A limited-aperture oriented inverse scattering imaging method

Abstract

The present application belongs to the field of electromagnetic inverse scattering imaging, and relates to an inverse scattering imaging method for a limited aperture, comprising: obtaining scattering field data of a target scatterer; obtaining a deterministic current of an induced current according to the scattering field data; wavelet compressing the deterministic current to obtain corresponding approximation coefficients; designing an LA-NET inverse scattering network model, inputting the approximation coefficients in a first network of the model to obtain low-frequency component information of the induced current, and then reconstructing a rough image and an initial estimated value of the induced current through the low-frequency component information; inputting the initial estimated value of the induced current in a second network of the model, introducing a contrast learning mechanism to gradually recover a detailed image of the induced current, thereby obtaining a high-precision induced current, and further reconstructing a high-quality scatterer image. The present application effectively integrates physical priors through a cascade architecture combining wavelet transform and physical information expansion mechanism, and reconstructs a high-quality scatterer image without additional model training.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of electromagnetic inverse scattering imaging, and relates to an inverse scattering imaging method for a limited aperture. BACKGROUND

[0002] Electromagnetic inverse scattering aims to recover the location, geometry and constitutive parameters of unknown scatterers in a domain of interest (DOI) from received scattered field data. Electromagnetic inverse scattering problems are widely used in various fields such as medical imaging, underground exploration, radar and through-wall imaging. In recent years, full-aperture electromagnetic inverse scattering calculation has developed rapidly. However, in most real-world applications, such as through-wall imaging, underground mineral exploration and security imaging, full-aperture data cannot be obtained. Therefore, it is more valuable to study imaging methods under limited aperture.

[0003] Due to the fact that the number of received antennas is much smaller than the number of unknowns, electromagnetic inverse scattering problems exhibit inherent ill-conditioning; at the same time, the multiple scattering effect of electromagnetic waves inside the object leads to severe nonlinearity. In the limited aperture problem, we can only place the transmitting and receiving antennas at extremely limited positions, so this ill-conditioning is particularly obvious. For the limited aperture imaging problem, there are three main solution ideas in traditional methods. The first type: improve the full-aperture method to adapt to the limited aperture, such as extending the orthogonal projection method and introducing boundary constraint conditions, which improves the stability of the solution, but the reconstruction accuracy decreases with the decrease of the aperture angle and the calculation cost increases; the second type: recover the full-aperture data from the limited aperture data, for example, the methods based on Green's formula (MGF) and single-layer potential (MSLP) recover data by solving an ill-posed integral equation, but this process highly depends on Tikhonov regularization, and improper parameter selection will lead to data distortion; the third type: directly optimize the limited aperture data processing, such as combining SVD and Bessel functions to achieve efficient positioning but there is a problem of multi-target resolution, or using multi-frequency frequency hopping technology and coarse-fine grid iteration strategy to improve robustness, but the calculation is time-consuming and strongly dependent on the initial guess. Overall, although these methods improve the imaging performance under limited aperture, there are still challenges such as efficiency, multi-target resolution and initial value dependence that need to be overcome.

[0004] Deep learning has also been used to solve the limited aperture problem in recent years. Due to the poor generalization and lack of interpretability of purely data-driven methods, more attention is paid to physically guided networks. Xu et al. proposed a network model based on the expansion of the integral equation of contraction, which integrates physical prior knowledge, but often needs to be retrained when the aperture changes. G. R. Karthik and P. K. Ghosh proposed a double-U-Net architecture for arbitrary apertures, which realizes reconstruction by combining back-projection estimation and shared networks. However, this method only changes the observation angle and number of transmitting antennas, and for each different angle of transmission, the receiving antenna is fixed to cover a 240° sector, which lacks flexibility. The scene with smaller transmitting and receiving apertures still needs to be expanded. SUMMARY

[0005] In order to solve the above technical problems existing in the prior art, the present application proposes a limited-aperture-oriented inverse scattering imaging method, and the specific technical scheme is as follows:

[0006] A limited-aperture-oriented inverse scattering imaging method, comprising: obtaining scattering field data of a target scatterer; obtaining deterministic current of induced current according to the scattering field data; wavelet compressing the deterministic current to obtain corresponding approximation coefficients; designing a LA-NET inverse scattering network model, including a first level network and a second level network, in the first level network, inputting the approximation coefficients to obtain low-frequency component information of the induced current, and then reconstructing a rough image and an initial estimate value of the induced current through the low-frequency component information; in the second level network, inputting the initial estimate value of the induced current, introducing a contrast learning mechanism to gradually recover a detailed image of the induced current, thereby obtaining a high-precision induced current.

