CN115079165A - Building layout tomography method based on direct wave time delay estimation - Google Patents

Building layout tomography method based on direct wave time delay estimation Download PDF

Info

Publication number
CN115079165A
CN115079165A CN202210782256.7A CN202210782256A CN115079165A CN 115079165 A CN115079165 A CN 115079165A CN 202210782256 A CN202210782256 A CN 202210782256A CN 115079165 A CN115079165 A CN 115079165A
Authority
CN
China
Prior art keywords
direct wave
time delay
building layout
scene
wave time
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202210782256.7A
Other languages
Chinese (zh)
Inventor
郭世盛
李念
陈家辉
余方睿
姚禹
崔国龙
孔令讲
杨晓波
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
University of Electronic Science and Technology of China
Original Assignee
University of Electronic Science and Technology of China
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by University of Electronic Science and Technology of China filed Critical University of Electronic Science and Technology of China
Priority to CN202210782256.7A priority Critical patent/CN115079165A/en
Publication of CN115079165A publication Critical patent/CN115079165A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • 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
    • G01S13/887—Radar or analogous systems specially adapted for specific applications for detection of concealed objects, e.g. contraband or weapons
    • G01S13/888—Radar or analogous systems specially adapted for specific applications for detection of concealed objects, e.g. contraband or weapons through wall detection
    • 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Remote Sensing (AREA)
  • Radar, Positioning & Navigation (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Mathematical Analysis (AREA)
  • Computational Mathematics (AREA)
  • Electromagnetism (AREA)
  • Mathematical Optimization (AREA)
  • General Engineering & Computer Science (AREA)
  • Software Systems (AREA)
  • Computing Systems (AREA)
  • Databases & Information Systems (AREA)
  • Algebra (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention discloses a building layout tomography method based on direct wave time delay estimation, which is characterized by accurately extracting a direct wave from a sampling signal with complex components, establishing a tomography projection model according to the relation between the propagation time delay of the direct wave and the relative dielectric constant of a medium on a path, reconstructing the building layout by using a minimum total variation augmented Lagrange alternating direction algorithm, realizing high-precision reconstruction of a conventional building only containing horizontal and vertical walls, accurately estimating the direct wave time delay, solving the problems of more artifacts, fuzzy walls and the like in an imaging result, being suitable for reconstruction of the conventional building layout, being beneficial to optimizing the reconstruction quality of the partial unconventional building layout, having the advantages of simple processing flow and low cost, and being directly applied to through-wall radar equipment.

