Feature space inversion method and device based on supervised descent method

Abstract

This application relates to the field of electromagnetic inversion imaging technology, and particularly to a feature space inversion method and apparatus based on supervised descent. The method includes: in an offline training phase, generating a training image containing the potential spatial location and electromagnetic properties of a target based on prior information, and using the training image to train a variational autoencoder (VAE) to obtain a trained VAE; inputting the training image into the encoder of the trained VAE to obtain a low-dimensional feature latent code, wherein the low-dimensional feature latent code and corresponding measurement data are used to train the supervised descent method as model parameters to be inverted; in an online prediction phase, inputting the measurement data of the unknown target into the trained supervised descent method to obtain the latent code of the unknown target, and inputting the latent code into the decoder of the trained VAE to obtain the final inverted image. This application can flexibly integrate various complex prior information, reduce computational and memory overhead, and improve inversion efficiency.

Description

Technical Field

[0001] This application relates to the field of inverse scattering imaging technology, and in particular to a feature space inversion method and apparatus based on supervised descent. Background Technology

[0002] Electromagnetic inversion technology is a method that uses electromagnetic data to infer the properties of objects. It is widely used in fields such as medical imaging, geophysical exploration, non-destructive testing, and remote sensing.

[0003] In traditional inversion imaging methods, the region to be imaged is typically discretized into a pixel-based image, where the electromagnetic parameters of each pixel sub-region are set to a constant. These electromagnetic parameters are treated as unknown parameters to be inverted and reconstructed using gradient-based optimization methods. In practical applications, the amount of measurement data is often much smaller than the number of parameters to be inverted. Therefore, the inversion problem is a nonlinear ill-conditioned problem, requiring the introduction of prior information to constrain the solution space and obtain reasonable inversion results. Traditional inversion methods in related technologies mainly employ various regularization methods to constrain the solution space based on the smoothness, sparsity, or block characteristics of the target within the imaging region.

[0004] However, in traditional inversion methods in related technologies, much of the prior information based on empirical data cannot be accurately expressed mathematically, which limits the flexibility of integrating prior information. Furthermore, pixel-based target region representation methods greatly increase the time and memory overhead of gradient-based optimization methods when calculating the gradient of the current model. Moreover, the gradient calculated based on the current inversion model only contains local characteristics of the objective function, which may increase the risk of the optimization process getting trapped in local minima, making it difficult to guarantee the accuracy and stability of the inversion results. These issues urgently need to be addressed. Summary of the Invention

[0005] This application provides a feature space inversion method and apparatus based on supervised descent, which solves the problems in traditional inversion methods in related technologies. Many prior information based on empirical data cannot be accurately expressed in mathematical form, which limits the flexibility of fusing prior information. Furthermore, pixel-based target region representation methods greatly increase the time and memory overhead of gradient-based optimization methods when calculating the gradient of the current model. Moreover, the gradient calculated based on the current inversion model only contains local characteristics of the objective function, which may increase the risk of the optimization process getting trapped in local minima, making it difficult to guarantee the accuracy and stability of the inversion results.

[0006] The first aspect of this application provides a feature space inversion method based on supervised descent, characterized by the following steps: In an offline training phase, a training image containing the potential spatial location and electromagnetic properties of a target is generated based on prior information, and a variational autoencoder is trained using the training image to obtain a trained variational autoencoder; the training image is input into the encoder of the trained variational autoencoder to obtain a low-dimensional feature latent code, wherein the low-dimensional feature latent code and corresponding measurement data are used to train the supervised descent method as model parameters to be inverted; In an online prediction phase, the measurement data of the unknown target is input into the trained supervised descent method to obtain the latent code of the unknown target, and the latent code is input into the decoder of the trained variational autoencoder to obtain the final inverted image.

[0007] Optionally, in one embodiment of this application, the step of generating a training image containing the potential spatial location and electromagnetic properties of the target based on prior information, and using the training image to train a variational autoencoder to obtain a trained variational autoencoder includes: minimizing the target loss function during the t-th iteration to calculate the gradient matrix.

[0008] Optionally, in one embodiment of this application, the target loss function is:

[0009]

[0010] Δv t =v * -v t ,

[0011]

[0012] Where the superscript n represents the nth training sample, N is the total number of training samples, and K t The gradient matrix, For the positive modeling function, d * For the training set measurement data, d t For the data of generation t, v * For implicit encoding of the training set, v t For the t-th generation encoding, ||·||2 represents the L2-norm, Δv t For encoding error, Δd t This is due to data error.

[0013] Optionally, in one embodiment of this application, the gradient matrix is ​​calculated using the following formula:

[0014]

[0015]

[0016] Among them, K t Let ΔD be the gradient matrix. t Let ΔV be the difference between the training set data matrix and the data matrix of generation t. t U is the difference between the training set encoding matrix and the t-th generation encoding matrix. t and Q t For ΔD t The two orthogonal matrices Λ obtained by the singular value decomposition t For ΔD t The eigenvalue matrix is ​​denoted by β, where β is the regularization coefficient and I is the identity matrix.

[0017] Optionally, in one embodiment of this application, the update formula for the hidden code of the unknown target is:

[0018]

[0019] Among them, v t For the encoding of generation t, K t The gradient matrix, For the positive modeling function, d obs These are actual measurement data.

[0020] A second aspect of this application provides a feature space inversion device based on supervised descent, comprising: a training module, configured to generate a training image containing the potential spatial location and electromagnetic properties of a target based on prior information during an offline training phase, and to train a variational autoencoder using the training image to obtain a trained variational autoencoder; a processing module, configured to input the training image into the encoder of the trained variational autoencoder to obtain a low-dimensional feature latent code, wherein the low-dimensional feature latent code and corresponding measurement data are used to train the supervised descent method as model parameters to be inverted; and an inversion module, configured to input the measurement data of an unknown target into the trained supervised descent method during an online prediction phase to obtain the latent code of the unknown target, and to input the latent code into the decoder of the trained variational autoencoder to obtain a final inverted image.

[0021] Optionally, in one embodiment of this application, the training module includes: a computation unit, used to minimize the target loss function during the t-th iteration to compute the gradient matrix.

[0022] Optionally, in one embodiment of this application, the target loss function is:

[0023]

[0024] Δv t =v * -v t ,

[0025]

[0026] Where the superscript n represents the nth training sample, N is the total number of training samples, and K t The gradient matrix, For the positive modeling function, d * For the training set measurement data, d t For the data of generation t, v * For implicit encoding of the training set, v t For the t-th generation encoding, ||·||2 represents the L2-norm, Δv t For encoding error, Δd t This is due to data error.

[0027] Optionally, in one embodiment of this application, the gradient matrix is ​​calculated using the following formula:

[0028]

[0029]

[0030] Among them, K t Let ΔD be the gradient matrix. t Let ΔV be the difference between the training set data matrix and the data matrix of generation t. t U is the difference between the training set encoding matrix and the t-th generation encoding matrix. t and Q t For ΔD t The two orthogonal matrices Λ obtained by the singular value decomposition t For ΔD t The eigenvalue matrix is ​​denoted by β, where β is the regularization coefficient and I is the identity matrix.

[0031] Optionally, in one embodiment of this application, the update formula for the hidden code of the unknown target is:

[0032]

[0033] Among them, v t For the encoding of generation t, K t The gradient matrix, For the positive modeling function, d obs These are actual measurement data.

[0034] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the feature space inversion method based on supervised descent as described in the above embodiments.

[0035] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described feature space inversion method based on supervised descent.

[0036] A fifth aspect of this application provides a computer program product, which, when executed, is used to implement the above-described feature space inversion method based on supervised descent.

[0037] This application embodiment can input the measurement data of the target to be inverted into a supervised descent method, and obtain the hidden code of the unknown target through iterative updates of the gradient direction during the offline training phase. The hidden code of the unknown target is then input into the decoder of the trained variational autoencoder to obtain the final inverted image. This enables the inversion imaging method to flexibly fuse various prior information, thereby accurately limiting the solution space, reducing computational and memory overhead during the inversion process, effectively reducing the risk of getting trapped in local minima during optimization, and improving the accuracy of target inversion recognition while achieving automated target recognition. This solves the problems in traditional inversion methods in related technologies, where much prior information based on empirical data cannot be accurately expressed mathematically, limiting the flexibility of fusing prior information. Furthermore, pixel-based target region representation methods significantly increase the time and memory overhead of gradient-based optimization methods when calculating the gradient of the current model. Additionally, the gradient calculated based on the current inversion model only contains local characteristics of the objective function, which may increase the risk of getting trapped in local minima during optimization, making it difficult to guarantee the accuracy and stability of the inversion results.

[0038] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0039] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0040] Figure 1 This is a flowchart of a feature space inversion method based on supervised descent, according to an embodiment of this application.

[0041] Figure 2 This is a schematic diagram of a variational autoencoder structure according to an embodiment of this application;

[0042] Figure 3 This is a flowchart of an offline training process according to an embodiment of this application;

[0043] Figure 4 This is a schematic diagram of the supervised descent normal training phase according to one embodiment of this application;

[0044] Figure 5 This is a flowchart of an online prediction process according to an embodiment of this application;

[0045] Figure 6 This is a schematic diagram of the training set images for a variational autoencoder according to an embodiment of this application;

[0046] Figure 7 This is a schematic diagram of the original image of the test set according to an embodiment of this application;

[0047] Figure 8 This is a schematic diagram of a test set decoding image according to an embodiment of this application;

[0048] Figure 9 This is a visual schematic diagram of the inversion process according to an embodiment of this application;

[0049] Figure 10 This is a schematic diagram of the feature space inversion device based on supervised descent according to an embodiment of this application;

[0050] Figure 11 This is a schematic diagram of the structure of an electronic device according to an embodiment of this application. Attached image description:

[0052] 10-Feature space inversion device based on supervised descent method; 100-Training module, 200-Processing module and 300-Inversion module; 1101-Memory, 1102-Processor and 1103-Communication interface. Detailed Implementation

[0053] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0054] The following description, with reference to the accompanying drawings, describes a feature space inversion method and apparatus based on supervised descent according to embodiments of this application. Addressing the problems mentioned in the background section, this application provides a feature space inversion method based on supervised descent. In this method, the measurement data of the target to be inverted can be input into the supervised descent algorithm. Through iterative updates of the gradient direction during the offline training phase, the hidden code of the unknown target is obtained. This hidden code is then input into the decoder of a trained variational autoencoder to obtain the final inverted image. Thus, the inversion imaging method can flexibly fuse various prior information, thereby accurately limiting the solution space, reducing computational and memory overhead during the inversion process, effectively reducing the risk of getting trapped in local minima during optimization, improving the accuracy of target inversion recognition, and achieving automated target recognition. This solves the problems in traditional inversion methods where much prior information based on empirical data cannot be accurately expressed mathematically, limiting the flexibility of fusing prior information. Furthermore, pixel-based target region representation methods greatly increase the time and memory overhead of gradient-based optimization methods when calculating the gradient of the current model. Additionally, the gradient calculated based on the current inversion model only contains local characteristics of the objective function, which may increase the risk of the optimization process getting trapped in local minima, making it difficult to guarantee the accuracy and stability of the inversion results.

[0055] Specifically, Figure 1 This is a flowchart of a feature space inversion method based on supervised descent, provided as an embodiment of this application.

[0056] like Figure 1 As shown, the feature space inversion method based on supervised descent includes the following steps:

[0057] In step S101, during the offline training phase, a training image containing the target's potential spatial location and electromagnetic properties is generated based on prior information, and the variational autoencoder is trained using the training image to obtain the trained variational autoencoder.

[0058] Understandably, prior information here can be understood as information about something that exists before actual observation or sample acquisition. This information can be based on past experience, historical data, domain knowledge, or personal experience.

[0059] Compared to traditional inversion imaging methods, deep learning-based inversion imaging methods have significant advantages. First, deep learning methods can automatically learn complex features of data, improving the ability to fuse prior information and overcoming the limitations of traditional methods in fusing empirical data. Second, by mapping high-dimensional data to a low-dimensional feature space, deep learning methods can reduce computational and memory overhead during the inversion process, improving inversion efficiency. Furthermore, deep learning methods reduce the risk of getting trapped in local minima through global optimization, improving the accuracy and stability of the inversion results. Deep learning-based inversion imaging methods outperform traditional methods in terms of data processing capabilities, computational efficiency, and inversion accuracy, providing new possibilities for the development of inversion imaging technology. Therefore, this application embodiment can establish a feature space inversion method based on supervised descent using a variational autoencoder (a deep learning method).

[0060] like Figure 2 The diagram shown is a schematic representation of a variational autoencoder according to an embodiment of this application. Here, ε represents a random vector following a standard normal distribution, and σ... v Let x represent the variance vector and x represent the binary image. Let E(x) represent the decoded binary image, and let μ represent the encoder of the variational autoencoder. v Let v be the mean vector, v be the hidden code in the low-dimensional feature space, D(v) be the decoder of the variational autoencoder, and q(v|x) be a normal distribution. p(x|v) follows a normal distribution Where diag(·) is the diagonal operator, and I is the identity matrix.

[0061] It should be noted that the structure of the variational autoencoder in the embodiments of this application is only illustrative and is not intended to be specific. The specific structure can be set by those skilled in the art according to the actual situation.

[0062] In actual implementation, embodiments of this application can generate a set of training images containing the potential spatial location and electromagnetic properties of the target based on prior information during the offline training phase, such as... Figure 3 The image shown is a training set image of a variational autoencoder according to an embodiment of this application. The variational autoencoder can be trained using this image to obtain a trained variational autoencoder.

[0063] Among them, the training dataset distribution for variational autoencoders Given the feature space latent coding distribution p(v), embodiments of this application may assume that q(v|x) is a normal distribution. Its mean vector μ v (x) and variance vector It is the output of the encoder E(x) of the variational autoencoder, assuming that p(x|v) follows a normal distribution. Its mean vector μ x D(v) is the output of the decoder D(v) of the variational autoencoder, with a fixed variance of c. The objective function for training the variational autoencoder can be expressed as:

[0064]

[0065]

[0066]

[0067] in, Indicates the KL divergence. The value represents the reconstruction error, c represents a fixed constant, and μ represents the reconstruction error. (k) and They represent μ respectively v and The k-th element, N v Let represent the length of the hidden code v, and α be a coefficient balancing the weighting of KL divergence and reconstruction error. After training, the variational autoencoder can establish a mapping between the binary image x and the hidden code v in the low-dimensional feature space:

[0068] v = E(x)

[0069]

[0070] Where x represents the binary image, and v represents the hidden code in the low-dimensional feature space. Let E(x) represent the decoded binary image, where E(x) is the encoder of the variational autoencoder and D(v) is the decoder of the variational autoencoder.

[0071] Optionally, in one embodiment of this application, a training image containing the potential spatial location and electromagnetic properties of the target is generated based on prior information, and a variational autoencoder is trained using the training image to obtain a trained variational autoencoder, including: minimizing the target loss function during the t-th iteration to calculate the gradient matrix.

[0072] Optionally, in one embodiment of this application, the target loss function can be expressed as:

[0073]

[0074] Δv t =v * -v t ,

[0075]

[0076] Where the superscript n represents the nth training sample, N is the total number of training samples, and K t The gradient matrix, For the positive modeling function, d * For the training set measurement data, d t For the data of generation t, v * For implicit encoding of the training set, v t For the t-th generation encoding, ||·||2 represents the L2-norm, Δv t For encoding error, Δd t This is due to data error.

[0077] Based on the descriptions of other embodiments, it is understood that the embodiments of this application can generate training images containing the potential spatial location and electromagnetic properties of the target based on prior information, and use the training images to train a variational autoencoder to obtain a trained variational autoencoder. The training of the autoencoder is an iterative process; therefore, the embodiments of this application can minimize the target loss function during the t-th iteration to calculate the gradient matrix.

[0078] For example, during offline training of supervised descent, the objective function can be set as, but is not limited to, the following expression:

[0079]

[0080] in, For the positive modeling function, d * Let be the scattered field measurement data, v be the hidden code to be solved, and ||·||² represent the L² norm. In the t-th iteration, the gradient matrix K... t It can be calculated, but is not limited to, by minimizing the following loss function:

[0081]

[0082] Δv t =v * -v t

[0083]

[0084] Where the superscript n represents the nth training sample, N is the total number of training samples, and K t Represents the gradient matrix. For the positive modeling function, d * For the training set measurement data, d t For the data of generation t, v * For implicit encoding of the training set, v t For the t-th generation encoding, ||·||2 represents the L2-norm, Δv tFor encoding error, Δd t This is due to data error.

[0085] Step S102: Input the training image into the encoder of the trained variational autoencoder to obtain the low-dimensional feature latent code. The low-dimensional feature latent code and the corresponding measurement data are used to train the supervised descent method as the model parameters to be inverted.

[0086] Optionally, in one embodiment of this application, the formula for calculating the gradient matrix can be expressed as:

[0087]

[0088]

[0089] Among them, K t Let ΔD be the gradient matrix. t Let ΔV be the difference between the training set data matrix and the data matrix of generation t. t U is the difference between the training set encoding matrix and the t-th generation encoding matrix. t and Q t For ΔD t The two orthogonal matrices Λ obtained by the singular value decomposition t For ΔD t The eigenvalue matrix is ​​denoted by β, where β is the regularization coefficient and I is the identity matrix.

[0090] As one possible approach, after obtaining the trained variational autoencoder and gradient matrix, embodiments of this application can input the training image into the encoder of the trained variational autoencoder and combine it with the gradient matrix to calculate the low-dimensional feature implicit code, i.e., the training set implicit code.

[0091] For example, in calculating K t Then, the implicit encoding of the training set for generation t+1 can be updated using the following formula:

[0092] v t+1 =v t +K t Δd t

[0093] In numerical computation, v t For the encoding of generation t, Δd t To account for data error, the N training set codes are assembled into an N-row matrix V, and the N measurement data are also assembled into an N-row matrix D. The gradient matrix K... t It can then be calculated using the following formula:

[0094]

[0095]

[0096] Where, ΔD t Let ΔV be the difference between the training set data matrix and the data matrix of generation t. t U is the difference between the training set encoding matrix and the t-th generation encoding matrix. t and Q t For ΔD t The orthogonal matrix obtained by the singular value decomposition is Λ t For ΔD t The eigenvalue matrix is ​​denoted by β, where β is the regularization coefficient and I is the identity matrix.

[0097] The training process terminates when the encoding error or data error reaches a predetermined value, or when the maximum preset number of iterations is reached. The encoding error and data error can be defined as follows:

[0098]

[0099]

[0100] Among them, RMS v and RMS d These represent normalized coding error and normalized data error, respectively.

[0101] After obtaining the low-dimensional feature latent code, the low-dimensional feature latent code can be used together with the corresponding measurement data to train the supervised descent method. In this case, the low-dimensional feature latent code can be used as the model parameter to be inverted.

[0102] For example, Figure 3 This is a flowchart of the offline training process according to one embodiment of this application. Figure 4 This is a flowchart of the offline training phase of one embodiment of this application. Figure 3 and Figure 4 As shown, in this embodiment, training images and labels can be generated first based on prior information. Then, a variational autoencoder is trained using the training images and labels, and a forward physical model of the measurement environment is established to calculate the low-dimensional feature latent code of the training images and the experimental measurement data of the training images. After this, this embodiment can use the low-dimensional feature latent code of the training images and the experimental measurement data of the training images to train a supervised descent inversion latent code, and then use the supervised descent inversion latent code and labels to train a support vector machine.

[0103] In step S103, during the online prediction phase, the measurement data of the unknown target is input into the supervised descent method after training to obtain the hidden code of the unknown target, and the hidden code is input into the decoder of the trained variational autoencoder to obtain the final inversion image.

[0104] Optionally, in one embodiment of this application, the update formula for the hidden code of the unknown target can be expressed as:

[0105]

[0106] Among them, v t For the encoding of generation t, K t The gradient matrix, For the positive modeling function, d obs These are actual measurement data.

[0107] In some embodiments, after supervised descent training is completed, the gradient matrix K for each iteration is... t All data will be saved and directly used in the online prediction phase. In the online prediction phase, embodiments of this application can input the measurement data of the unknown target into the trained supervised descent method to obtain the hidden code of the unknown target. The hidden code of the unknown target can be updated using the following formula:

[0108]

[0109] Among them, v t For the encoding of generation t, K t The gradient matrix, For the positive modeling function, d obs These are actual measurement data. It should be noted that the initial encoding v0 is consistent during offline training and online prediction. When the data error RMS... d The online forecast terminates when the predetermined value is reached or increases.

[0110] After obtaining the hidden code of the unknown target, the embodiments of this application can input the hidden code into the decoder of the trained variational autoencoder, thereby obtaining the final inverted image.

[0111] like Figure 5 The diagram shown is a flowchart of online prediction according to an embodiment of this application. In the online prediction process, the measurement data of the unknown target can be input into the supervised descent method after training. Then, the hidden code of the target is inverted using the supervised descent method after training. The target image is then reconstructed using the decoder of the variational autoencoder and the hidden code of the target is classified and identified using a support vector machine.

[0112] The image decoding and inversion process of the embodiments of this application will be further described below.

[0113] like Figure 6 The image shown is a training set of images for a variational autoencoder according to an embodiment of this application. This training set of images can be used to train the variational autoencoder. Figure 7 and Figure 8The test set original image and decoded image are respectively from one embodiment of this application. The test set original image is input into the trained variational autoencoder, and the image decoded by the trained variational autoencoder using the obtained low-dimensional hidden code and decoder can be obtained. It can be clearly seen that the trained variational autoencoder has a good decoding effect.

[0114] Figure 9 This is a visualization diagram of the inversion process of an embodiment of this application. The first column is the real target image, the second column is the image after encoding and decoding by the variational autoencoder, and the third to twelfth columns are the images obtained after decoding the hidden code obtained by each iteration of the test sample. It can be seen that the feature space inversion method based on supervised descent proposed in this embodiment of the application effectively reconstructs the real target.

[0115] According to the feature space inversion method based on supervised descent proposed in this application, the measurement data of the target to be inverted can be input into the supervised descent method. Through iterative updates of the gradient direction during the offline training phase, the hidden code of the unknown target is obtained. The hidden code is then input into the decoder of the variational autoencoder to obtain the final inverted image. This enables the inversion imaging method to flexibly fuse various prior information, thereby accurately limiting the solution space, reducing the computational and memory overhead during the inversion process, effectively reducing the risk of getting trapped in local minima during optimization, and improving the accuracy of target inversion recognition while achieving automated target recognition. This solves the problems in traditional inversion methods in related technologies, where much prior information based on empirical data cannot be accurately expressed mathematically, limiting the flexibility of fusing prior information. Furthermore, pixel-based target region representation methods significantly increase the time and memory overhead of gradient-based optimization methods when calculating the gradient of the current model. Additionally, the gradient calculated based on the current inversion model only contains local characteristics of the objective function, which may increase the risk of getting trapped in local minima during optimization, making it difficult to guarantee the accuracy and stability of the inversion results.

[0116] Next, with reference to the accompanying drawings, a feature space inversion apparatus based on supervised descent proposed according to an embodiment of this application is described.

[0117] Figure 10 This is a schematic diagram of the feature space inversion device based on supervised descent method according to an embodiment of this application.

[0118] like Figure 10 As shown, the feature space inversion device 10 based on supervised descent includes: a training module 100, a processing module 200, and an inversion module 300.

[0119] The training module is used in the offline training phase to generate training images containing the potential spatial location and electromagnetic properties of the target based on prior information, and to train the variational autoencoder using the training images to obtain the trained variational autoencoder.

[0120] The processing module is used to input the training image into the encoder of the trained variational autoencoder to obtain a low-dimensional feature latent code, wherein the low-dimensional feature latent code and the corresponding measurement data are used to train the supervised descent method as model parameters to be inverted.

[0121] The inversion module is used in the online prediction stage to input the measurement data of the unknown target into the supervised descent method after training to obtain the hidden code of the unknown target, and input the hidden code into the decoder of the trained variational autoencoder to obtain the final inversion image.

[0122] Optionally, in one embodiment of this application, the training module includes: a computation unit, used to minimize the target loss function during the t-th iteration to compute the gradient matrix.

[0123] Optionally, in one embodiment of this application, the target loss function can be expressed as:

[0124]

[0125] Δv t =v * -v t ,

[0126]

[0127] Where the superscript n represents the nth training sample, N is the total number of training samples, and K t The gradient matrix, For the positive modeling function, d * For the training set measurement data, d t For the data of generation t, v * For implicit encoding of the training set, v t For the t-th generation encoding, ||·||2 represents the L2-norm, Δv t For encoding error, Δd t This is due to data error.

[0128] Optionally, in one embodiment of this application, the formula for calculating the gradient matrix can be expressed as:

[0129]

[0130]

[0131] Among them, Kt Let ΔD be the gradient matrix. t Let ΔV be the difference between the training set data matrix and the data matrix of generation t. t U is the difference between the training set encoding matrix and the t-th generation encoding matrix. t and Q t For ΔD t The two orthogonal matrices Λ obtained by the singular value decomposition t For ΔD t The eigenvalue matrix is ​​denoted by β, where β is the regularization coefficient and I is the identity matrix.

[0132] Optionally, in one embodiment of this application, the update formula for the hidden code of the unknown target can be expressed as:

[0133]

[0134] Among them, v t For the encoding of generation t, K t The gradient matrix, For the positive modeling function, d obs These are actual measurement data.

[0135] It should be noted that the foregoing explanation of the feature space inversion method based on supervised descent also applies to the feature space inversion device based on supervised descent in this embodiment, and will not be repeated here.

[0136] According to the feature space inversion device based on supervised descent proposed in this application, the measurement data of the target to be inverted can be input into the supervised descent method. Through iterative updates of the gradient direction during the offline training phase, the hidden code of the unknown target is obtained, and the hidden code is input into the decoder of the variational autoencoder to obtain the final inverted image. This enables the inversion imaging method to flexibly fuse various prior information, thereby accurately limiting the solution space, reducing the computational and memory overhead during the inversion process, effectively reducing the risk of getting trapped in local minima during optimization, improving the accuracy of target inversion recognition, and achieving automated target recognition. This solves the problems in traditional inversion methods in related technologies, where much prior information based on empirical data cannot be accurately expressed mathematically, limiting the flexibility of fusing prior information. Furthermore, pixel-based target region representation methods greatly increase the time and memory overhead of gradient-based optimization methods when calculating the gradient of the current model. Additionally, the gradient calculated based on the current inversion model only contains local characteristics of the objective function, which may increase the risk of getting trapped in local minima during optimization, making it difficult to guarantee the accuracy and stability of the inversion results.

[0137] Figure 11 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include:

[0138] The memory 1101, the processor 1102, and the computer program stored on the memory 1101 and executable on the processor 1102.

[0139] When the processor 1102 executes the program, it implements the feature space inversion method based on supervised descent provided in the above embodiments.

[0140] Furthermore, electronic devices also include:

[0141] Communication interface 1103 is used for communication between memory 1101 and processor 1102.

[0142] The memory 1101 is used to store computer programs that can run on the processor 1102.

[0143] The memory 1101 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0144] If the memory 1101, processor 1102, and communication interface 1103 are implemented independently, then the communication interface 1103, memory 1101, and processor 1102 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 11 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0145] Optionally, in a specific implementation, if the memory 1101, processor 1102, and communication interface 1103 are integrated on a single chip, then the memory 1101, processor 1102, and communication interface 1103 can communicate with each other through an internal interface.

[0146] The processor 1102 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0147] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described feature space inversion method based on supervised descent.

[0148] This application also provides a computer program product that can run computer instructions. When these computer instructions are executed by a processor, they implement the feature space inversion method based on supervised descent provided in this application.

[0149] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0150] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0151] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0152] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0153] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or more of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0154] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0155] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0156] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A feature space inversion method based on supervised descent, characterized in that, Includes the following steps: During the offline training phase, training images containing the target's potential spatial location and electromagnetic properties are generated based on prior information, and the variational autoencoder is trained using the training images to obtain the trained variational autoencoder. The training image is input into the encoder of the trained variational autoencoder to obtain a low-dimensional feature latent code, wherein the low-dimensional feature latent code and the corresponding measurement data are used to train the supervised descent method as the model parameters to be inverted. In the online prediction phase, the measurement data of the unknown target is input into the supervised descent method after training to obtain the hidden code of the unknown target, and the hidden code is input into the decoder of the trained variational autoencoder to obtain the final inverted image. The step of generating a training image containing the potential spatial location and electromagnetic properties of the target based on prior information, and using the training image to train a variational autoencoder to obtain a trained variational autoencoder includes: minimizing the target loss function during the t-th iteration to calculate the gradient matrix. The formula for calculating the gradient matrix is: ， ， in, The gradient matrix, For the training set data matrix and the first The difference between the data matrices The encoding matrix for the training set and the first The difference between the encoding matrices, and for The two orthogonal matrices obtained from the singular value decomposition, for eigenvalue matrix, The regularization coefficient is . It is an identity matrix.

2. The method according to claim 1, characterized in that, The target loss function is: ， ， ， Among them, superscript Indicates the first training samples, The total number of training samples, The gradient matrix, For positive modeling function, For the training set measurement data, For the first Data substitutes For training set implicit encoding, For the first Code Describing the L2 norm, For encoding error, This is due to data error.

3. The method according to claim 1, characterized in that, The update formula for the hidden code of the unknown target is: ， in, For the first Code The gradient matrix, For positive modeling function, These are actual measurement data.

4. A feature space inversion device based on supervised descent, characterized in that, include: The training module is used in the offline training phase to generate training images containing the potential spatial location and electromagnetic properties of the target based on prior information, and to train the variational autoencoder using the training images to obtain the trained variational autoencoder. The processing module is used to input the training image into the encoder of the trained variational autoencoder to obtain a low-dimensional feature latent code, wherein the low-dimensional feature latent code and the corresponding measurement data are used to train the supervised descent method as model parameters to be inverted. The inversion module is used in the online prediction stage to input the measurement data of the unknown target into the supervised descent method after training to obtain the hidden code of the unknown target, and input the hidden code into the decoder of the trained variational autoencoder to obtain the final inversion image. The training module includes a computation unit, used to minimize the target loss function during the t-th iteration to calculate the gradient matrix; The formula for calculating the gradient matrix is: ， ， in, The gradient matrix, For the training set data matrix and the first The difference between the data matrices The encoding matrix for the training set and the first The difference between the encoding matrices, and for The two orthogonal matrices obtained from the singular value decomposition, for eigenvalue matrix, The regularization coefficient is . It is an identity matrix.

5. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, the processor executing the program to implement the feature space inversion method based on supervised descent as described in any one of claims 1-3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the feature space inversion method based on supervised descent as described in any one of claims 1-3.

7. A computer program product, characterized in that, When the computer program is executed, it is used to implement the feature space inversion method based on supervised descent as described in any one of claims 1-3.

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