[0007] Further, the scattering field data includes: obtaining the induced current and the scattering field of the target scatterer by using the method of moments, the Green function of the target scatterer, and the incident field.

[0008] Further, the Green function is singular value decomposed by using the SOM method to obtain the deterministic current of the induced current.

[0009] Further, the wavelet compression selects a haar wavelet basis to perform wavelet transform.

[0010] Further, the low-frequency component information is compressed and recovered by the wavelet inverse transform method through high-frequency 0 to obtain the initial estimate value of the induced current.

[0011] Further, the second level network includes a least square operator and a CNN network, the initial estimate value of the induced current is used to calculate a corresponding contrast function by using the least square operator, the contrast function is input into the CNN network after being concatenated with the corresponding initial estimate value of the induced current, and the predicted induced current is output through the CNN network.

[0012] Further, the second-level network recovers the permittivity of the scatterer by using a SOM method, and calculates the scattering field by the predicted induced current.

[0013] Further, the second-level network optimizes the recovered predicted induced current, permittivity distribution and scattering field by using a physically guided weighted loss function, and further reconstructs a high-quality scatterer image.

[0014] Further, the physically constrained weighted loss function includes a data loss function and a physical equation loss function, the data loss function is a mean square error (MSE) loss based on wavelet approximation coefficient learning, the physical equation loss function is an MSE loss between the predicted induced current and the real current, and an MSE and structural similarity (SSIM) index between the predicted permittivity distribution and the real value, and a difference between the scattering field calculated by the predicted induced current and the measured scattering field.

[0015] The beneficial effects of the present application are as follows:

[0016] Wide-aperture range quantitative imaging: the method can realize quantitative imaging in a wide-aperture range of 90° to 360°, and can adapt to changes in observation angles without retraining the network.

[0017] Wavelet transform-based data compression and physical expansion: the principal components of the induced current are compressed by wavelet transform, and redundant high-frequency components are removed, so that the input data dimension is reduced from 2N*2N to N*N, which significantly reduces the computational burden of the network. In addition, the CIE-I physical model is expanded by combining the neural network, which effectively alleviates the nonlinear characteristics of the inverse scattering problem.

[0018] Hybrid optimization with physical constraints: the network introduces physical constraints in the loss function, optimizing the model from the perspectives of data-driven and physical modeling. Experiments show that, compared with other methods, the LA-Net has significant advantages in scatterer profile identification, imaging accuracy and robustness under limited aperture conditions. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 is a two-dimensional limited-aperture electromagnetic inverse scattering model diagram of the embodiment;

[0020] Figure 2 is an LA-NET network flowchart of the embodiment;

[0021] Figure 3 is a wavelet transform principle diagram of the embodiment;

[0022] Figure 4 is a specific network structure of the CNN in the LA network structure of the embodiment;

[0023] Figure 5 is the imaging effect diagram of the method compared with other existing methods at a certain observation angle in the embodiment;

[0024] Figure 6 is the imaging effect diagram of the proposed LA-NET at different apertures. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical scheme and technical effects of the present application more clear, the present application is further described in detail below in combination with the drawings and examples of the specification.

[0026] The embodiment proposes a limited aperture network (LA-NET) structure applicable to any aperture without repeated training, specifically, the network main structure is divided into two stages: the first stage uses Figure 4 The first stage network of the CNN structure shown in the figure takes the wavelet approximation coefficient of the deterministic current as input to learn the approximation coefficient of the induced current. In this stage, only the low-frequency component information of the induced current is obtained, which can reflect the main information of the induced current, and the initial estimated value of the induced current obtained by inverse wavelet transform is relatively fuzzy due to the lack of high-frequency information, but this provides a good initial estimated value for the unfolding network in the second stage.

