CN113324470A - Microwave multi-target imaging and classifying method based on limited aperture - Google Patents
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Abstract
The invention provides a microwave multi-target imaging and classifying method based on a limited caliber, which comprises the following steps: the method comprises the steps of realizing three-dimensional electromagnetic backscattering imaging under a limited caliber based on an SOM method, dividing induction current into a deterministic part and a fuzzy part, then constructing a target function, and optimizing the target function by using a conjugate gradient method to obtain the dielectric constant distribution condition which enables the data model and the simulation model to be matched most; s2, arranging a transmitter and a receiver on three surfaces of x-lambda, x + lambda and z + lambda respectively to detect scattered field data; s3, placing the multi-target object to be detected in a detection area of the limited-caliber three-dimensional imaging system, performing inversion imaging on the target area through microwave super-resolution imaging and technology to obtain characteristics of the target, and finally classifying the multiple targets according to the obtained characteristics. The method can effectively extract the geometric characteristics and physical characteristics of the target, and successfully realize the detection, imaging and classification of multiple targets.
Description
[ technical field ] A method for producing a semiconductor device
The invention relates to the technical field of three-dimensional microwave imaging, and provides a microwave multi-target imaging and classifying method based on limited aperture by utilizing the characteristic that a microwave vision technology is used for extracting geometric parameters and physical parameters of an unknown target in a non-contact mode.
[ background of the invention ]
Microwave imaging refers to an imaging means using microwaves as information carriers, and the principle is to irradiate a measured object with microwaves, and then reconstruct the shape or dielectric constant distribution of the object through the measurement value of a scattered field outside the object. Microwave imaging has wide application prospect in various fields, and in the field of biomedical imaging, compared with the existing electronic computed tomography imaging technology, the electromagnetic backscattering imaging technology has the advantages of no ionizing radiation and little harm to human bodies. Compared with the magnetic resonance imaging technology, the electromagnetic backscattering imaging technology has the advantages of low device cost and convenient use. In the field of biomedical imaging, particularly brain imaging, cancer detection, etc., there have been some advances in electromagnetic backscatter imaging research. In addition, because the electromagnetic wave has certain penetrability and has no damage to the detected object, the electromagnetic backscattering problem is widely applied to the fields of microwave remote sensing, security inspection imaging and the like.
From the mathematical model of the electromagnetic backscattering problem, the solution process of the backscattering problem is actually an optimization problem for solving the extreme value under the constraint condition. The complexity of the back scattering itself makes it difficult to solve this optimization problem directly, and the scattering field obtained by actual measurement needs to be approximated step by step through an iterative process, i.e., the scattering field under different dielectric constant distributions is calculated for many times. From the iterative strategy, electromagnetic optimization algorithms are mainly divided into deterministic optimization algorithms and stochastic optimization algorithms. The deterministic optimization algorithm is an optimization algorithm for obtaining a search target by determining a search direction and a search step length through a certain mathematical principle in an iteration process, and the smaller the target function is in each iteration process, the closer the real solution is. A Contrast source Inversion algorithm (CSI) based on a conjugate gradient method is a deterministic algorithm which is earlier than the CSI in the field of electromagnetic backscattering imaging, and the basic idea is to construct an objective function in a source equation through a scattering field and to reduce the value of the objective function after each iteration by applying the conjugate gradient method. In recent years, a deterministic method, Subspace-based optimization method (SOM), has been proposed to solve the two-dimensional electromagnetic backscattering problem in transverse magnetic wave (TM) scenes. The core idea of the SOM is to analyze a deterministic portion and an ambiguous portion of the induced current in a current space, obtain the deterministic portion by a spectral analysis method, and obtain the ambiguous portion by an optimization method similar to the CSI algorithm, which converges rapidly and stably and has good noise immunity. The computational cost of the SOM algorithm comes mainly from two aspects: 1) carrying out singular value decomposition on a mapping operator from the induced current to the scattered field; 2) fuzzy portions of the induced current are constructed in each optimization iteration. The computational complexity of these two operations becomes greater when dealing with the three-dimensional backscattering problem, because in the three-dimensional backscattering problem the number of unknowns is much larger than in the two-dimensional problem. To overcome this drawback, the SOM method is applied to solve the three-dimensional back scattering problem, and a new current construction method is proposed to reduce the computational complexity of the algorithm. The new construction method only needs to carry out sparse singular value decomposition on the mapping operator, so that the cost of the current construction can be greatly reduced in each optimization iteration. Therefore, with the new construction method, the SOM can be effectively applied to the solution of the three-dimensional backscattering problem.