Description

Building layout tomography method based on direct wave time delay estimation
Technical Field
The invention belongs to the technical field of through-wall radar imaging, and particularly relates to a building layout imaging technology based on direct wave time delay estimation.
Background
The through-wall radar imaging technology can effectively detect the layout of buildings and hidden targets behind walls, and plays an important role in surveying, mapping, monitoring and disaster relief. Building layout reconstruction is a key step in the through-wall radar imaging technology, and has attracted extensive attention and research.
The traditional building layout reconstruction adopts a synthetic aperture radar imaging technology as a main means, and the technology reconstructs the building layout by utilizing the reflection echo of the building through a back projection imaging algorithm and multi-view fusion. The document "multiple channel and multiple view imaging approach to building layout determination of through-wall radar", IEEE geosci.remote sens.lett., vol.11, No.5, pp.970-974, May 2014 "adopts a multiple-transmit and multiple-receive broadband signal radar to acquire building layout images of multiple channels under multiple views, and proposes a non-coherent fusion method to fuse the multiple channel images, and then proposes an M-N-K detector to realize fusion of multiple single-view images, so as to obtain a complete building layout image. Although the above research can obtain a better building layout reconstruction result, the method is still limited by factors such as serious back wall echo attenuation, easy generation of echo oscillation in the wall body, complex system, high cost and the like.
In recent years, tomographic-based building layout reconstruction has been gradually developed. The tomography adopts a bistatic radar working mode, a transmitting end and a receiving end are distributed on two sides of a scene in parallel, signals of the transmission scene are sampled, and then physical parameters of media in an unknown scene are estimated according to the sampled signals, so that building layout reconstruction is realized. Common tomographic methods can be classified into a tomographic model based on the intensity of a received signal and a tomographic model based on the propagation delay of a signal.
The use of the Wentzel-Kramers-Brillouin (WKB) model to establish the relationship between received signal strength and image gray scale and to regularize the inverse imaging problem is discussed In the 3d through-wall imaging with integrated acoustic imaging using wifi, In Proc. However, in practical applications, the received signal strength is easily interfered by multipath propagation signals, resulting in the occurrence of burrs, holes and other problems in the imaging result. The separation of direct waves and multipath signals using the propagation delay of a broadband signal is considered as a method for effectively improving the imaging quality.
The document "A novel ct-mode through-the-wall imaging method based on time delay estimation", IEEE geosci.Remote.S., vol.18, No.8, pp.1381-1385,2021 "considers that multi-path signals are more seriously attenuated by multiple reflections, and provides a maximum peak direct wave time delay estimation algorithm; the literature "Image retrieval in chirp-pulse microwave ct (cp-mct)", IEEE trans. biomed. eng, vol.47, No.5, pp.690-699,2000 "proposes a first peak direct wave time delay estimation algorithm assuming that the direct wave always reaches first. However, as the scene structure becomes complex, the multipath signal may have stronger signal strength or shorter propagation delay than the direct wave. However, the results obtained by the two algorithms are not ideal or even unreliable. The accuracy of the direct wave time delay estimation directly influences the accuracy of the building layout reconstruction result. Therefore, the research on the building layout tomography method for accurately estimating the time delay of the direct wave has important practical significance.
Disclosure of Invention
In order to solve the technical problem, the invention provides a building layout tomography method based on direct wave time delay estimation, which can accurately reconstruct the scene structure of an unknown area.
The technical scheme adopted by the invention is as follows: a building layout tomography method based on direct wave time delay estimation comprises the following specific steps:
s1, multi-position scanning is carried out on the unknown scene along the 0-degree and 90-degree visual angles by adopting a single-transmitting single-receiving bistatic radar, and a broadband signal of the transmission scene is sampled;
s2, extracting direct waves of all the sampling signals acquired in the step S1 by adopting a direct wave time delay estimation algorithm based on a convolution kernel;
s3, establishing a tomography projection model according to the relation between the direct wave time delay and the projection matrix and the scene vector;
and S4, solving a scene vector by adopting a minimum total variation augmented Lagrange alternating direction algorithm based on the chromatographic projection model established in the step S3, and realizing building layout reconstruction.
Further, step S2 performs direct wave delay estimation based on a convolution kernel on the sampling signal obtained in step S1, specifically:
designing a convolution kernel theta ═ alpha 3 ,α 2 ,α 1 ,α 2 ,α 3 ]Convolving the new observation signal with the sampling signal on the dimension of the sampling point to obtain a new observation signal of the m detection position:
C(m,t)＝θ*R(m,t)
＝α 3 R(m-2,t)+α 2 R(m-1,t)+α 1 R(m,t)+α 2 R(m+1,t)+α 3 R(m+2,t)
wherein, 0 < alpha 3 ＜α 2 ＜α 1 For the confidence of the sampling signal at the current detection position and the adjacent detection position, R (m, t) is the sampling signal obtained at the mth detection position, t represents the time, and then the maximum peak is found in the new observation signal to obtain the direct wave time delay, the expression is as follows:
Figure BDA0003729824510000021
wherein the content of the first and second substances,
Figure BDA0003729824510000022
is an estimate of the propagation delay of the direct wave at the mth probe location.
The tomographic projection model in step S4 specifically includes:
P＝AO
wherein the content of the first and second substances,
Figure BDA0003729824510000031
the time delay of the direct wave at all the detection positions is formed into an observation vector, and M is the total measurement quantity;
Figure BDA0003729824510000032
for scene vectors, representing the unknown scene is discretized into N grids of equal size, ε (r) n ) The relative dielectric constant of a medium in the nth grid is shown, c is the speed of light in free space, and T represents matrix transposition operation; a is an M × N projection matrix.
Step S4 specifically includes:
