Magnetic field super-resolution imaging training method and imaging system based on physical information

Abstract

The invention discloses a magnetic field super-resolution imaging training method based on physical information 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 down-sampling; inputting the second image sample into a super-resolution network, and outputting a predicted high-resolution magnetic field distribution image through the network; extracting corresponding current density distribution from the predicted high-resolution magnetic field distribution image, reversely calculating the magnetic field distribution according to the obtained current density, and generating a calculated high-resolution magnetic field distribution image; and comparing the calculated high-resolution magnetic field distribution image with the corresponding high-resolution magnetic field distribution image in the first image sample, calculating a data loss value, constructing a comprehensive loss optimization network, and finally outputting a precise super-resolution magnetic field graph. According to the invention, the demand of the network for training data volume is reduced, and the stability of the network is improved.

Description

Technical Field

[0001] This invention belongs to the field of neural network image processing technology, specifically relating to a magnetic field super-resolution imaging training method and imaging system based on physical information. Background Technology

[0002] With the rapid development of new energy vehicles, the demand for condition monitoring of automotive equipment is increasing. This is especially true for batteries and motors, which are core components of the electric vehicle's three-electric system, making their health monitoring crucial. Effective monitoring not only improves vehicle safety but also extends equipment lifespan. Currently, monitoring methods for batteries and motors mainly include: 1) Battery Management System (BMS): assessing the battery's charge / discharge status and health by monitoring parameters such as voltage, temperature, and current in real time. 2) Vibration Monitoring: using sensors to detect the vibration characteristics of the motor to determine its operating status and potential faults. 3) Thermal Imaging Technology: monitoring the temperature distribution of the battery and motor using thermal imagers to identify overheating or abnormal hotspots. 4) Data-Driven Approaches: analyzing historical data based on machine learning algorithms to predict battery and motor failure trends. Among these methods, magnetic field detection, as an emerging technology, is gradually gaining attention. Batteries and motors generate weak magnetic fields during operation; analyzing these magnetic field changes can provide information on the equipment's health status and potential faults. Magnetic field detection has advantages such as being non-destructive, real-time, and highly sensitive, providing an important supplementary means for condition monitoring of electric vehicles and promoting the further development of new energy vehicle technology.

[0003] However, in magnetic field detection, high-resolution magnetic field images require the acquisition of a large number of data points to ensure the capture of subtle magnetic field changes and structural features. This process typically involves complex sensors and data processing techniques; however, as the number of data points increases, the acquisition speed often decreases significantly. This not only prolongs data acquisition time but may also lead to untimely responses in rapidly changing environments. Meanwhile, while low-resolution magnetic field images are acquired more quickly, their image quality is often insufficient for accurate analysis. Low-resolution images may fail to clearly reveal subtle features and changes in the magnetic field, thus affecting the accuracy of subsequent analysis and decision-making. In some cases, this low-quality data may even lead to misjudgments, hindering the progress of subsequent work. Summary of the Invention

[0004] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

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

[0006] One of the objectives of this invention is to provide a training method for magnetic field super-resolution imaging based on physical information.

[0007] To address the aforementioned technical problems, this invention provides the following technical solution: a magnetic field super-resolution imaging training method based on physical information, comprising,

[0008] A first image sample and a second image sample are provided; 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] The second image sample is input into the super-resolution network, and the network outputs a predicted high-resolution image of the magnetic field distribution.

[0010] Extract the corresponding current density distribution from the predicted high-resolution magnetic field distribution image, and use the obtained current density to calculate the magnetic field distribution in reverse, thereby generating the calculated high-resolution magnetic field distribution image.

[0011] The calculated high-resolution magnetic field distribution image is compared with the corresponding high-resolution magnetic field distribution image in the first image sample, and the data loss value is calculated.

[0012] The super-resolution network is optimized by calculating the data loss value.

[0013] The "magnetic field distribution image" referred to in this invention is a two-dimensional image of the magnetic field strength.

[0014] The "high-resolution magnetic field distribution image" referred to in this invention means an image with a resolution of 128×128.