[ summary of the invention ]
The invention aims to solve the problems in the prior art, provides a microwave multi-target imaging and classifying method based on limited aperture, and can realize the imaging of an unknown target area and the classification of targets according to different imaging shapes and physical parameters.
In order to achieve the purpose, the invention provides a microwave multi-target imaging and classifying method based on a limited caliber, which comprises the following steps:
s1, a three-dimensional imaging algorithm based on a subspace optimization algorithm: the method comprises the steps of realizing three-dimensional electromagnetic backscattering imaging under a limited caliber based on an SOM method, dividing induction current into a deterministic part and a fuzzy part, then constructing an objective function by linearly combining residual terms of a data equation and a state equation, and optimizing the objective function by using a conjugate gradient method to obtain the dielectric constant distribution condition which enables the data model and a simulation model to be matched most;
s2, detection setting of a limited caliber: arranging a transmitter and a receiver on three surfaces of x-lambda, x-lambda and z-lambda to detect scattered field data, wherein lambda is wavelength;
s3, detecting and classifying the targets: the method comprises the steps of placing a multi-target object to be detected in a detection area of a three-dimensional imaging system with a limited caliber, carrying out inversion imaging on the target area through microwave super-resolution imaging and technology, thereby obtaining characteristics related to a target, and finally carrying out classification processing on the multi-target according to the obtained characteristics.
Preferably, step S1 specifically includes the following steps:
s11, adopting a three-dimensional Cartesian coordinate system, selecting a rectangular domain as a region of interest, dividing the rectangular domain into M small rectangular regions, and assuming that the coordinates of the central point of the small regions are xm＝(x1；m，x2；m，x3；m) M1, 2, …, M, the values of which are reconstructed using the measured scattered field data;
the current/electric field integral equation in three dimensions is as follows:
wherein,
representing the relative permittivity of the unknown object, will
Defined as the induced current
Representing a dyadic Green function operator under a uniform background;
s12, dispersing the current/electric field integral equation into a compact discrete matrix equation by adopting a coupled dipole method, wherein the dispersed data equation and the state equation are respectively as follows:
wherein
A mapping operator representing the induced current to the scattered field over the measurement area, and
a mapping operator representing the induced current to the scattered field in the field of interest,
a diffusion intensity tensor, expressed as
Where n, M is 1,2, …,3M, q is mod (M, M) when M is not equal to M,2M,3M, or q is M, VqRepresents the size of a small region, epsilon0Dielectric constant value, e, representing the background of free spacer；qThe dielectric constant value corresponding to the qth small region is shown;
s13, the induced current is divided into two parts, namely a deterministic current part
And ambiguity part
By means of the operator of the corresponding Green function
Performing singular value decomposition, i.e.
Arranging singular values in a descending order, and forming a matrix by taking right singular vectors corresponding to the first L singular values
The space generated by these vectors corresponds to the signal subspace, and the remaining right singular vectors form a matrix
The generated space is a noise subspace;
obtaining a deterministic current portion of the induced current by spectral analysis
Wherein
Representing left singular vectors representing the m-th
Denotes a conjugate transpose;
wherein
Induced current ambiguity part
Expressed as:
s14, constructing an objective function for optimization by using a data equation and a state equation as follows:
wherein
Preferably, in step S2, 16 antennas are provided on each surface, arranged in 4 rows and 4 columns, and the spacing between each antenna is λ/3.
Preferably, in step S2, the polarization directions of the waves are set to the y and z directions for the x- λ and x- λ planes, respectively, and the polarization direction of the wave is set to the x direction for the z- λ plane.
Preferably, in step S3, the acquired features include shape and dielectric constant.
Preferably, in step S3, the classification of the objects is performed in such a manner that the dielectric constant has a higher priority than the shape size.
Preferably, in step S3, the same range dielectric constant is defined as one type of object, and different range dielectric constants, the same range size target is defined as one type of object.
