阅读说明：本技术 基于神经网络解决电磁逆散射问题的两步无相位成像法 (Two-step phase-free imaging method for solving electromagnetic backscattering problem based on neural network ) 是由 吴亮 徐魁文 马振超 张璐 于 2020-05-28 设计创作，主要内容包括：本发明公开了一种基于神经网络解决电磁逆散射问题的两步无相位成像法。在电磁逆散射成像领域,全波数据反演算法需要用到全波数据,然而全波数据的实际测量相当困难；无相位反演算法仅需要使用无相位总场数据,无相位总场数据的实际测量要容易很多,但是无相位反演算法具有更高的非线性度,计算较为困难。本发明正是针对全波数据反演算法和无相位反演算法的优缺点而产生的,结合CNN,先对无相位数据进行相位恢复,然后再结合全波数据反演算法重建图像。(The invention discloses a two-step phase-free imaging method for solving the problem of electromagnetic backscattering based on a neural network. In the field of electromagnetic backscatter imaging, a full-wave data inversion algorithm needs to be used for full-wave data, but actual measurement of the full-wave data is quite difficult; the phase-free inversion algorithm only needs to use phase-free total field data, the actual measurement of the phase-free total field data is easy, but the phase-free inversion algorithm has higher nonlinearity and is difficult to calculate. The invention is generated aiming at the advantages and disadvantages of the full-wave data inversion algorithm and the phase-free inversion algorithm, combines with CNN, firstly carries out phase recovery on the phase-free data, and then combines with the full-wave data inversion algorithm to reconstruct the image.)

1. A two-step phase-free imaging method for solving the problem of electromagnetic backscattering based on a neural network is characterized by comprising the following steps of:

step one, a phase-free data processing stage, which is to restore phase-free total field data into scattered field data;

and step two, an image inversion stage, namely reconstructing an image of the unknown scatterer.

2. The two-step phase-free imaging method for solving the electromagnetic backscattering problem based on neural networks of claim 1, wherein: the phase-free total field data in the first step are obtained in the following mode:

assuming that an unknown object exists in the target region D in the free space background,in the method, the total number of the meshes of the target area after being divided is assumed to be N, and the position of each mesh is r_nN is 1,2,3, N; and outside this area, a transmitting antenna and a receiving antenna are installed, the position of the transmitting antenna being indicated by r_p,p＝1,2,…,N_iThe position of the receiving antenna is denoted as r_q,q＝1,2,…,N_rObtaining N_i×N_rScatter field data; the scattering body is composed of a non-magnetic and isotropic inhomogeneous medium, and a scattering field E is applied^sca(r_q) Solving for the dielectric constant distribution (r) in the target region D_n)：

Obtaining a total field integral equation by a Lippmann-Schwigger electric field integral equation:

wherein E^inc(r) represents the incident field at r located inside the region; chi (r) -₀)/₀As a function of contrast within the region; k is a radical of₀Represents the wave vector in free space; green function of green

integral equation of scattered field:

wherein E^sca(r_q) Is shown at r_qInformation of the scattered field received by the receiving antenna,

I(r)＝χ(r)E^tot(r) (3)

discretizing equations (1) - (3):

wherein ⊙ denotes the corresponding element multiplication, Green function

whereinRepresenting an identity matrix;

the definition of the total field without phase is as follows:

whereinRepresenting the field information received by the receiving antenna in the absence of unknown scatterers.

3. The two-step phase-free imaging method for solving the electromagnetic backscattering problem based on neural networks of claim 1, wherein: the neural network is a U-net neural network, and comprises the following concrete steps:

the left side of the U-net neural network is a contraction path which consists of convolution and pooling operations, and each layer on the left side is subjected to convolution operation twice; each convolution is processed by Batch Normalization (BN) and an activation function (ReLU), then the maximum pooling merging operation enters the next layer, and in each down-sampling step, the picture size is reduced by half, and the number of characteristic channels is doubled; an expansion path is arranged on the right side of the U-net neural network and used for recovering a matrix, each step comprises up-sampling of a characteristic diagram, then deconvolution is carried out, the number of characteristic channels is halved, and meanwhile, the size of the matrix is doubled and used for recovering the matrix to the original size; the signature graph obtained by each convolutional layer of the U-net neural network is connected to the corresponding upsampling layer.