[0015] The "low-resolution magnetic field distribution image" referred to in this invention means an image with a resolution of 32×32.

[0016] In this invention, "downsampling" refers to reducing image resolution.

[0017] The "super-resolution network" referred to in this invention is SRResNet (Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network).

[0018] As a preferred embodiment of the magnetic field super-resolution imaging training method based on physical information of the present invention, wherein: the extraction of the corresponding current density distribution, specifically,

[0019] Preparing high-resolution magnetic field distribution images from the output of a super-resolution network The resolution is x×y, and the pixel value represents the magnetic field strength.

[0020] right Perform two-dimensional Fourier transforms on the x and y magnetic field components respectively to obtain the frequency domain magnetic field strength. Combined with formula (1), the frequency domain current density is calculated;

[0021] Performing a two-dimensional inverse Fourier transform on the frequency domain current density yields the spatial current density distribution in the x×y domain. ;

[0022] Among them, in position Current density at It can be represented as:

[0023]

[0024] In the formula, and These are the spatial frequencies in the x and y directions of the magnetic field distribution image; The height of the magnetometer; For in position The magnetic field strength measured at the location; The permeability of free space, 4 ; It is a constant.

[0025] As a preferred embodiment of the magnetic field super-resolution imaging training method based on physical information of the present invention, wherein: a Gaussian low-pass filter is used to filter noise during the extraction of the corresponding current density distribution;

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

[0027]

[0028] The value of σ ranges from 400 to 600.

[0029] As a preferred embodiment of the magnetic field super-resolution imaging training method based on physical information of the present invention, wherein: the generation and calculation of the high-resolution magnetic field distribution image specifically...

[0030] Will Discretize the current element into x×y current elements, and calculate the small magnetic field of each current element at the corresponding observation point according to the Biot-Savart law. For each current element... In position The tiny magnetic field generated at that location Represented as:

[0031]

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

[0033] Summing the minute magnetic field components of all current elements and iterating through the x×y observation points generates a calculated high-resolution image of the magnetic field distribution. .

[0034] As a preferred embodiment of the magnetic field super-resolution imaging training method based on physical information of the present invention, wherein: the calculation of the data loss value specifically...

[0035] Determine the calculated high-resolution magnetic field distribution image With the first image sample ;

[0036] ensure and The pixel spatial positions correspond one-to-one;

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

[0038]

[0039] in, They are respectively and Image length and width.

[0040] As a preferred embodiment of the magnetic field super-resolution imaging training method based on physical information of the present invention, wherein: the optimization of the super-resolution network by calculating the data loss value, specifically,

[0041] The calculated physical loss With data loss Construct a comprehensive loss value , Represented as:

[0042]

[0043] in, The coefficient for physical loss. The value range is 0 to 50.

[0044] Another object of the present invention 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 is used to generate or acquire a first image sample and preprocess 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 downsampling the corresponding first image sample;

[0046] A super-resolution network module is used to output a predicted high-resolution magnetic field distribution image from the second image sample through the network.

[0047] The current density inversion module is used to extract the current density distribution from the predicted high-resolution magnetic field map;

[0048] The magnetic field inverse calculation module is used to calculate a high-resolution magnetic field map that conforms to physical laws through current density distribution;

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

[0050] The imaging result output and storage module is used to output the final super-resolution magnetic field image and store the data.

[0051] As a preferred embodiment of the magnetic field super-resolution imaging system based on physical information of the present invention, the super-resolution network module is an SRResNet super-resolution network. The input layer receives the preprocessed second image sample, performs initial feature extraction through convolutional and activation layers, enhances feature learning through residual blocks, and then enlarges the feature map to x×y pixels through upsampling blocks. Finally, the output layer outputs the predicted high-resolution magnetic field distribution image.