The invention has the beneficial effects that:
the method is based on the fast convergence characteristic of the SOM algorithm, is applied to the three-dimensional electromagnetic backscattering problem, can effectively extract the characteristics of unknown target such as shape, dielectric constant and the like, and then classifies the target according to the obtained characteristics. In consideration of a real measurement scene, the invention adopts the scattered field data measured under a limited caliber to carry out inversion.
The features and advantages of the present invention will be described in detail by embodiments in conjunction with the accompanying drawings.
[ description of the drawings ]
FIG. 1 is a three-dimensional finite aperture imaging model;
FIG. 2 is a block flow diagram of image classification and detection;
figure 3 is a representation of some of the results obtained with the imaging system.
[ detailed description ] embodiments
The invention provides a microwave multi-target imaging and classifying method based on a limited caliber, which is realized based on a three-dimensional limited caliber imaging system and is used for classifying and detecting targets by using scattered field data obtained by measurement under the limited caliber. Fig. 1 shows a three-dimensional finite aperture imaging model, in which a transmitter and a receiver are respectively disposed on three planes, x- λ (wavelength), x + λ, and z + λ, to acquire scattered field information outside a detection region, and reconstruction of a target is achieved based on an SOM algorithm. Fig. 2 shows a flow chart of detecting and classifying targets by using a three-dimensional finite aperture imaging system, that is, placing a measured object in a detection area of the imaging system, extracting characteristics such as the shape and dielectric constant value of the target, and finally classifying the target according to the extracted characteristics.
The invention relates to a microwave multi-target imaging and classifying method based on a limited caliber, which specifically comprises the following steps:
s1 three-dimensional imaging algorithm based on subspace optimization algorithm
Assuming that in a three-dimensional stereo cartesian coordinate system, there is a detection target, which is located in a closed and bounded cubic detection region D,
like the two-dimensional case, assume that the entire detection region is illuminated by three sets of planar sources (TM waves). Assuming that each group of plane waves consists of N distributed uniformlyiMultiple emitters are generated, each emitter being located at x'l＝(x′x；l,x′y；l,x′z；l),l＝ 1,2,…，NiFor each incident wave, there are three corresponding sets of receivers for receiving the scattered field data generated by the irradiated medium, each set containing NrA receiver, wherein the position of the receiver is x's＝(x′x；s，x′y；s，x′z；s)，s＝1，2，…，Nr. Usually, a rectangular field is selected as the field of interest and divided into M small rectangular regions, and the coordinates of the center point of these small regions are assumed to be xm＝(x1；m，x2；m，x3；m) And M is 1,2, …, M. The problem of three-dimensional electromagnetic backscattering is to reconstruct the values of the M dielectric constants using the measured scattered field data.
The current/electric field integral equation in three dimensions is as follows:
wherein,
representing the relative permittivity of the unknown object, will
Defined as the induced current
Representing the dyadic green function operator in a uniform background. Because the region of interest is divided into M small cubic grids, the above current/electric field integral equation can be discretized into a compact discrete matrix equation by a coupled dipole method, and the discretized data equation and state equation are respectively:
wherein
A mapping operator representing the induced current to the scattered field over the measurement area, and
representing the mapping operator of the induced current to the scattered field in the field of interest.
The scattering intensity tensor, which represents the associated incident and induced current, can be expressed as
Wherein n, M is 1,2, …,3M, when M is not equal to M2M,3M, q ═ mod (M, M), otherwise q ═ M, VqRepresents the size of a small region, epsilon0Dielectric constant value, e, representing the background of free spacer；qAnd (3) showing the dielectric constant value corresponding to the qth small region. When solving the three-dimensional electromagnetic backscattering problem, it is usually transformed into an optimization problem. The most intuitive idea is to solve a dielectric constant distribution such that the calculated scattered field is as close as possible to the measured scattered field under such a distribution. An objective function is generally constructed by linearly combining the residuals of the data equation and the state equation, and then an appropriate optimization method is selected to minimize the objective function, and the dielectric constant value of the detection region is solved.
The invention realizes three-dimensional electromagnetic backscattering imaging under the limited caliber based on an SOM method, and when solving an inverse problem, an induced current is generally divided into two parts, namely a deterministic current part
And ambiguity part
By means of the operator of the corresponding Green function
Performing singular value decomposition, i.e.