based on the established chromatographic projection model, adding a minimum total variation condition as an objective function, wherein the expression is as follows:
Figure BDA0003729824510000033
wherein D is ij Ο＝[O i+1,j -O i,j ,O i,j+1 -O i,j ] T Representing variation values of the image, T representing a matrix transposition operation, O i,j Represents the pixel value of the ith row and the jth column in the image, | | · | | luminous 2 Representing the matrix 2-norm.
The problem is transformed into an optimization problem without constraints by using an augmented Lagrangian method, and the objective function is expressed as:
Figure BDA0003729824510000034
wherein, λ is an augmentation coefficient, and μ is a penalty coefficient;
finally by introducing a relaxation variable omega ij ≈D ij O, dividing the original problem into solving omega by using an alternating direction algorithm ij Performing alternate iterative solution on two subproblems of the sum O to finally obtain a scene vector meeting the objective functionEstimated value
Figure BDA0003729824510000035
And realizing the reconstruction of the building layout.
The invention has the beneficial effects that: the method accurately extracts the direct wave from the sampling signal with complex components, establishes a chromatographic projection model according to the relation between the propagation delay of the direct wave and the relative dielectric constant of a medium on a path, reconstructs the building layout by using a minimum total variation augmented Lagrange alternating direction algorithm, can realize high-precision reconstruction on the conventional building only containing horizontal and vertical walls, accurately estimates the direct wave delay, solves the problems of more artifacts, fuzzy walls and the like in an imaging result, is suitable for reconstructing the conventional building layout, is favorable for optimizing the reconstruction quality of partial unconventional building layout, has the advantages of simple processing flow and low cost, and can be directly applied to through-wall radar equipment.
Drawings
Fig. 1 is a schematic diagram of a radar operating mode and a simulation scenario according to an embodiment of the present invention.
FIG. 2 is a distance diagram of a sampled signal according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a specific sampling signal according to an embodiment of the present invention.
Fig. 3(a) is a schematic diagram of a specific detection position, fig. 3(b) is a time delay-amplitude diagram of a sampling signal at the position, and fig. 3(c) is a time delay-amplitude diagram after a convolution operation.
FIG. 4 is a schematic view of a tomographic projection model according to the present invention.
Fig. 5 is a time delay estimation result diagram under electromagnetic simulation according to an embodiment of the present invention.
Fig. 5(a) is a time delay estimation result diagram by the maximum amplitude method, and fig. 5(b) is a time delay estimation result diagram of the proposed algorithm.
Fig. 6 is a view of a scene reconstruction result under electromagnetic simulation according to an embodiment of the present invention.
Fig. 6(a) is a graph of the result reconstructed based on the maximum amplitude method, and fig. 6(b) is a graph of the result reconstructed based on the proposed algorithm.
Fig. 7 is an experimental scenario diagram according to an embodiment of the present invention.
In which fig. 7(a) is a top view and fig. 7(b) is a side view.
Fig. 8 is a time delay estimation result diagram in an experimental scenario according to an embodiment of the present invention.
Fig. 8(a) is a time delay estimation result graph by a maximum amplitude method, and fig. 8(b) is a time delay estimation result graph by the proposed algorithm.
Fig. 9 is a view of a scene reconstruction result under electromagnetic simulation according to an embodiment of the present invention.
Fig. 9(a) is a graph of a result reconstructed based on the maximum amplitude method, and fig. 9(b) is a graph of a result reconstructed by the proposed algorithm.
Detailed Description
The following description of the embodiments of the present invention is provided in connection with the accompanying drawings.
The working schematic diagram of the radar transmitting-receiving antenna pair is shown in fig. 1, a transmitting antenna and a receiving antenna are arranged on two sides outside an unknown area, and move synchronously along paths of 0 degree and 90 degrees to detect the whole scene and sample broadband signals of a transmission scene.
The present invention is described with the simulation scenario and the antenna scanning path shown in fig. 1, and the specific steps are as follows:
step 1: the analysis of the sampled signal is carried out,
the broadband signal is transmitted by the transmitting antenna at the mth detection position and is sampled after transmitting the scene. Since the broadband signal is scattered by the medium during propagation, the sampled signal can be represented in the form of direct wave, multipath signal, and clutter superposition:
Figure BDA0003729824510000041
wherein, R (m, t) is a sampling signal obtained from the mth detection position, t is time, s (t) is a transmitting signal, sigma is a signal attenuation coefficient, tau is a signal propagation delay, and sigma is m s(t-τ m ) Representing the direct wave part, τ m Is the true value of the propagation delay of the direct wave at the mth detection position,
Figure BDA0003729824510000042
represents the multipath signal portion, I represents the total multipath signal number, and n (t) represents the spur.
Since the propagation path of the multipath signal in the unknown scene is difficult to describe, the direct wave is considered as the most effective information for reconstructing the building layout, and the direct wave needs to be accurately estimated from the sampling signal.
Step 2: based on the estimation of the direct wave delay of the convolution kernel,
due to the ductility of the wall body, the structure, the thickness and the material of the wall body at a section of continuous detection positions cannot be changed. Therefore, the sampled signals obtained by detecting the positions have the same direct wave time delay, and the multipath signals are distributed randomly or in a curve. In view of the above features, the present embodiment designs a convolution kernel θ ═ α 3 ,α 2 ,α 1 ,α 2 ,α 3 ]Convolving the signal with the sampling signal on the dimension of the detection position to obtain a new observation signal of the mth detection position:
Figure BDA0003729824510000051
wherein, 0 < alpha 3 ＜α 2 ＜α 1 R (m, t) is a sampling signal obtained from the mth detection position, and t represents time, wherein the confidence of the sampling signal at the current detection position and the adjacent detection position is the confidence of the sampling signal, and the convolution kernel is used for considering the front and back extensibility of the wall body and the abrupt change of the wall body cut-off position, so that the amplitude of the direct wave is accumulated, and the influence brought by the continuous detection position at the wall body cut-off position is effectively reduced.