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

[0053] This invention proposes a novel physical information neural network to achieve high-precision super-resolution imaging of magnetic fields; by embedding the Biot-Savart law into the neural network, the network's requirement for training data is reduced, while the network's stability is improved. Attached Figure Description

[0054] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0055] Figure 1 This is a schematic diagram of the movement of the mobile platform of the verification experimental platform of the present invention;

[0056] Figure 2 This is a schematic diagram of the network structure of the present invention;

[0057] Figure 3 This demonstrates the effect of 4x magnification of the simulated heart-shaped magnetic field image generated by interpolation, SRResNet, SRGAN, ESRGAN, and physical information neural network.

[0058] Figure 4 Box plots of two SRResNet models, one with physical information and one without, were generated after testing on 13 simulated images with different training set sizes.

[0059] Figure 5 This is a comparison chart of experimental results for different experimental circuit boards. Detailed Implementation

[0060] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the examples in the specification.

[0061] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0062] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0063] Example 1

[0064] The main method of this invention is to add physical information to the super-resolution imaging network.

[0065] First, current density is inverted based on the output 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 utilizes the detail enhancement information generated by the network to estimate a finer current distribution in space.

[0066] Next, the magnetic field distribution is calculated by reverse-engineering the current density obtained from the Biot-Savart law. The Biot-Savart law is used here to accurately calculate the spatial distribution of the magnetic field strength based on changes in current density; this step achieves a physical model mapping from current density to magnetic field strength.

[0067] After obtaining the calculated magnetic field distribution, this 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 to which the current density inversion result conforms to physical laws, thus obtaining a physical loss that reflects physical laws. This physical loss value is used to measure the physical rationality of the network output, ensuring that the super-resolution network not only achieves high-resolution image reconstruction visually, but also conforms to the fundamental laws of electromagnetism.

[0068] Finally, this physical loss value is combined with the network's original loss value (i.e., the data-based loss value) to form a hybrid loss value. The hybrid loss integrates the accuracy of image reconstruction with the consistency with physical laws, ensuring that network optimization not only focuses on improving image quality but also on the physical plausibility of its output. This hybrid loss, by adjusting the weights between data loss and physical loss, achieves comprehensive optimization of the super-resolution network, making its application in complex physical scenarios more reliable and consistent with actual physical laws.

[0069] Specifically, the primary physical formula used in calculating current density to magnetic field strength is the Biot-Saffar law. It is one of the fundamental laws in electromagnetism describing the magnetic field generated by current. It states that the magnetic field produced by a current element (i.e., a short segment of current-carrying wire) at a point in space is inversely proportional to the distance from that point to the current element, and the direction of the magnetic field is perpendicular to both the current element and the position vector of that point. Specifically, for a current element… In position The tiny magnetic field generated at that location :

[0070]

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

[0072] Biot-Savart law is widely used to calculate magnetic fields generated by complex current distributions, and is particularly suitable for calculating magnetic fields generated by long straight conductors, circular currents, or coils.

[0073] The method used to convert magnetic field strength into current density is the Fourier transform algorithm.

[0074] When considering the excitation effect of current on the spatial magnetic field in a two-dimensional flat plate, let... For in 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 can obtain the following formula:

[0101]

[0102] As can be seen from the formula, when When approaching zero, The equation tends towards infinity, leading to no solution, which indicates that... Uniform current cannot be generated in the direction The direction of the magnetic field, the current density is equivalent to the magnetic field strength processed by a high-pass filter.

[0103] To implement this algorithm on a computer, discretization over a finite region needs to be considered. The periodicity in the time domain of the Fourier transform corresponds to the discretization in the frequency domain. Let... and For current density at and The period in direction. Although the actual measured current is usually not periodic, it should be maximized as much as possible when selecting the measurement area. and To reduce the impact of periodicity on the results. Let... and for and The number of sampling points in the direction, 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, a large sampling rate is required. , and more sampling points , .

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

[0105]

[0106] in and Two coordinates in the frequency domain, The standard deviation of the Gaussian distribution determines the width of the filter.