Arranging singular values in a descending order, and forming a matrix by taking right singular vectors corresponding to the first L singular values
The space generated by these vectors corresponds to the signal subspace, and the remaining right singular vectors form a matrix
The resulting space is the noise subspace. A deterministic portion of the induced current can be obtained by spectral analysis:
wherein
Representing left singular vectors representing the m-th
Denotes the conjugate transpose.
Wherein
Since the singular value values in the noise space are inaccurate, the ambiguity current cannot be determined, and an optimization algorithm needs to be designed to obtain the ambiguity current. The blur current can be expressed as:
the objective function for optimization is constructed using data equations and state equations as follows:
wherein
The invention optimizes this objective function using Conjugate Gradient (CG) method to obtain the best matching dielectric constant distribution between data model and simulation model.
S2 detection setting of limited caliber
In the conventional full-aperture three-dimensional imaging algorithm, plane wave sources are generally arranged in three planes of xoy, xoz and yoz to irradiate a detection area, and transmitters and receivers of each plane are respectively distributed uniformly in a ring shape to irradiate a target at a full angle of 360 degrees. However, in many practical situations, it is not possible to arrange the detection device as described above, so the present invention proposes to detect unknown objects with a limited aperture, namely x ═ λ (wavelength), x ═ λ, z ═ λ, three planes, on which the emitter and the detector are arranged, 16 antennas are arranged on each plane, arranged in 4 rows and 4 columns, and spaced at λ/3 intervals, where for a rectangular field of interest of λ, the illumination angle of each plane to the field of interest is not greater than 180 °. For the x- λ and x- λ planes, the polarization directions of the waves are set to be y and z directions, respectively, and the polarization direction on the z- λ plane is set to be the x direction. Through numerical simulation, the invention proves the effectiveness of the finite caliber detection scheme.
S3, detecting and classifying the target
The method comprises the following steps of placing a multi-target object to be detected in a detection area of a limited-caliber three-dimensional imaging system, performing inversion imaging on the target area through microwave super-resolution imaging and technology, so as to obtain characteristics such as the shape and the dielectric constant value of a target, and then classifying the multiple targets according to the obtained characteristics (mainly the shape and the dielectric constant): the same range dielectric constant is defined as one type of object, while different ranges of dielectric constant, the same range size target is also defined as one type of object, where: physical parameters such as dielectric constant have a higher priority than shape size.
Example 1.
Fig. 1 shows a structural diagram of an experimental apparatus designed and used in the present invention, in which a TM wave having an operating frequency of 400MHz (λ ═ 0.75m) is selected to irradiate a size of 0.75 × 0.75 × 0.75m3The scatter field is divided into 30 x 30 small grids in the forward calculation and into 30 x 30 small grids in the inverse problem. The detection antennas are arranged on three planes of x-0.75 m, x +0.75m and z +0.75m, each plane is provided with 16 antennas,the antenna is orderly arranged into 4 rows and 4 columns, and the interval between every two antennae is 0.25 m. The invention selects to detect some objects with different shapes and dielectric constants, and fig. 3 shows a real image of the objects and a reconstruction result image obtained by an imaging algorithm. It can be seen that the SOM-based three-dimensional imaging algorithm can effectively extract the features such as the shapes and dielectric constants of the targets, and the targets can be successfully classified according to the features, for example, the first line graph of fig. 3(b) can distinguish three targets with different dielectric constants, the second line graph can accurately distinguish targets with different dielectric constants, and the third line graph can distinguish objects with different sizes and shapes.
The invention is based on an iterative optimization algorithm of a physical model, utilizes scattered field data obtained by measurement under a limited caliber to extract the characteristics of the object shape, the dielectric constant and the like of multiple targets, and then extracts and classifies the information (including the shape, the physical parameters and the like) of the multiple targets according to the obtained characteristics. As can be known from simulation calculation, the method can effectively extract the geometric characteristics and the physical characteristics of the target, and successfully realize the detection, imaging and classification of multiple targets.
The above embodiments are illustrative of the present invention, and are not intended to limit the present invention, and any simple modifications of the present invention are within the scope of the present invention.