After the convolution operation is completed, the maximum peak value detection is carried out on the new sequence in the time dimension to obtain the direct wave time delay, and the specific expression is as follows:
Figure BDA0003729824510000052
wherein the content of the first and second substances,
Figure BDA0003729824510000053
is an estimate of the propagation delay of the direct wave at the mth probe location.
And step 3: the modeling of the tomographic projection is carried out,
integrating the direct wave time delay values of all the detection positions to obtain an observation vector
Figure BDA0003729824510000054
M is the total number of measurements. The unknown scene is discretized into N meshes of equal size and the N meshes are represented in vector form, i.e. scene vector
Figure BDA0003729824510000055
Wherein, epsilon (r) n ) And (3) representing the relative dielectric constant of a medium in the nth grid, and T representing matrix transposition operation, wherein the tomography projection model is as follows:
P＝AΟ (4)
wherein the content of the first and second substances,
Figure BDA0003729824510000056
representing the propagation path of the direct wave for a projection matrix;
Figure BDA0003729824510000057
representing the real space, c is the speed of light in free space. For the m detection position, the n scene grid, A mn Can be expressed as:
Figure BDA0003729824510000058
wherein L is m Representing the direct straight path of the transmitting and receiving antennas, r n Representing the position vector of the nth grid.
And 4, step 4: the imaging is carried out in an inversion way,
this step aims to solve for O in the tomographic projection model, and due to the limitations of the detection position and path, the obtained observations are much smaller than the number of meshes in the scene, which results in a severely underdetermined underlying system. Without any additional conditions, O has an infinite number of solutions. According to the characteristic of wall ductility, the invention introduces the constraint of minimum total variation to improve the solving result of O.
The method comprises the following specific steps:
based on the established chromatographic projection model, adding a minimum total variation condition as an objective function, wherein the expression is as follows:
Figure BDA0003729824510000061
wherein D is ij Ο＝[O i+1,j -O i,j ,O i,j+1 -O i,j ] T Representing the variation value of the image, T representing a matrix transposition operation, O i,j Represents the pixel value of the ith row and the jth column in the image, | | · | | luminous 2 Representing the matrix 2-norm.
Using the augmented lagrange method to transform the problem into an optimization problem without constraints, the objective function is then expressed as:
Figure BDA0003729824510000062
wherein, λ is a vector and is an augmentation coefficient, and μ is a penalty coefficient;
finally by introducing a relaxation variable omega ij ≈D ij O, dividing the original problem into solving omega by using an alternating direction algorithm ij And performing alternate iterative solution on two subproblems of the sum O to finally obtain a scene vector estimation value meeting the objective function
Figure BDA0003729824510000063
And realizing the reconstruction of the building layout.
The effects of the invention are further illustrated by the following simulation and experiment as examples:
fig. 1 shows a simulation scenario and antenna scan paths. In the scene, the relative dielectric constant of the wall is 4.5, and the conductivity is 0.01. The type of the transmitted signal is a Rake wavelet, and the center frequency is 2 GHz. The whole scene is sampled from two paths of 0 degrees and 90 degrees, each path is 4m long, and the antenna movement interval is 0.05 m. A total of 160 simulated electromagnetic data were generated by the gprMax electromagnetic simulation software.
Fig. 2 shows a sampling signal of a part of continuous detection positions, and it can be found that the propagation delay of a direct wave in a continuous part of a wall is basically kept unchanged, and the delay of a multipath signal is distributed randomly or in a curve.
Fig. 3 shows the result of sampling signals at a specific detection position, and it can be seen from fig. 3(b) that multipath signals with larger amplitude than direct waves exist in the sampling signals; fig. 3(c) shows the result of convolution operation, and it can be found that the amplitude of the direct wave exceeds the multipath signal, so that the direct wave energy is extracted by searching the maximum peak.
The delay estimation result in the 90 ° sampling path is shown in fig. 5, and fig. 5(a) shows the result of the maximum amplitude delay estimation algorithm, which can be found to be seriously deviated from the ideal value; fig. 5(b) shows the time delay estimation result based on the convolution kernel, which can be found to be very close to the ideal value, and the wall structure can be more intuitively understood through the time delay curve.
As shown in fig. 6, fig. 6(a) and fig. 6(b) are respectively reconstruction results using the time delay values obtained by the two algorithms as observation vectors, and a comparison shows that the direct wave estimation algorithm provided by the present invention can effectively solve the problems of artifacts, wall blurring, and the like in the reconstruction results, and realize high-quality building layout reconstruction.
Experimental scenes as shown in fig. 7, the scene size is 2m × 2m × 1.5 m. And generating a broadband stepped frequency signal with the frequency range of 1.6GHz-2.6GHz by using a vector network instrument, wherein the broadband stepped frequency signal comprises 1048 frequency points. The two horn antennas are respectively fixed on the two remote control cars to realize the transmission and the receiving of signals. In the experiment, two detection paths of 0 degree and 90 degrees are preset, each path is 3m long, and the remote control trolley moves synchronously in steps of 0.05m to obtain 120 sampling signals. The sampling signal is processed in the same way as the simulation, and the obtained delay estimation result and imaging result are respectively shown in fig. 8 and 9. The result shows that the direct wave time delay estimation algorithm and the reconstruction algorithm provided by the invention can obtain a high-quality reconstruction result when being applied to actual measurement.
The invention gives play to high-efficiency performance aiming at the conventional building layout only comprising horizontal and vertical walls by integrating simulation and actual measurement results, and solves the problems of more artifacts and fuzzy walls in the prior art to a great extent.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (4)

