steps:
(1) initializing residual r m0 ＝y m Support set Ω 0 For an empty set, the number of iterations k=0;
(2) calculating residual r mk Index set corresponding to maximum value in column vector inner product of dictionary matrix, namely lambda k ＝argmax q {u m (q) } wherein the correlation coefficient u m (q)＝|<r mk ，a q >|，q＝0，1，…，Q-1；
(3) Updating support set Ω k+1 ＝Ω k ∪Λ k Calculation of
(4) Updating residual errors
(5) Adding 1 to the iteration times k, returning to the step (2) when k is less than 2, otherwise stopping iteration;
(6) obtaining reflected waves of the front surface and the rear surface of the wall bodyIs recorded as the estimated value of the two-way transmission delay difference
Step 5: calculating theoretical time delay difference delta t of reflected waves of front surface and rear surface of wall body through geometric model m (d，ε r ，L m ) At the mth observation position, the theoretical time delay difference of the reflected waves of the front surface and the rear surface of the wall is expressed as follows:
wherein 2L m Is the distance between the transmitting antenna and the receiving antenna at the m observation position, c is the propagation speed of electromagnetic wave in vacuum, d is the thickness of the wall body, epsilon r Is the relative dielectric constant of the wall. X is x m The position of the refraction point P corresponding to the mth observation position can be expressed as
Step 6: constructing an objective function f (d, ε) r ) Obtaining the thickness d of the wall body and the relative dielectric constant epsilon r Is a function of the estimated value of (2);
utilizing the delay difference estimated values of M observation positions obtained in the step 4
And the delay difference theoretical value delta t of M observation positions obtained in the step 5 m (d，ε r ，L m ) The objective function is constructed as follows:
by solving the minimum value of the objective function shown in the formula (5) for the wall thickness d and the relative dielectric constant epsilon r Is used for the estimation of the estimated value of (a).
Step 7: and (3) estimating the conductivity sigma of the wall body by using the solving result in the step (6), wherein the specific method is as follows:
the transmitting and receiving co-located antenna is placed at a position R away from the front surface of the wall body to obtain the amplitude R of reflected waves of the front surface and the rear surface of the wall body 1 And R is 2 Therefore, the amplitude ratio of the reflected waves of the rear surface and the front surface of the wall is
Solving the formula (6) to obtain the wall loss attenuation rate expression as
The wall thickness d and the relative dielectric constant epsilon estimated in the step 6 are calculated r And (5) carrying out the formula (8) to obtain the wall loss attenuation rate alpha. Aiming at the wall body with lower electromagnetic wave loss, the conductivity sigma of the wall body can be accurately calculated by using the following formula
Wherein the free space wave impedance η 0 ＝120π。
In this example, a simulation model was used to perform parametric inversion on a wall having a thickness of 0.15m, a relative permittivity of 6, and a conductivity of 0.012S/m. As shown in fig. 2 (a), the transmitting antenna and the receiving antenna are placed in parallel at a distance of 0.3 m from the wall body by 0.45 m, the transmitting antenna is not moving, the receiving antenna moves for 9 times along the azimuth direction according to the step length of 0.1 m, corresponding to 10 observation positions, the center frequency of the excitation source at each observation position is 2GHz, the bandwidth is 2GHz, the stepping frequency is 10MHz, and corresponding to 201 working frequency points. When estimating the thickness and relative dielectric constant of a wall body, selecting measurement data of 10 observation positions and 201 frequency points for sparse reconstruction, setting the maximum double-pass transmission delay as 5ns and the time interval as 0.0025n in the time delay difference estimation process by utilizing an orthogonal matching pursuit sparse reconstruction algorithms, constructing 201×2000 dimension dictionary matrix. As shown in FIG. 2 (b), the transmitting and receiving co-located antenna was placed at a distance of 0.45 m from the wall to measure the reflected wave amplitude R of the front and rear surfaces of the wall 1 And R is 2 And calculating the conductivity of the wall body by using the estimated values of the wall body thickness and the relative dielectric constant. In this embodiment, the wall parameter estimation result of the through-wall radar is shown in fig. 3, which shows the relative errors of the wall parameter (thickness, relative dielectric constant and conductivity) estimation values when the signal-to-noise ratio is 5dB, 10dB, 15dB, 20dB, 25dB, 30dB respectively, so that the invention can accurately estimate the thin-layer wall parameter under low signal-to-noise ratio.
By adopting the wall parameter estimation method of the through-wall radar, the requirement on high-resolution time delay estimation is remarkably met in the wall parameter estimation process, meanwhile, the influence of noise can be better reduced, and the accuracy of wall parameter estimation is improved.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions, which are defined by the scope of the appended claims.
Claims (2)
1. The method is characterized in that the method is realized by the following steps:
step 1: through-wall radar transmitting antenna and receiving antennaThe distance of the front surface of the wall body is r, the transmitting antenna is kept motionless, the receiving antenna moves for M times along the horizontal line direction according to fixed step length, M observing positions are obtained, measuring data of N uniform frequency points are recorded at each observing position, and the measuring data of the mth observing position is expressed as an N multiplied by 1 dimension vector T m ＝[T m (f 0 ),T m (f 1 ),…,T m (f N-1 )] T ，m＝0,1,…,M-1，f n ＝f 0 +nΔf is the frequency of the nth frequency point, f 0 For the starting frequency of the through-wall radar system, Δf is the frequency step interval, n=0, 1, …, N-1;
step 2: the receiving and transmitting antennas are arranged in a free space, corresponding to each receiving and transmitting antenna interval same as that in the step 1, the antenna direct wave measurement data of N uniform frequency points are recorded, and the m-th observation position measurement data is expressed as an Nx 1-dimensional vector b m ＝[b m (f 0 ),b m (f 1 ),…,b m (f N-1 )] T ，m＝0,1,…,M-1；
Step 3: removing the antenna direct wave signal in the measured data obtained in the step 1 by adopting a background cancellation method to obtain wall echo measured data, and expressing the wall echo measured data at the mth observation position as an Nx1dimension vector y m ＝T m -b m Setting maximum double-pass transmission delay tau max The maximum double-pass transmission delay tau is calculated max Evenly dividing the two-way transmission delay vector into Q delay grids, and obtaining a Q multiplied by 1-dimensional two-way transmission delay vector tau= [ tau ] 0 ,τ 1 ,…,τ Q-1 ] T M=0, 1, …, M-1, then the mth observation position wall echo measurement data is expressed in the form of a matrix vector, as shown in formula (1):
y m ＝As m +n m (1)
wherein y is m ＝[y m (f 0 ),y m (f 1 ),…,y m (f N-1 )] T For the Nx1 dimension wall echo measurement data vector corresponding to the mth observation position, f n ＝f 0 +nΔf is the frequency of the nth frequency point, f 0 For the initial frequency of a through-wall radar system, deltaf is the step frequency, n=0, 1, …, N-1, s m ＝[s m (0),s m (1),…,s m (Q-1)] T For Q x 1-dimensional magnitude vector, n m For n×1-dimensional measurement of noise vectors, a= [ a ] 0 ,a 1 ,…,a Q-1 ]For an n×q-dimensional dictionary matrix, the Q (q=0, 1, …, Q-1) column is shown in formula (2):
step 4: in the m observation position, carrying out time delay estimation on wall echo measurement data under each receiving and transmitting antenna interval by adopting an orthogonal matching pursuit sparse reconstruction algorithm to obtain a time delay difference estimation value of reflected waves of the front surface and the rear surface of the wall
The method comprises the following specific steps:
(1) initializing residual r m0 ＝y m Support set Ω 0 For an empty set, the number of iterations k=0;
(2) calculating residual r mk Index set corresponding to maximum value in column vector inner product of dictionary matrix, namely lambda k ＝argmax q {u m (q) } wherein the correlation coefficient u m (q)＝|〈r mk ,a q >|,q＝0,1,…,Q-1；
(3) Updating support set Ω k+1 ＝Ω k ∪Λ k Calculation of
(4) Updating residual errors
(5) Adding 1 to the iteration times k, returning to the step (2) when k is less than 2, otherwise stopping iteration;
(6) obtaining the estimated value of the double-pass transmission delay difference of the reflected waves of the front surface and the rear surface of the wall body, and marking the estimated value as
Step 5: calculating theoretical time delay difference delta t of reflected waves of front surface and rear surface of wall body through geometric model m (d,ε r ,L m ) At the mth observation position, the theoretical time delay difference of the reflected waves of the front surface and the rear surface of the wall is expressed as follows:
wherein 2L m Is the distance between the transmitting antenna and the receiving antenna at the m observation position, c is the propagation speed of electromagnetic wave in vacuum, d is the thickness of the wall body, epsilon r Is the relative dielectric constant of the wall body, x m The position of the refraction point P corresponding to the mth observation position can be expressed as
Step 6: constructing an objective function f (d, ε) r ) Obtaining the thickness d of the wall body and the relative dielectric constant epsilon r Is a function of the estimated value of (2);
utilizing the delay difference estimated values of M observation positions obtained in the step 4
And the delay difference theoretical value delta t of M observation positions obtained in the step 5 m (d,ε r ,L m ) The objective function is constructed as follows:
by solving the minimum value of the objective function shown in the formula (5) for the wall thickness d and the relative dielectric constant epsilon r Is a function of the estimated value of (2);
step 7: and (3) estimating the conductivity sigma of the wall body by using the solving result in the step (6), wherein the specific method is as follows:
the receiving and transmitting co-located antenna is placed at a position R away from the front surface of the wall body, and the amplitude R of reflected waves of the front surface and the rear surface of the wall body is obtained 1 And R is 2 Therefore, the amplitude ratio of the reflected waves of the rear surface and the front surface of the wall is
Solving the formula (6) to obtain the wall loss attenuation rate expression as
The wall thickness d and the relative dielectric constant epsilon estimated in the step 6 are calculated r Taking in (8), obtaining the wall loss attenuation rate alpha, and accurately calculating the conductivity sigma of the wall by using the following formula aiming at the wall with lower electromagnetic wave loss
Wherein the free space wave impedance η 0 ＝120π。
2. The method for estimating parameters of a wall-penetrating radar wall according to claim 1, wherein the method comprises the steps of: the simulation model is utilized to carry out parameter inversion on a wall body with the thickness of 0.15m, the relative dielectric constant of 6 and the conductivity of 0.012S/m, a transmitting antenna and a receiving antenna are placed in parallel at a position which is 0.45 m away from the wall body and is 0.3 m away from the wall body, the transmitting antenna is not moved, the receiving antenna moves for 9 times along the azimuth direction according to the step length of 0.1 m, 10 observation positions are corresponding to the receiving antenna, the center frequency of an excitation source at each observation position is 2GHz, the bandwidth is 2GHz, the stepping frequency is 10MHz, 201 working frequency points are corresponding to the stepping frequency, and when the thickness and the relative dielectric constant of the wall body are estimated, the measurement data of 10 observation positions and 201 frequency points are selected for useIn the process of performing time delay difference estimation by utilizing an orthogonal matching pursuit sparse reconstruction algorithm, setting the maximum double-pass transmission time delay as 5ns and the time interval as 0.0025ns, constructing a 201X 2000-dimensional dictionary matrix, receiving and transmitting co-located antennas at a position 0.45 m away from a wall body, and measuring the back scattering echo amplitude R of the front surface and the back surface of the wall body 1 And R is 2 And calculating the conductivity of the wall by using the estimated values of the thickness and the relative dielectric constant of the wall, and displaying the relative errors of the estimated values of the thickness, the relative dielectric constant and the conductivity when the signal-to-noise ratio is 5dB, 10dB, 15dB, 20dB, 25dB and 30dB respectively.
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| CN106772365A (en) * | 2016-11-25 | 2017-05-31 | 南京理工大学 | A kind of multipath based on Bayes's compressed sensing utilizes through-wall radar imaging method |
| CN107894591A (en) * | 2017-09-30 | 2018-04-10 | 沈阳航空航天大学 | Through-wall radar diffraction tomography method based on compressed sensing |
| CN108896990A (en) * | 2018-05-10 | 2018-11-27 | 桂林电子科技大学 | A kind of building masonry wall imaging method and device using coupled mode dictionary learning |
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