4. The two-step phase-free imaging method for solving the electromagnetic backscattering problem based on neural networks of claim 2, wherein: in the first step

Scattered field calculation formula:

the phase-free total field calculation formula:

scattered field calculation formula:

calculating scattered fields and phase-free total fields of all scatterers by using a formula (7) and a formula (8), and taking the result as a training set, wherein one part of the result is taken as a test set; the scattered field is a complex matrix, the phase-free total field is a real matrix, and the real part and the imaginary part of the scattered field are separated, so that one dimension is added to store the information; the phase-free total field is also added with one dimension, and the imaginary parts of the phase-free total field are all 0;

the size formula of the matrix after convolution operation is as follows:

O＝(W-F+2P)/S+1 (9)

where O denotes the output matrix size, W denotes the input matrix size, F denotes the convolution kernel (Filter) size, P denotes the Padding value (Padding) size, and S denotes the step size.

5. The two-step phase-free imaging method for solving the electromagnetic backscattering problem based on neural networks of claim 4, wherein:

the second step is as follows:

assuming that the induced current is proportional to the electromagnetic field:

according to equation (5), an objective function of the BP algorithm is defined:

the minimum value of formula (11) is obtained by only letting F^bThe derivative of (χ) with respect to χ is zero, resulting in an analytical solution for χ:

wherein T represents transpose operation and x represents conjugate operation, and after x is obtained, the induced current can be obtained according to the formula (10)And an updated total field can be obtained:

for the p-th incident antenna, the contrast ratio is defined according to the induced currentAndthe following relationship is satisfied:

all the incident antennas in equation (13) are combined and the contrast can be found

by

Technical Field

The invention belongs to the technical field of electromagnetic backscattering imaging, and particularly relates to a two-step phase-free imaging method for solving the problem of electromagnetic backscattering based on a neural network.

Background

Electromagnetic wave backscatter imaging is an important method for obtaining electromagnetic or physical properties of an object without loss and contact. Electromagnetic detection methods have been widely used in many fields such as positioning, microwave remote sensing, geophysical prospecting, nondestructive testing, biomedical imaging, and the like. In general, the electromagnetic backscattering problem is to utilize the scattering of incident waves by an object to be measured, and to invert or reconstruct the physical and geometrical characteristics of the object, including its position, size, number, boundary, electromagnetic parameter distribution, etc., by measuring the scattered field outside the object or its far-field pattern.

Over the past few decades, electromagnetic backscatter imaging techniques have become more mature due to the continuing efforts of researchers, and many different inversion methods have been developed to more efficiently and reliably detect unknown scatterers within an area. However, the inadequacy and nonlinearity remain two major difficulties faced in solving the electromagnetic backscattering problem. In order to improve the inversion efficiency, researchers neglect the multiple scattering effect in the Domain of Interest (DoI), and propose a linear method based on Born Approximation (BA) and Rytov approximation. The linear algorithm has small calculation amount and high calculation speed, but the approximation condition is harsh, and the linear algorithm is generally only used for weak scatterers. In order to cope with strong scatterers, multiple scattering effects should be included in the modeling, and nonlinear methods such as Deformable Born Iteration Method (DBIM), contrast source-type inversion Method (CSI), Subspace Optimization algorithm (SOM), Two-fold Subspace Method (TSOM) and some global Optimization methods were developed. The nonlinear algorithm approximates the real solution through successive iteration by an optimization algorithm, the application range is wide, and the calculated amount is huge. In recent years, neural network algorithms have gradually penetrated into various research fields. In the art, Convolutional Neural Networks (CNN) have been successfully applied to the solution of the nonlinear inverse scattering problem, and the CNN-based inversion method is superior to the conventional nonlinear inversion algorithm in both image quality and computation speed.