1. A building layout tomography method based on direct wave time delay estimation is characterized in that:
s1, multi-position scanning is carried out on the unknown scene along detection paths of 0 degrees and 90 degrees by adopting a single-transmitting single-receiving bistatic radar, and broadband signals of the transmission scene are sampled;
s2, extracting direct waves of all the sampling signals acquired in the step S1 by adopting a direct wave time delay estimation algorithm based on a convolution kernel;
s3, establishing a tomography projection model according to the relation between the direct wave time delay and the projection matrix and the scene vector;
and S4, solving a scene vector by adopting a minimum total variation augmented Lagrange alternating direction algorithm based on the chromatographic projection model established in the step S3, and realizing building layout reconstruction.
2. The building layout tomography method based on direct wave time delay estimation as claimed in claim 1, wherein the specific process of step S2 is as follows:
designing a convolution kernel theta ═ alpha 3 ,α 2 ,α 1 ,α 2 ,α 3 ]Convolving the new observation signal with the sampling signal on the dimension of the sampling point to obtain a new observation signal of the m detection position:
C(m,t)＝θ*R(m,t)
＝α 3 R(m-2,t)+α 2 R(m-1,t)+α 1 R(m,t)+α 2 R(m+1,t)+α 3 R(m+2,t)
wherein, 0 < alpha 3 ＜α 2 ＜α 1 For the confidence of the sampling signal at the current detection position and the adjacent detection position, R (m, t) is the sampling signal obtained at the mth detection position, t represents the time, and then the maximum peak is searched in the new observation signal to obtain the direct wave time delay:
Figure FDA0003729824500000011
wherein the content of the first and second substances,
Figure FDA0003729824500000012
is an estimate of the propagation delay of the direct wave at the mth probe location.
3. The building layout tomography method based on direct wave time delay estimation as claimed in claim 2, wherein the tomographic projection model in step S3 specifically is:
P＝AΟ
wherein the content of the first and second substances,
Figure FDA0003729824500000013
the observation vectors are formed by the time delay of the direct wave at the detected position, and M is the total detection quantity;
Figure FDA0003729824500000014
for scene vectors, representing the unknown scene is discretized into N grids of equal size, ε (r) n ) The relative dielectric constant of a medium in the nth grid is shown, c is the speed of light in free space, and T represents matrix transposition operation; a is an M × N projection matrix.
4. The building layout tomography method based on direct wave time delay estimation as claimed in claim 3, wherein the step S4 is specifically performed by:
based on the established chromatographic projection model, adding a minimum total variation condition as an objective function, wherein the expression is as follows:
Figure FDA0003729824500000021
wherein D is ij Ο＝[O i+1,j -O i,j ,O i,j+1 -O i,j ] T Representing the variable value of the image, O i,j Represents the pixel value of the ith row and the jth column in the image, | | · | | luminous 2 Representing the matrix 2-norm.
Using the augmented lagrange method to transform the problem into an optimization problem without constraints, the objective function is then expressed as:
Figure FDA0003729824500000022
wherein, λ is an augmentation coefficient, and μ is a penalty coefficient;
finally by introducing a relaxation variable omega ij ≈D ij O, dividing the original problem into solving omega by using an alternating direction algorithm ij Performing alternate iterative solution on two subproblems of the sum O to finally obtain a scene vector estimation value meeting the objective function
Figure FDA0003729824500000023
And realizing the reconstruction of the building layout.
CN202210782256.7A 2022-07-05 2022-07-05 Building layout tomography method based on direct wave time delay estimation Pending CN115079165A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210782256.7A CN115079165A (en) 2022-07-05 2022-07-05 Building layout tomography method based on direct wave time delay estimation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210782256.7A CN115079165A (en) 2022-07-05 2022-07-05 Building layout tomography method based on direct wave time delay estimation