[0027] The second stage uses the second network structure to simulate the iterative process of the CIE-SOM based on the contrast mechanism, gradually guides the model learning through physical knowledge, increases the interpretability of the model, and the prediction result is more accurate and reliable. The main strategy is to alternately optimize the double modules, and the second network is responsible for updating the induced current, while the least square method is used to optimize the corrected contrast function. Since a good initial value estimation has been obtained in the first stage, only two layers of the second network are needed to obtain the ideal recovery result. It is worth noting that the optimized contrast function serves as auxiliary information, and together with the estimated induced current, it constitutes the input features of the CNN in the second network. Through this unfolding network architecture, the lost high-frequency detail information can be gradually recovered, and finally a high-precision induced current distribution is obtained.

[0028] In the second network, in order to prevent the denominator from tending to 0 when restoring the contrast, the SOM method is used to restore the dielectric constant of the scatterer, and the scattering field is calculated through the predicted induced current, and finally all are added in the loss function to form a weighted loss, and the weights are adjusted according to the order of magnitude difference, which can better constrain the network.

[0029] More specifically, based on the above inverse scattering network structure, as shown in Figure 2As shown, the embodiment proposes an inverse scattering imaging method suitable for any finite aperture, including:

[0030] Step 1, obtaining the scattering field data of the target scatterer.

[0031] Step 1.1, as shown in the two-dimensional finite aperture electromagnetic inverse scattering model structure, an unknown scatterer with a certain permittivity value Figure 1 is placed in the region of interest D, in order to solve numerically, the region of interest D is discretized into several rectangular subunits, when the grid division quantity is enough, that is, the grid area is small enough, the relative permittivity value at each subunit is equivalent to a constant. In the surrounding observation domain S, there are transmitting antennas Tx and x receiving antennas Rx placed uniformly. The method of moments is used to obtain the induced current and the scattering field of the ideal scatterer as network learning labels.

[0032] Step 1.2, calculate the Green function , and the incident field , which are used to calculate other physical auxiliary loss variables subsequently.

[0033] Step 2, spatial division of induced current, specifically including:

[0034] Step 2.1, deterministic current acquisition; the idea of subspace optimization of SOM method is adopted to perform singular value decomposition on the Green function to obtain the induced current in the dominant part of the solution space. In this way, the induced current is divided into deterministic current and fuzzy current :

[0035] ;

[0036] Wherein the deterministic current is represented as:

[0037] ;

[0038] Step 2.2, the fuzzy current is obtained by iterative optimization, in the method of extending the induced current based on wavelet basis, a suitable wavelet basis is selected to reconstruct the fuzzy current , specifically:

[0039] ;

[0040] Wherein represents the wavelet coefficients of the fuzzy current, and the operator W ​is represented as a two-dimensional discrete wavelet transform, which maps the two-dimensional wavelet function to a sparse coefficient space , correspondingly is represented as a two-dimensional inverse discrete wavelet transform.

[0041] As shown in Figure 3 , the original image with the dimension of 2N x 2N is subjected to a two-dimensional discrete wavelet transform to obtain four image components in different frequency bands, namely, A representing a low-frequency component, H representing a horizontal component, V representing a vertical component, and D representing a visible high-frequency component, each with the dimension of N x N. It decomposes the signal into approximate and detail components at different scales, thereby allowing the signal to be observed at different time and frequency resolutions. The low-frequency component of the image is almost the same as the original image and can fully reflect the basic features of the original image. Based on this characteristic, the low-frequency component of the image can be used as the input of the first-level network, and the data dimension is reduced to N x N. This not only enables the effective learning of the low-frequency features of the induced current, but also enables the reconstruction of the rough image of the induced current through the low-frequency component, which is used for the image network enhancement of the induced current in the next part.

[0042] Step 3, wavelet compression;

[0043] The determined current and the induced current are subjected to wavelet compression to obtain corresponding approximate coefficients and as the input and label of the first-level network CNN. The compression formula is as follows:

[0044] ;

[0045] When performing wavelet compression, the haar wavelet basis is selected for one layer of wavelet transform, which is simple, efficient and can save a lot of storage space. The approximate coefficients of the determined current are used as the network input.

[0046] Step 4, wavelet reconstruction;

[0047] According to the wavelet transform characteristics of the image, different resolution sub-images correspond to different frequency components. Among them, the coefficient values in the high-frequency sub-image are generally close to zero, and with the increase of frequency, this sparsity feature becomes more and more significant. The first-level network learns the information of the low-frequency part of the induced current, i.e., the low-frequency component information , which basically contains the main information of the image, while the high-frequency part contains the detail information. Based on this characteristic, the simplest and most efficient lossy compression strategy is adopted in the embodiment of the application: the low-frequency part information of the image is saved while the high-frequency part information is discarded. Specifically, the compressed induced current is recovered by the method of high-frequency 0 supplementing and then performing inverse wavelet transform, and the formula is as follows:

[0048] ;

[0049] Due to the lack of high-frequency information, the recovered current image is relatively blurred, and the second-level network needs to be enhanced to obtain more accurate induced current.

[0050] Step 5, the establishment of the limited aperture expansion network.

[0051] The initial value of the induced current obtained is used as one of the inputs of the CNN of the second-level network. Specifically, the second-level network includes a CNN network and a least square operator, which simulates the iterative process of CIE-SOM. The number of sub-modules k can be adjusted according to the problem complexity and network depth. Specifically, it includes:

[0052] Step 5.1, define the number of iterations k, loop k=2,3;

[0053] Step 5.2, use the least square method to calculate the induced current at this stage from the current ;

[0054] ;

[0055] where is a constant matrix with dimension MxM and positive real part and non-negative imaginary part, p represents the pth antenna incidence, the superscript H represents the conjugate transpose, represents the total field, which can be obtained by formula ;

[0056] Step 5.3, concatenate and the contrast function calculated in step 5.2 as the input of the CNN in the second-level network. When data splicing, the real part and the imaginary part of the induced current occupy two channels, and the contrast function occupies one channel. The combined data channel number is 3, and the network output is only the further clear induced current distribution, so the channel number is two channels of real part and imaginary part.

[0057] Step 5.4, return to step 5.1 and loop iteration.

[0058] Step 6, the network learns the induced current , and the scattering field is obtained according to the calculation formula (7), and the calculation formula is as follows:

[0059] ;

[0060] In the second-level network, the purpose of this invention is to recover the dielectric constant image of the scatterer, which is achieved by using the CIE-SOM method to update and modify the contrast function. And through the formula Restoring contrast, because in the initial iteration of the neural network, the last module's... The value may be close to 1, which will make The denominator is close to 0, which prevents the neural network from converging. Therefore, in the last optimization layer, after obtaining the final induced current R, equation (8) is used to recover the contrast function of the scatterer. In addition, the corresponding scattering field is also calculated based on the current, with the corresponding formula (7) and used as part of the loss function.

[0061] ;

[0062] After obtaining the final contrast, it can be determined according to... The dielectric constant of the target scatterer is obtained.

[0063] To improve the accuracy of reconstructing the quantitative parameters of the target scatterer, a novel weighted loss function based on physical constraints is employed. This function comprises a data loss function and a physical equation loss function: one is the mean square error (MSE) loss based on wavelet approximation coefficient learning. Secondly, predicting the induced current. With real current MSE loss between and the predicted dielectric constant distribution Compared with the true value MSE loss between and Structural Similarity (SSIM) index loss Scattered field calculated by predicting induced current Compared with the measured scattered field Differences between .

[0064] These two parts together constitute the composite loss function, which significantly improves the reconstruction quality through joint optimization.

[0065] ;

[0066] The loss function , , , The weights are the parameters for the loss, and each term in the loss is defined as follows:

[0067] ;

[0068] in, , and denote the predicted induced current, predicted scattered field and permittivity distribution image, respectively. Ni and Nr represent the number of transmitting and receiving antennas, respectively.

[0069] In summary, the LA-NET proposed in the present application takes the deterministic current component compressed by wavelet as input, and can simultaneously predict the permittivity, scattered field and induced current. Through the cascade architecture combining wavelet transform and physical information expansion mechanism, it effectively integrates physical priors, and at the same time reduces the input dimension from 2N×2N to N×N, thereby significantly reducing the computational burden. The data set contains scatterers illuminated by different numbers of antennas, and the LA-NET can process single antenna illumination data each time, which enables the network to process any limited aperture without additional training. Under the joint constraint of wavelet compression and multi-physical field loss function, the network can reconstruct high-quality scatterer images. As shown in FIG. 6, it is the imaging effect diagram of the method and other existing methods under the condition of fixing a certain observation angle; as shown in FIG. 7, it is the imaging effect diagram of the proposed LA-NET under different apertures. The experimental results show that the LA-NET achieves excellent inversion performance in a wide range of apertures. Figure 5 Figure 6

[0070] The above is only the preferred embodiment of the present application, and does not limit the present application in any form. Although the implementation process of the present application has been described in detail above, those skilled in the art can still modify the technical solutions recorded in the foregoing examples, or replace some of the technical features with equivalent ones. Any modification, equivalent replacement, etc. within the spirit and principles of the present application shall be included in the protection scope of the present application.​​

Claims

1. A method for inverse scattering imaging with a finite aperture, characterized in that, include: Acquire the scattering field data of the target scatterer; Deterministic current of induced current is obtained from scattered field data; Wavelet compression is applied to the deterministic current to obtain the corresponding approximate coefficients; Design an LA-NET inverse scattering network model, including a first-level network and a second-level network. In the first-level network, an approximation coefficient is input to obtain the low-frequency component information of the induced current, and then the coarse image and initial estimate of the induced current are reconstructed through the low-frequency component information. In the second-level network, the initial estimate of the induced current is input, and a contrastive learning mechanism is introduced to gradually recover the detailed image of the induced current, thereby obtaining a high-precision induced current.

2. The inverse scattering imaging method as described in claim 1, characterized in that, The scattered field data includes: the induced current and scattered field of the target scatterer obtained by the method of moments, the Green's function of the target scatterer and the incident field.

3. The inverse scattering imaging method as described in claim 2, characterized in that, The Singular Value Decomposition (SOM) method is used to perform singular value decomposition on the Green's function to obtain the deterministic current of the induced current.

4. The inverse scattering imaging method as described in claim 1, characterized in that, The wavelet compression uses the Haar wavelet basis for wavelet transform.

5. The inverse scattering imaging method as described in claim 1, characterized in that, The low-frequency component information is compressed and recovered by high-frequency zero-padding and then inverse wavelet transform to obtain the initial estimate of the induced current.

6. The inverse scattering imaging method as described in claim 1, characterized in that, The second-level network includes a least squares operator and a CNN network. The initial estimate of the induced current is used to calculate the corresponding contrast function using the least squares operator. The contrast function and the corresponding initial estimate of the induced current are concatenated and input into the CNN network. The CNN network outputs the predicted induced current.

7. The inverse scattering imaging method as described in claim 6, characterized in that, The second-level network uses the SOM method to recover the dielectric constant of the scatterer and calculates the scattering field using the predicted induced current.

8. The inverse scattering imaging method as described in claim 7, characterized in that, The second-level network uses a physically constrained weighted loss function to optimize the recovery of the predicted induced current, dielectric constant distribution, and scattering field.

9. The inverse scattering imaging method as described in claim 8, characterized in that, The weighted loss function of the physical constraints includes a data loss function and a physical equation loss function. The data loss function is the mean square error (MSE) loss based on wavelet approximation coefficient learning. The physical equation loss function is the MSE loss between the predicted induced current and the actual current, the MSE between the predicted dielectric constant distribution and the actual value, the structural similarity index (SSIM), and the difference between the scattered field calculated by predicting the induced current and the measured scattered field.

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