The above mentioned methods all use fringe field data (full wave data) with amplitude and phase information to reconstruct the geometry and physics of the scatterers. Accurate measurement of the fringe field amplitude and phase has also been a difficulty. Phase measurement usually involves considerable difficulties and non-negligible hardware costs, and even when the frequency is high to some extent, phase information cannot be directly measured. Thus, the requirement to reconstruct scatterers from the scattered field data limits the application of this technique to many practical scenarios. In Contrast, the acquisition of the phase-free total field is much easier, so researchers have proposed methods for reconstructing scatterers using phase-free total field Data, such as newton Method (newton Method), phase-free Subspace Optimization Method (PD-SOM), phase-free Contrast Source Inversion (PD-CSI), and phase-free Regularized Contrast Source Inversion (PD-MRCSI). But the phase-free algorithm has the disadvantages that the noise resistance is poorer and the nonlinearity is higher. In general, the full-wave data inversion algorithm and the phase-less inversion algorithm have respective advantages and disadvantages, so that it is very significant to develop a method capable of saving hardware cost and effectively processing high nonlinearity.

Disclosure of Invention

The invention aims to provide a two-step phase-free imaging method for solving the problem of electromagnetic inverse scattering based on a neural network, aiming at the advantages and disadvantages of a full-wave data inversion algorithm and a phase-free inversion algorithm. By "two steps" is meant that the process is carried out in two steps: the first step is a phase-free data processing stage, which aims to recover phase-free total field data into scattered field data; the second step is an image inversion stage, aimed at reconstructing an image of the unknown scatterer. The method has the advantages that the scattered field information is not directly measured, and only the phase-free total field is measured. After the phase-free total field data is obtained, the phase-free data is restored to scattered field data using the first of the "two steps", and then a scatterer image is reconstructed using the second of the "two steps". The present invention requires the training of two different CNNs to implement.

The technical scheme of the invention is as follows:

the invention proposes to reconstruct the scatterer image in two steps. The first step is phase recovery, i.e., recovering the phase-free total field data into scattered field data. The second step involves an electromagnetic inverse scattering inversion algorithm. The main contents are as follows:

firstly, obtaining phase-free total field data and scattered field data through electromagnetic field correlation knowledge:

assuming that an unknown object exists in a target area under a free space background

And (4) the following steps. In general, the solution of the back scattering problem requires that the target region is subdivided according to a certain rule. Assuming that the total number of the meshes of the divided target area is N, and the position of each mesh is r_nN is 1,2,3. And outside this area, a transmitting antenna and a receiving antenna are installed (the transmitting antenna position is denoted by r)_p,p＝1,2,…,N_iThe position of the receiving antenna is denoted as r_q,q＝1,2,…,N_r) Applying this arrangement N is obtained_i×N_rA scatter field data. Given that the scatterer is composed of a non-magnetic and isotropic inhomogeneous medium, the problem of backscatter imaging can be attributed to the application of a scattered field E^sca(r_q) Solving for the dielectric constant distribution (r) in the target region D_n)。

The total field integral equation can be obtained by the Lippmann-Schwigger electric field integral equation:

wherein E^inc(r) represents the incident field at r located inside the region; chi (r) -₀)/₀As a function of contrast within the region; k is a radical of₀Represents the wave vector in free space; green function of greenRepresenting the field generated by a point source located in space r' to a point r in the space surrounding it,representing a zero order first class hank function.

Integral equation of scattered field:

wherein E^sca(r_q) Is shown at r_qInformation of the scattered field received by the receiving antenna;

the contrast source is the product of contrast and total field, defined as:

I(r)＝χ(r)E^tot(r) (3)

discretizing equations (1) - (3):

wherein ⊙ denotes the corresponding element multiplication, Green function

As a discrete Green function G (r)_qR '), an integral operator of r'),as a discrete Green function G (r)_nR') of the same. The induced current calculated by equation (6) is substituted into equation (5) to calculate the required scattered field data. The formula is as follows:

wherein

Representing an identity matrix.

The definition of the total field without phase is as follows:

wherein

Representing the field information received by the receiving antenna in the absence of unknown scatterers.

Secondly, building a neural network:

the neural network used in the present invention is a U-net neural network. The U-net is typically characterized by a "U" -shaped symmetrical network (as shown in FIG. 2). On the left side of the U-net is a shrink path, which consists mainly of convolution and pooling operations. Each layer on the left is subjected to two convolution operations. Each convolution is processed by Batch Normalization (BN) and activation function (ReLU), and the BN can effectively accelerate deep network training. Then the max-pooling merge operation proceeds to the next layer, and at each down-sampling step, the picture size is reduced by half while the number of feature channels is doubled. To the right of the U-net is an extended path. The extended path is mainly used to recover the matrix, each step of which consists of upsampling of the eigen-map, followed by deconvolution, halving the number of eigen-channels, while doubling the matrix size for recovering the matrix to the original size. The signature obtained from each convolutional layer of the U-net will be connected to the corresponding upsampling layer so that more information of the original matrix can be retained in subsequent calculations. The U-net architecture was originally used for medical segmentation, which can predict the value of each pixel well.

The invention has the beneficial effects that:

the invention mainly aims at the advantages and disadvantages of a full-wave data inversion algorithm and a phase-free inversion algorithm, and provides a 'two-step' phase-free imaging method for solving the problem of electromagnetic backscattering based on a neural network. In the field of electromagnetic backscatter imaging, a full-wave data inversion algorithm has more scatterer information (amplitude and phase information), and is lower in nonlinearity than a phase-free inversion algorithm, so that the calculation is easier. However, full-wave data inversion algorithms require the use of fringe field data with amplitude and phase information, and in practice accurate measurement of the fringe field is quite difficult. The invention can obtain the scattered field information by avoiding a method of directly measuring the scattered field and shows good inversion effect.

Drawings

FIG. 1 is a diagram of an experimental setup for measuring field information;

FIG. 2 is a diagram of a U-net structure;

FIG. 3 is a partial training sample presentation diagram for training a neural network;

FIGS. 4a and 4b are a view of an Austria scatterer structure and an inverted view, respectively;

fig. 5a and 5b are graphs of a foamdielex ext structure and an inversion of measured data foamdielex ext, respectively.

Detailed Description

The invention will be further explained with reference to the drawings.

The invention proposes to reconstruct the scatterer image in two steps. The first step is phase recovery, i.e., recovering the phase-free total field data into scattered field data. The second step involves an electromagnetic inverse scattering inversion algorithm. The main contents are as follows:

firstly, obtaining phase-free total field data and scattered field data through electromagnetic field correlation knowledge:

assuming that an unknown object exists in a target area under a free space backgroundAnd (4) the following steps. In general, the solution of the back scattering problem requires that the target region is subdivided according to a certain rule. Assuming that the total number of the meshes of the divided target area is N, and the position of each mesh is r_nN is 1,2,3. And outside this area, a transmitting antenna and a receiving antenna are installed (the transmitting antenna position is denoted by r)_p,p＝1,2,…,N_iThe position of the receiving antenna is denoted as r_q,q＝1,2,…,N_r) Applying this arrangement N is obtained_i×N_rA scatter field data. Given that the scatterer is composed of a non-magnetic and isotropic inhomogeneous medium, the problem of backscatter imaging can be attributed to the application of a scattered field E^sca(r_q) Solving for the dielectric constant distribution (r) in the target region D_n)。

The total field integral equation can be obtained by the Lippmann-Schwigger electric field integral equation:

wherein E^inc(r) represents the incident field at r located inside the region; chi (r) -₀)/₀As a function of contrast within the region; k is a radical of₀Represents the wave vector in free space; green function of greenRepresenting the field generated by a point source located in space r' to a point r in the space surrounding it,representing a zero order first class hank function.