Publications (1)

Publication Number Publication Date
CN115079165A true CN115079165A (en) 2022-09-20

Family

ID=83256837

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210782256.7A Pending CN115079165A (en) 2022-07-05 2022-07-05 Building layout tomography method based on direct wave time delay estimation

Country Status (1)

Country Link
CN (1) CN115079165A (en)

Similar Documents

Publication Publication Date Title
Chen et al. Joint estimation of NLOS building layout and targets via sparsity-driven approach
Solimene et al. Three-dimensional through-wall imaging under ambiguous wall parameters
Sakamoto et al. A target shape estimation algorithm for pulse radar systems based on boundary scattering transform
Ambrosanio et al. The tomographic approach to ground-penetrating radar for underground exploration and monitoring: A more user-friendly and unconventional method for subsurface investigation
CN107894591A (en) Through-wall radar diffraction tomography method based on compressed sensing
Doğu et al. Truncated singular value decomposition for through‐the‐wall microwave imaging application
Zheng et al. Application of TRM in the UWB through wall radar
Zhang et al. A novel moving target imaging algorithm for HRWS SAR based on local maximum-likelihood minimum entropy
CN113447915B (en) Ultra-wideband tomography method suitable for complex multipath environment
Pan et al. 3D imaging of moving targets for ultra‐wideband MIMO through‐wall radar system
CN109782279A (en) Bistatic ISAR imaging method based on compressed sensing
CN110554384A (en) imaging method based on microwave signal
Buonanno et al. A new measurement method for through-the-wall detection and tracking of moving targets
Tivive et al. Toward moving target detection in through-the-wall radar imaging
Chen et al. Ultrawideband tomographic imaging in multipath-rich environment
Guo et al. A novel CT-mode through-the-wall imaging method based on time delay estimation
Wu et al. NLOS positioning for building layout and target based on association and hypothesis method
CN113534140B (en) Ground penetrating radar three-dimensional imaging method based on wave field cross correlation
Liang et al. Through the wall imaging of human vital signs based on UWB MIMO bioradar
Li et al. Building layout tomographic imaging with improved delay estimation algorithm
CN115079165A (en) Building layout tomography method based on direct wave time delay estimation
Ozsoy et al. Pencil back-projection method for SAR imaging
Xu et al. Backward projection imaging of through-wall radar based on airspace nonuniform sampling
Guo et al. FIAA-based super-resolution forward-looking radar imaging method for maneuvering platforms
Gu et al. Autofocus imaging simulation for through-wall radar by using FDTD with unknown wall characteristics

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination