Physical information-based magnetic field super-resolution imaging training method and imaging system

Abstract

The application discloses a physical information-based magnetic field super-resolution imaging training method and an imaging system, and belongs to the technical field of neural network image processing. The method provides a high-resolution first image sample and a low-resolution second image sample generated by downsampling; the second image sample is input into a super-resolution network, a predicted high-resolution magnetic field distribution image is output through the network; a corresponding current density distribution is extracted from the predicted high-resolution magnetic field distribution image, the obtained current density is reversely calculated to obtain a calculated high-resolution magnetic field distribution image; the calculated high-resolution magnetic field distribution image is compared with a corresponding high-resolution magnetic field distribution image in the first image sample, a data loss value is calculated, a comprehensive loss optimization network is constructed, and finally a precise super-resolution magnetic field image is output. The application reduces the demand of the network on the training data amount, and improves the stability of the network.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of neural network image processing, and particularly relates to a magnetic field super-resolution imaging training method and an imaging system based on physical information. BACKGROUND

[0002] With the rapid development of new energy vehicles, the demand for vehicle equipment state monitoring is increasing. Especially for batteries and motors, which are the core components of the three-electric system of electric vehicles, the monitoring of their health status is crucial. Effective monitoring not only improves the safety of vehicles, but also prolongs the service life of equipment. Currently, the monitoring methods for batteries and motors mainly include: 1) battery management system: by monitoring the voltage, temperature and current of the battery in real time, the charge and discharge state and health condition of the battery are evaluated. 2) vibration monitoring: using sensors to detect the vibration characteristics of the motor to determine its operating state and potential faults. 3) thermal imaging technology: using a thermal imager to monitor the temperature distribution of the battery and motor to identify overheating or abnormal hot spots. 4) data-driven method: based on machine learning algorithms to analyze historical data to predict the failure trend of the battery and motor. Among these methods, magnetic field detection, as a new technology, is gradually gaining attention. Batteries and motors produce weak magnetic fields during operation, and analyzing these magnetic field changes can provide information on the health status and potential faults of the equipment. Magnetic field detection has the advantages of non-destructive, real-time and high sensitivity, providing an important supplement to the state monitoring of electric vehicles, and promoting the further development of new energy vehicle technology.

[0003] However, in the process of magnetic field detection, high-resolution magnetic field images require a large number of data points to be collected to ensure that subtle magnetic field changes and structural features are captured. This process usually involves complex sensors and data processing technology. However, as the number of data points increases, the acquisition speed often decreases significantly. This not only prolongs the time of data acquisition, but also may cause a delay in responding to rapidly changing environments. At the same time, low-resolution magnetic field images, although faster to acquire, often do not have sufficient image quality to meet the needs of accurate analysis. Low-resolution images may not clearly present the subtle features and changes of the magnetic field, thereby affecting the accuracy of subsequent analysis and decision-making. In some cases, such low-quality data may even lead to misjudgment, hindering the progress of subsequent work. SUMMARY

[0004] This section is intended to summarize some aspects of the embodiments of the application and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the abstract and title of the specification to avoid obscuring the purpose of this section, abstract and title, and such simplifications or omissions cannot be used to limit the scope of the application.

[0005] In view of the above and / or problems existing in the prior art, the present application is proposed.

[0006] One of the objects of the present application is to provide a magnetic field super-resolution imaging training method based on physical information.

[0007] To solve the above technical problems, the present application provides the following technical solutions: a magnetic field super-resolution imaging training method based on physical information, comprising,

[0008] providing a first image sample and a second image sample; the first image sample is a high-resolution magnetic field distribution image, and the second image sample is a low-resolution magnetic field distribution image generated by downsampling the corresponding first image sample;

[0009] inputting the second image sample into a super-resolution network, and outputting a predicted high-resolution magnetic field distribution image through the network;

[0010] extracting a corresponding current density distribution from the predicted high-resolution magnetic field distribution image, and inversely calculating the magnetic field distribution by using the obtained current density to generate a calculated high-resolution magnetic field distribution image;

[0011] comparing the calculated high-resolution magnetic field distribution image with the corresponding high-resolution magnetic field distribution image in the first image sample, and calculating a data loss value;

[0012] optimizing the super-resolution network by using the data loss value.

[0013] The magnetic field distribution image referred to in the present application refers to a two-dimensional image of magnetic field strength.

[0014] The high-resolution magnetic field distribution image referred to in the present application refers to an image with a resolution of 128x128.

[0015] The low-resolution magnetic field distribution image referred to in the present application refers to an image with a resolution of 32x32.

[0016] The downsampling referred to in the present application refers to reducing the resolution of an image.

[0017] The super-resolution network referred to in the present application refers to an SRResNet (Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network) super-resolution network.

[0018] As a preferred scheme of the magnetic field super-resolution imaging training method based on physical information of the present application, wherein the extracting a corresponding current density distribution specifically comprises,

[0019] Preparing a predicted high-resolution magnetic field distribution image for output of a super-resolution network , the pixel value represents the magnetic field intensity;

[0020] The x and y direction magnetic field components of are respectively subjected to two-dimensional Fourier transform to obtain the frequency domain magnetic field intensity , and the frequency domain current density is calculated in combination with formula (1);

[0021] The two-dimensional inverse Fourier transform is performed on the frequency domain current density to obtain the x×y spatial domain current density distribution ;

[0022] Wherein, the current density at the position can be expressed as:

[0023]

[0024] In the formula, and are the spatial frequencies in the x direction and the y direction of the magnetic field distribution image; is the height of the magnetometer; is the magnetic field intensity measured at the position ; is the vacuum permeability, 4 ; is a constant.

[0025] As a preferred scheme of the magnetic field super-resolution imaging training method based on physical information provided by the application, in the process of extracting the corresponding current density distribution, a Gaussian low-pass filter is used to filter noise;

[0026] The Gaussian low-pass filter is calculated according to formula (2):

[0027]

[0028] Wherein, σ is in the range of 400-600.

[0029] As a preferred scheme of the magnetic field super-resolution imaging training method based on physical information provided by the application, in the process of extracting the corresponding current density distribution, a Gaussian low-pass filter is used to filter noise;

[0030] The is discretized into x×y current elements, and the micro magnetic field of each current element at the corresponding observation point is calculated according to the Biot-Savart law. For the current element , the micro magnetic field generated at the position is expressed as:

[0031]

[0032] In the formula, is the current intensity, is the direction vector of the current element, is the unit vector from the current element to the observation point, is the distance between the observation point and the current element;

[0033] Summing the magnetic field components of all current elements, traversing the x×y observation points, and generating a calculated high-resolution magnetic field distribution image .

[0034] As a preferred scheme of the magnetic field super-resolution imaging training method based on physical information of the application, wherein: the calculated data loss value is determined, specifically,

[0035] determining the calculated high-resolution magnetic field distribution image and the first image sample ;

[0036] ensure one-to-one correspondence with the pixel space position of ;

[0037] The loss is calculated by using the mean square error formula, and the formula is:

[0038]

[0039] wherein, respectively, the image length, width of and .

[0040] As a preferred scheme of the magnetic field super-resolution imaging training method based on physical information of the application, wherein: the super-resolution network is optimized by calculating the data loss value, specifically,

[0041] The calculated physical loss and the data loss are combined to construct a comprehensive loss value , is expressed as:

[0042]

[0043] wherein, is the coefficient of the physical loss, The value range is 0~50.

[0044] Another object of the application is to provide a magnetic field super-resolution imaging system based on physical information, comprising,

[0045] a magnetic field image sample generation and preprocessing module, configured to generate or collect a first image sample and pre-process the first image sample to obtain a second image sample; wherein the first image sample is a high-resolution magnetic field distribution image, and the second image sample is a low-resolution magnetic field distribution image generated by down-sampling the corresponding first image sample;

[0046] a super-resolution network module, configured to output a predicted high-resolution magnetic field distribution image from the second image sample through a network;

[0047] a current density inversion module, configured to extract a current density distribution from the predicted high-resolution magnetic field image;

[0048] a magnetic field reverse calculation module, configured to calculate a high-resolution magnetic field image conforming to physical laws from the current density distribution;

[0049] a loss calculation and network optimization module, configured to calculate a loss value and optimize parameters of the super-resolution network; and

[0050] an imaging result output and storage module, configured to output a final super-resolution magnetic field image and store data.