Integral equation of scattered field:

wherein E^sca(r_q) Is shown at r_qInformation of the scattered field received by the receiving antenna;

the contrast source is the product of contrast and total field, defined as:

I(r)＝χ(r)E^tot(r) (3)

discretizing equations (1) - (3):

wherein ⊙ denotes the corresponding element multiplication, Green functionAs a discrete Green function G (r)_qR '), an integral operator of r'),as a discrete Green function G (r)_nR') of the same. The induced current calculated by equation (6) is substituted into equation (5) to calculate the required scattered field data. The formula is as follows:

whereinRepresenting an identity matrix.

The definition of the total field without phase is as follows:

wherein

Representing the field information received by the receiving antenna in the absence of unknown scatterers.

Secondly, building a neural network:

the neural network used in the present invention is a U-net neural network. The U-net is typically characterized by a "U" -shaped symmetrical network (as shown in FIG. 2). On the left side of the U-net is a shrink path, which consists mainly of convolution and pooling operations. Each layer on the left is subjected to two convolution operations. Each convolution is processed by Batch Normalization (BN) and activation function (ReLU), and the BN can effectively accelerate deep network training. Then the max-pooling merge operation proceeds to the next layer, and at each down-sampling step, the picture size is reduced by half while the number of feature channels is doubled. To the right of the U-net is an extended path. The extended path is mainly used to recover the matrix, each step of which consists of upsampling of the eigen-map, followed by deconvolution, halving the number of eigen-channels, while doubling the matrix size for recovering the matrix to the original size. The signature obtained from each convolutional layer of the U-net will be connected to the corresponding upsampling layer so that more information of the original matrix can be retained in subsequent calculations. The U-net architecture was originally used for medical segmentation, which can predict the value of each pixel well.

Derived from previous calculations, we derive:

scattered field calculation formula:

the phase-free total field calculation formula:

scattered field calculation formula:

5000 real scatterers are randomly generated, and are randomly acquired from MNIST types of a common training set (as shown in FIG. 3), and the relative dielectric constant of the scatterers randomly changes from 1.1 to 1.5. Then, the scattered field and the total field without phase of all scatterers are calculated by formula (7) and formula (8), and the result is used as a training set, wherein 1000 are used as a test set. It should be noted that the scattered field is a complex matrix, and the total field without phase is a real matrix, so the real part and the imaginary part of the scattered field need to be separated, and a dimension is added to store the information. The phase-free total field is likewise increased by one dimension, the imaginary part of which is all 0. The dimensions of the processed scattered field and the phase-free total field are kept consistent, wherein the scattered field serves as a label.

The size formula of the matrix after convolution operation is as follows:

O＝(W-F+2P)/S+1 (9)

where O denotes the output matrix size, W denotes the input matrix size, F denotes the convolution kernel (Filter) size, P denotes the Padding value (Padding) size, and S denotes the step size. The matrix is reduced in size by a factor of two after the maximum pooling operation. When the convolution kernel size is 1 × 1, the matrix size is unchanged. Whereas deconvolution can restore the matrix to the size before convolution, upsampling can restore the matrix to the size before pooling. Therefore, the left side and the right side of the U-net are basically in a symmetrical structure, and the left side has the pooling times, and the right side has the corresponding up-sampling times.

From the above, the first CNN can be trained, which is used for phase recovery, with the input being the phase-free total field and the output being the scattered field, so that the first step can be completed. The second step needs to be completed next.

Assuming that the induced current is proportional to the electromagnetic field:

from equation (5), the objective function of the BP algorithm can be defined:

the minimum value of formula (11) is obtained by only letting F^bThe derivative of (χ) with respect to χ is zero, resulting in an analytical solution for χ:

where T represents a transpose operation and x represents a conjugate operation. After obtaining χ, the induced current can be obtained according to the formula (10)And an updated total field can be obtained:

for the p-th incident antenna, the contrast ratio is defined according to the induced current

And

the following relationship is satisfied:

all the incident antennas in equation (13) are combined and the contrast can be foundThe nth element of (c):

contrast ratio

(byReassigned size change) is the initial image of the scatterer, which is blurry and needs to be optimized by CNN. The CNN before the use is continued, and only the training set needs to be replaced. The input to the second CNN at this time is the blurred initial image and the output is the final scatterer image.