Claims (7)
1. The microwave multi-target imaging and classifying method based on the limited caliber is characterized by comprising the following steps: the method comprises the following steps:
s1, a three-dimensional imaging algorithm based on a subspace optimization algorithm: the method comprises the steps of realizing three-dimensional electromagnetic backscattering imaging under a limited caliber based on an SOM method, dividing induction current into a deterministic part and a fuzzy part, then constructing an objective function by linearly combining residual terms of a data equation and a state equation, and optimizing the objective function by using a conjugate gradient method to obtain the dielectric constant distribution condition which enables the data model and a simulation model to be matched most;
s2, detection setting of a limited caliber: arranging a transmitter and a receiver on three surfaces of x-lambda, x-lambda and z-lambda to detect scattered field data, wherein lambda is wavelength;
s3, detecting and classifying the targets: the method comprises the steps of placing a multi-target object to be detected in a detection area of a three-dimensional imaging system with a limited caliber, carrying out inversion imaging on the target area through microwave super-resolution imaging and technology, thereby obtaining characteristics related to a target, and finally carrying out classification processing on the multi-target according to the obtained characteristics.
2. The microwave multi-target imaging and classification method based on the finite aperture as claimed in claim 1, wherein: step (ii) of
S1 specifically includes the following steps:
s11, adopting a three-dimensional Cartesian coordinate system, selecting a rectangular domain as a region of interest, dividing the rectangular domain into M small rectangular regions, and assuming that the coordinates of the central point of the small regions are xm＝(x1；m,x2；m,x3；m) M1, 2, …, M, the values of which are reconstructed using the measured scattered field data;
the current/electric field integral equation in three dimensions is as follows:
wherein,
representing the relative permittivity of the unknown object, will
Defined as the induced current
Representing a dyadic Green function operator under a uniform background;
s12, dispersing the current/electric field integral equation into a compact discrete matrix equation by adopting a coupled dipole method, wherein the dispersed data equation and the state equation are respectively as follows:
wherein
A mapping operator representing the induced current to the scattered field over the measurement area, and
a mapping operator representing the induced current to the scattered field in the field of interest,
a diffusion intensity tensor, expressed as
Where n, M is 1,2, …,3M, q is mod (M, M) when M is not equal to M,2M,3M, or q is M, VqRepresents the size of a small region, epsilon0Dielectric constant value, e, representing the background of free spacer；qThe dielectric constant value corresponding to the qth small region is shown;
s13, the induced current is divided into two parts, namely a deterministic current part
And ambiguity part
By means of the operator of the corresponding Green function
Performing singular value decomposition, i.e.
Arranging singular values in a descending order, and forming a matrix by taking right singular vectors corresponding to the first L singular values
The space generated by these vectors corresponds to the signal subspace, and the remaining right singular vectors form a matrix
The generated space is a noise subspace;
obtaining a deterministic current portion of the induced current by spectral analysis
Wherein
Representing left singular vectors representing the m-th
Denotes a conjugate transpose;
wherein
Induced current ambiguity part
Expressed as:
s14, constructing an objective function for optimization by using a data equation and a state equation as follows:
wherein
3. The microwave multi-target imaging and classification method based on the finite aperture as claimed in claim 1, wherein: in step S2, 16 antennas are disposed on each surface, and arranged in 4 rows and 4 columns, and the spacing between each antenna is λ/3.
4. The microwave multi-target imaging and classification method based on the finite aperture as claimed in claim 1, wherein: in step S2, the polarization directions of the waves are set to the y and z directions for the x- λ plane and the x- λ plane, respectively, and the polarization direction of the wave is set to the x direction for the z- λ plane.
5. The microwave multi-target imaging and classification method based on the finite aperture as claimed in claim 1, wherein: in step S3, the obtained features include shape and dielectric constant.
6. The microwave multi-target imaging and classification method based on the finite aperture as claimed in claim 5, wherein: in step S3, the classification processing of the objects is performed such that the dielectric constant has a higher priority than the shape size.
7. The microwave multi-target imaging and classification method based on the finite aperture as claimed in claim 6, wherein: in step S3, the same range dielectric constant is defined as a class of objects, and the same range size target with a different range dielectric constant is defined as a class of objects.
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| CN115184927A (en) * | 2022-07-25 | 2022-10-14 | 北京众智信安信息技术研究院 | Microwave nondestructive imaging target detection method |
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