[0051] As a preferred scheme of the magnetic field super-resolution imaging system based on physical information according to the present application, the super-resolution network module is an SRResNet super-resolution network, the input layer receives the pre-processed second image sample, performs initial feature extraction through a convolution layer and an activation layer, strengthens feature learning through a residual block, enlarges the feature map to x*y pixels through an up-sampling block, and finally outputs the predicted high-resolution magnetic field distribution image through a final output layer.

[0052] Compared with the prior art, the present application has the following beneficial effects:

[0053] The present application proposes a new physical information neural network to realize high-precision magnetic field super-resolution imaging; by embedding the Biot-Savart law in the neural network, the demand for the amount of training data of the network is reduced, and the stability of the network is improved. BRIEF DESCRIPTION OF DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor. Among them:

[0055] Figure 1 It is a mobile platform moving schematic diagram of the experimental platform of the present application;

[0056] Figure 2 Fig. 1 is a schematic diagram of the network structure of the present application;

[0057] Figure 3 Fig. 6 is a comparison diagram of the simulation-generated heart-shaped magnetic field image in interpolation, SRResNet, SRGAN, ESRGAN and physical information neural network respectively, showing the effect of 4 times magnification;

[0058] Figure 4 Fig. 7 is a box plot of two indicators of two models, respectively, the SRResNet model with physical information and the SRResNet model without physical information under different training set quantities, based on 13 simulation images after testing;

[0059] Figure 5 Fig. 8 is a comparison diagram of experimental results of different experimental circuit boards. DETAILED DESCRIPTION

[0060] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the embodiments of the present application.

[0061] In the following description, many specific details are set forth in order to provide a thorough understanding of the present application, but the present application can also be implemented in other ways different from those described herein, and those skilled in the art can make similar generalizations without departing from the concept of the present application, therefore the present application is not limited to the specific embodiments disclosed below.

[0062] Secondly, the "one embodiment" or "embodiment" referred to herein means that the specific features, structures or characteristics can be included in at least one implementation of the present application. "In one embodiment" appearing in different places in the specification does not mean the same embodiment, nor is it an embodiment that is separate or alternative to other embodiments.

[0063] Embodiment 1

[0064] The main method of the present application is to add physical information in the super-resolution imaging network.

[0065] Firstly, the inversion of current density is carried out based on the output results of the super-resolution imaging network, that is, the corresponding current density distribution is extracted from the high-resolution image output by the super-resolution network. This inversion process uses the detail enhancement information generated by the network to estimate the finer current distribution in space.

[0066] Next, the magnetic field distribution is calculated inversely from the inverted current density by using the Biot-Savart law. The Biot-Savart law is used here to accurately calculate the spatial distribution of magnetic field strength according to the change of current density, which realizes the physical model mapping from current density to magnetic field strength.

[0067] After obtaining the calculated magnetic field distribution, the magnetic field is compared with the original magnetic field input, and the difference between the two is calculated. This difference measures the physical consistency of the network output, that is, the degree of conformity of the current density inversion result with the physical law, so as to obtain a physical loss reflecting the physical law. This physical loss value is used to measure the physical rationality of the network output, to ensure that the super-resolution network not only visually realizes the high-resolution reconstruction of the image, but also conforms to the basic laws of electromagnetism.

[0068] Finally, the physical loss value is combined with the original loss value of the network (i.e. the data-based loss value) to form a hybrid loss value. The hybrid loss combines the accuracy of image reconstruction and the consistency of physical laws to ensure that the network is optimized not only to improve image quality, but also to consider the rationality of its output results at the physical level. This hybrid loss achieves comprehensive optimization of the super-resolution network by adjusting the weight between the data loss and the physical loss, making it more reliable and in line with actual physical laws in complex physical scenarios.

[0069] Specifically, the main physical formula used when calculating the current density to the magnetic field strength is the Biot-Savart law. It is one of the basic laws of electromagnetism that describes the magnetic field generated by an electric current. It shows that the magnetic field generated by a current element (i.e. a small section of current-carrying wire) at a point in space is inversely proportional to the distance from the current element to the point, and the direction of the magnetic field is perpendicular to the direction of the position vector of the current element and the point. Specifically, for a current element at position , the small magnetic field :

[0070]

[0071] where: is the vacuum permeability, with a value of 4 , is the current intensity, is the direction vector of the current element, is the unit vector from the current element to the observation point, is the distance between the observation point and the current element.

[0072] The Biot-Savart law is widely used to calculate the magnetic field generated by complex current distributions, especially for calculating the magnetic field generated by long straight wires, ring currents or coils.

[0073] When the magnetic field strength is inverted to the current density, the Fourier transform algorithm is used.

[0074] When considering the excitation effect of the current in a two-dimensional plate on the spatial magnetic field, let be the current density at position The magnetic field strength measured at the location, where the height of the magnetometer is... It is fixed. Let... Let be the current density at that location. Assume the thickness of the thin plate is . Furthermore, the current distribution is thin enough that, under approximate conditions, the current density... exist The current is uniform in direction and can be considered a two-dimensional distribution. Furthermore, according to the current continuity equation, the divergence of the current density is zero.

[0075]

[0076] According to the principles of electromagnetism, the relationship between electric current and magnetic field can be established using the Biot-Savart law. This law states that the magnetic field strength... The relationship with the current element is:

[0077]

[0078] in The free permeability in space (value 4) , For along the integration path The direction vector of the current element. It is the unit vector pointing from the position of the current element to the observation point.

[0079] Based on the definition of current density, the relationship between current and current density can be derived:

[0080]

[0081] Substituting the above relationship into the Biot-Savart law, we can obtain the relationship between current density and magnetic field. Because in The direction assumes that the current density is uniform, therefore The integral in the direction is a constant, i.e., the thickness of the thin plate. Therefore, we can conclude that:

[0082]

[0083]

[0084] Thus, the relationship between the current distribution in a two-dimensional flat plate and the magnetic field it induces in space has been obtained. However, even if a magnetometer is used to measure the magnetic field at a specified location... direction and The magnetic field strength in the direction is still difficult to determine the corresponding current distribution. .

[0085] According to the two-dimensional convolution formula:

[0086]

[0087] Comparing equations (10) and (11), it can be seen that they have the same form as the convolution formula. Therefore, equation (10) can be written as follows:

[0088]

[0089] Therefore, The expression is:

[0090]

[0091] According to the convolution theorem, spatial convolution is equivalent to frequency domain multiplication. Therefore, performing a Fourier transform on the above formula yields:

[0092]

[0093] Here, and They are respectively directional magnetic field and Two-dimensional Fourier transform of current distribution in direction, and It is a function The Fourier transform of . Based on the known expression, it can be directly calculated:

[0094]

[0095] This shows that the function along with and The increase of and the decrease mean that yes The result obtained after passing through a low-pass filter is that the change in the magnetic field mainly consists of the low-frequency part of the change in current density.

[0096] Assuming the current in the plate is constant, since the divergence of the current density is zero, performing a Fourier transform on the aforementioned formula and applying the differential theorem yields:

[0097]

[0098] Further transformations yield the following:

[0099]

[0100] Based on the above results, the current density can be calculated by measuring any one of the magnetic field components. and The value in direction. Finally, magnetic field information is needed to obtain the current density distribution, because the magnetic field can be measured by instruments. Combined formula , , , we have

[0101]

[0102] It can be seen from the above equation that when approaches zero, will tend to infinity, leading to no solution of the equation, which indicates that a uniform current in the direction cannot generate a magnetic field in the direction, and the current density is equivalent to the magnetic field strength after high-pass filtering.

[0103] To implement the algorithm on a computer, discretization in a finite region needs to be considered. The periodicity of the time domain in the Fourier transform corresponds to the discreteness of the frequency domain. Let and be the periods of the current density in the and directions. Although the actual measured current usually does not have periodicity, the periods and should be as large as possible when selecting the measurement region to reduce the impact of periodicity on the results. Let and be the number of sampling points in the and directions, and the spatial distance between two adjacent points is and . The distance between two adjacent discrete points in the frequency domain is and . According to the sampling theorem, to avoid frequency aliasing errors, it is necessary to ensure a large , and more sampling points , .

[0104] When measuring magnetic field data using an instrument, a low-pass filter should be added at the end to restore the signal in the continuous domain and reduce the impact of noise. Therefore, in the frequency domain, a Gaussian filter is used to multiply the magnetic field,

[0105]

[0106] where and are two coordinates in the frequency domain, is the standard deviation of the Gaussian distribution, which determines the width of the filter.

[0107] ​​​Since the experimental device needs a lot of time to collect the magnetic field image, especially under high resolution conditions, it takes a lot of time to collect enough magnetic field data for the construction of the experimental data set. Therefore, the Biot-Savart law is used to generate a large number of simulated magnetic field image data to greatly improve the efficiency of data set construction and save experimental time. By using the calculation model of the Biot-Savart law, magnetic field strength distribution of different shapes can be generated according to a specific mathematical analytical function. This not only makes the generation of magnetic field images more flexible, but also produces a large amount of high-quality simulation data in a short time. In addition, the resolution of the simulation image can be freely adjusted according to the experimental requirements, adapting to various precision requirements. Compared with the collection process of the actual experimental device, the generation process of the simulation data is more convenient and efficient, providing rich data resources for subsequent experiments and model training.

[0108] In order to verify the effectiveness of the method, the present application introduces the above-mentioned physical formula into SRResNet (Super-Resolution Residual Network) to construct a physical information neural network. The network structure is mainly composed of a plurality of convolutional layers and residual blocks, and the input is a low-resolution magnetic field distribution image. First, a convolutional layer is used for feature extraction, and then a plurality of residual blocks (each block contains two convolutional layers, a batch normalization layer and a PReLU activation layer) are used for further feature processing. The output of each residual block is added to the input through an addition layer to preserve information. Finally, the network performs high-resolution reconstruction through several convolutional layers, a depth-to-space layer and a PReLU activation layer, and finally outputs the prediction result through a convolutional layer. The overall network structure adopts residual connection, aiming to improve the training stability and performance.

[0109] Next, the physical information is introduced. First, the corresponding current density distribution is obtained through magnetic field inversion, and then the Biot-Savart law is applied to calculate the magnetic field distribution at this time from the current density. After obtaining the high-resolution magnetic field image, the image is down-sampled to a low-resolution image and compared with the input low-resolution image to calculate the mean square error (MSE). This loss term is combined with the mean square error between the high-resolution image output by the network and the given standard high-resolution image to form the comprehensive loss function of the physical information neural network. Through back propagation, this loss function will be fed back to the network to promote the network to further train, so as to improve the accuracy of the network in considering the physical information while improving the reconstruction and prediction accuracy. Figure 2 The network structure diagram of the present application.

[0110] The 100 simulated generated magnetic field images are used as a training set to train and save the model. The configuration of the training platform is as follows: CPU AMD Ryzen 5 5600X, GPU RTX 4080, operating system WIN 10 64-bit, programming language and version MATLAB 2021.

[0111] Two key parameters are included in the added physical information, the coefficient of physical loss and the bandwidth of the Gaussian filter . The size of these two parameters will directly affect the training effect of the model. Therefore, in order to optimize the model, a random search method is used to find the best values of these two parameters, and the optimization process and results are shown in Table 1. The best parameter values obtained by this method are .

[0112] Table 1

[0113]

[0114] Experimental Example 1

[0115] When evaluating the experimental results, two indicators, Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), are used. PSNR is used to measure the difference between the original image and the reconstructed image. It is calculated based on the Mean Square Error (MSE) of the image, which represents the ratio of the peak value of the signal to the noise. The higher the value, the smaller the difference between the reconstructed image and the original image, and the better the quality. SSIM not only considers the difference between pixel values, but also pays attention to the similarity of image structure, brightness, contrast and texture. The closer the value is to 1, the higher the similarity.

[0116] In order to test the effect of the model, first, the simulated magnetic field images are used for testing. As Figure 3 shown, the effects of the simulated magnetic field images in interpolation, SRResNet, SRGAN, ESRGAN and the physical information neural network of the present application are shown respectively. The corresponding PSNR and SSIM values are listed in Table 2. From the figures, it can be seen that in some subtle places, the model of the present application will achieve better results than other models.

[0117] Table 2

[0118]

[0119] Figure 4The box plots of two indicators of the two models, the SRResNet model with physical information and the SRResNet model without physical information, under different training set quantities, based on 13 simulation images after testing are shown in FIG. Figure 4 As can be clearly seen from FIG.

[0120] Experimental Example 2

[0121] In order to further verify the effect of the model, a circuit board with different patterns is designed for testing.

[0122] (1) Construction of experimental platform

[0123] The magnetic field acquisition platform based on a sensor array constructed by the application realizes high-precision and multi-dimensional magnetic field data acquisition through multi-module collaborative operation. Figure 1 As shown in FIG.

[0124] In terms of acquisition circuit design, the two 8-channel magnetic sensor chips are installed side by side on a non-magnetic material base. This special non-magnetic base design effectively avoids external magnetic field interference, ensuring the stability and accuracy of the detection data. During the experiment, the magnetic field circuit to be measured is stably installed on the surface of the base, and two stepper motors are used to move along the x and y axes respectively to realize the coverage of the entire acquisition area, and the scanning line is as shown in FIG. Figure 1 These two stepper motors can respectively push the base to move back and forth in a straight line in the x and y directions, gradually scanning the entire magnetic field area, ensuring that there is no omission in the acquisition process.

[0125] During the experiment, the stepper motor moves according to the preset path. Each time the motor moves forward, it stops for a short time. During the short stop, the NI USB-6289 data acquisition card starts to record the magnetic field intensity data in real time. The adjacent channels of the two sensor chips are arranged vertically, so they can sense the magnetic field components in different directions, thus obtaining more accurate multi-dimensional magnetic field information. The collected data is automatically stored in an electronic table, which not only facilitates data arrangement, but also provides convenience for subsequent in-depth analysis and processing. The entire motion and data acquisition process will continue until the entire area of the circuit layout is covered, ensuring that comprehensive and complete magnetic field sampling data is obtained to provide reliable data support for the research. In addition, the step distance of the stepper motor can be adjusted flexibly. By setting different moving step distances, magnetic field image data collection with different resolutions can be achieved. The specific parameters can be referred to Table 3. This function can flexibly control the collection accuracy according to different experimental requirements, greatly improving the applicability and practicality of the platform.

[0126] Table 3

[0127]

[0128] Due to the presence of other electronic equipment in the experimental environment, their magnetic fields will interfere with the collected signals. To reduce the impact of these noises, the circuit is powered off before the experiment, and the background magnetic field data is collected as a noise reference. Then, the circuit under test is powered on and the magnetic field intensity is collected. During data processing, the magnetic field data collected with power on is subtracted from the background noise, thus obtaining a relatively pure circuit magnetic field signal graph, enhancing the accuracy of the experimental results.

[0129] Experimental procedure:

[0130] (1) Power the acquisition circuit. In the case where the circuit under test is not powered on, adjust the adjustable resistor of the acquisition circuit module to zero to eliminate zero drift.

[0131] (2) Power the linear motor, adjust the base to the initial position, and record it as the origin.

[0132] (3) Set the appropriate collection interval. In the case where the circuit under test is not powered on, start the linear motor to move according to the predetermined path. At this time, the acquisition card records the background magnetic field noise data.

[0133] (4) After the background noise collection is completed, reset the motor position to the recorded origin.

[0134] (5) Power on the circuit under test and set the current to 3A. Start the linear motor again according to the predetermined path, and collect the magnetic field signal intensity data at this time.

[0135] The circuit board is connected to a current of 3A, and low-resolution and high-resolution magnetic field images are collected through the experimental device. Then the low-resolution magnetic field image is input into the network, and the image is enlarged by 4 times and 8 times respectively, and the effects of various methods are as follows. As shown in Figure 5 A test circuit board composed of four wire loops is designed, and the spacing of each loop is 0.6 cm, 0.8 cm, 1.0 cm and 1.5 cm respectively. These different spacings simulate different magnetic field interactions between the wires. When the wire spacing is small, the magnetic field interaction is more significant, and the cancellation effect of the magnetic field lines is stronger, resulting in a magnetic field image showing a lighter color area. That is, when the wire spacing is small, the magnetic field distribution becomes more complex, and it is difficult to accurately distinguish the boundaries between the loops. This situation also includes the star and pine tree shapes shown in Figure 5

[0136] Table 4

[0137]

[0138] The corresponding PSNR and SSIM values are listed in Table 4. As can be seen from Table 4, in this case, the performance of many models has declined, especially when the loop spacing is small, the model often cannot clearly distinguish the subtle differences between the loops, resulting in unclear loop spacing, affecting the accuracy and resolution of the model. However, the model of the present application can not only achieve good recognition effect when the loop spacing is large, but also maintain high resolution and clearly identify the boundaries of each loop when the loop spacing is small.

[0139] The present application proposes a new physical information neural network to realize high-precision magnetic field super-resolution imaging; by embedding the Biot-Savart law into the neural network, the demand for training data volume of the network is reduced, and the stability of the network is improved.

[0140] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit it. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced by equivalents without departing from the spirit and scope of the present application, and they should be covered in the scope of the claims of the present application.​

Claims

1. A training method for physical information based magnetic field super-resolution imaging, characterized in that: The method comprises the following steps: S1, providing a first image sample and a second image sample; the first image sample is a high-resolution magnetic field distribution image, and the second image sample is a low-resolution magnetic field distribution image generated by down-sampling the corresponding first image sample; S2, inputting the second image sample into a super-resolution network to output a predicted high-resolution magnetic field distribution image through the network; S3, extracting a corresponding current density distribution from the predicted high-resolution magnetic field distribution image, and inversely calculating a magnetic field distribution by using the obtained current density to generate a calculated high-resolution magnetic field distribution image; In the process of extracting the corresponding current density distribution, a Gaussian low-pass filter is used to filter noise. Preparing a predicted high-resolution magnetic field distribution image for output by a super-resolution network , resolution x x y, pixel values representing magnetic field strength; On The two-dimensional Fourier transform is performed on the x and y direction magnetic field components of the magnetic field, respectively, to obtain the frequency domain magnetic field strength The frequency domain current density is calculated in combination with formula (1). A two-dimensional inverse Fourier transform is performed on the frequency domain current density to obtain an x by y spatial domain current density distribution ; wherein the current density at the position is represented by: is represented by: ； wherein and are spatial frequencies in the x and y directions of the magnetic field distribution image; is the height of the magnetometer; is the magnetic field strength measured at position ; is the vacuum permeability, 4   ; is a constant; The Gaussian low-pass filter is calculated according to formula (2): Wherein, σ is in the range of 400-600. ； In the process of generating the calculated high-resolution magnetic field distribution image, the following steps are further included: S4, comparing the calculated high-resolution magnetic field distribution image with the corresponding high-resolution magnetic field distribution image in the first image sample to calculate a data loss value; Will be Discrete into x × y current elements, according to the Biot-Savart law, the micro-magnetic field of each current element at the corresponding observation point is calculated, and for the current element The micro-magnetic field generated at the position The micro-magnetic field generated at the position Is expressed as: ； wherein is the current intensity, is the direction vector of the current element, is the unit vector from the current element to the observation point, is the distance between the observation point and the current element; Summing up the small magnetic field components of all current elements, traversing the x x y observation points, generating the calculated high-resolution magnetic field distribution image ; S5, optimizing the super-resolution network by calculating the data loss value; specifically, The data loss value is calculated according to the following formula: The calculated physical loss with the data loss constructing a comprehensive loss value , is represented as: ； wherein, is a coefficient of physical loss, ranges from 0 to 50.

2. The training method of claim 1, wherein the physical information-based magnetic field super-resolution imaging training method is characterized by: The method comprises the following steps: Determining a computed high-resolution magnetic field distribution image With the first image sample ; guarantee with pixel spatial positions one-to-one correspondence; A magnetic field image sample generation and preprocessing module is configured to generate or collect a first image sample and to pre-process the first image sample to obtain a second image sample; wherein the first image sample is a high-resolution magnetic field distribution image, and the second image sample is a low-resolution magnetic field distribution image generated by down-sampling the corresponding first image sample; ； wherein respectively and image length, width.

3. A physical information based magnetic field super-resolution imaging system, performing the method of claim 1 or 2, characterized by: A super-resolution network module is configured to output a predicted high-resolution magnetic field distribution image through the network by inputting the second image sample into the network; A current density inversion module is configured to extract a current density distribution from the predicted high-resolution magnetic field image; A magnetic field reverse calculation module is configured to calculate a high-resolution magnetic field image conforming to physical laws by using the current density distribution; A loss calculation and network optimization module is configured to calculate a loss value and to optimize the parameters of the super-resolution network; and An imaging result output and storage module is configured to output a final super-resolution magnetic field image and to store data. The super-resolution network module is an SRResNet super-resolution network, the input layer of which receives the pre-processed second image sample, the initial feature extraction is performed through a convolution layer and an activation layer, the feature learning is strengthened through a residual block, the feature map is enlarged to x×y pixels through an up-sampling block, and finally the output layer outputs a predicted high-resolution magnetic field distribution image.

4. The physical information based magnetic field super-resolution imaging system of claim 3, wherein: ​

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