[0107] Acquiring magnetic field images using experimental setups is time-consuming, especially at high resolutions, making it extremely time-consuming to collect a sufficient amount of magnetic field data for experimental dataset construction. Therefore, the Biot-Savart law was employed to generate a large amount of simulated magnetic field image data, significantly improving dataset construction efficiency and saving experimental time. By using the computational model of the Biot-Savart law, magnetic field intensity distributions of different shapes can be generated according to specific mathematical analytical functions. This not only makes magnetic field image generation more flexible but also enables the generation of a large amount of high-quality simulation data in a shorter time. Furthermore, the resolution of the simulated images can be freely adjusted according to experimental needs, adapting to various accuracy requirements. Compared to the acquisition process of actual experimental setups, the generation process of simulated data is more convenient and efficient, providing rich data resources for subsequent experiments and model training.

[0108] To verify the effectiveness of this method, this invention introduces the aforementioned physical formula into SRResNet (Super-Resolution Residual Network) to construct a physical information neural network. The network structure mainly consists of several convolutional layers and residual blocks, with the input being a low-resolution image of the magnetic field distribution. First, feature extraction is performed through a convolutional layer, followed by further feature processing through multiple residual blocks (each block containing two convolutional layers, a batch normalization layer, and a PReLU activation layer). The output of each residual block is added to the input through an additive 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 outputs the prediction result through a final convolutional layer. The overall network structure employs residual connections to improve training stability and performance.

[0109] Next, physical information is incorporated. First, the corresponding current density distribution is obtained through magnetic field inversion. Then, the Biot-Saffar law is applied to calculate the magnetic field distribution from the current density. After obtaining a high-resolution magnetic field image, this image is downsampled to a low-resolution image and compared with the input low-resolution image to calculate the mean squared error (MSE). This loss term is combined with the MSE between the high-resolution image output by the network and a given standard high-resolution image to form the comprehensive loss function of the physical information neural network. Through backpropagation, this loss function is fed back into the network, driving further training and improving the accuracy of reconstruction and prediction while considering physical information. Figure 2 This is a schematic diagram of the network structure of the present invention.

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

[0111] The added physical information includes two key parameters: the coefficient of physical loss. and the bandwidth of the Gaussian filter The magnitudes of these two parameters directly affect the training performance of the model. Therefore, to optimize the model, a random search method is used to find the optimal values ​​of these two parameters. The optimization process and results are shown in Table 1. The optimal parameter values ​​obtained through this method are... .

[0112] Table 1

[0113]

[0114] Experimental Example 1

[0115] To evaluate the experimental results, this invention employed two metrics: Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM). PSNR measures the difference between the original and reconstructed images. It is calculated based on the mean squared error (MSE) of the image, representing the ratio of peak signal to noise. A higher PSNR value indicates a smaller difference between the reconstructed and original images, and thus better quality. SSIM considers not only the differences between pixel values ​​but also the similarity in terms of image structure, brightness, contrast, and texture. A value closer to 1 indicates higher similarity.

[0116] To test the model's effectiveness, simulated magnetic field images were first used for testing. For example... Figure 3 The figures show the effects of interpolation, SRResNet, SRGAN, ESRGAN, and the physical information neural network of this invention, magnified by 4 times, on the simulated magnetic field images. Table 2 lists the corresponding PSNR and SSIM values. As can be seen from the figures, in some subtle details, the model of this invention achieves better results than other models.

[0117] Table 2

[0118]

[0119] Figure 4The image shows box plots of two models: SRResNet with and without physical information, tested on 13 simulated images with different training set sizes. Figure 4 It is evident that as the training set size decreases, the model incorporating physical information exhibits better stability in terms of performance degradation, with a smaller decline. Especially with low training set sizes, the performance gap between the model with and without physical information increases significantly, indicating that adding physical information effectively improves the model's generalization ability and robustness when samples are limited. Therefore, the introduction of physical information demonstrates its significant advantage in low-sample learning, maintaining high model performance even with scarce data.

[0120] Experiment Example 2

[0121] To further verify the effectiveness of the model, tests were conducted using circuit boards with different designs.

[0122] (1) Construction of the experimental platform

[0123] The magnetic field acquisition platform based on a sensor array constructed in this invention achieves high-precision, multi-dimensional magnetic field data acquisition through the collaborative operation of multiple modules. For example... Figure 1 As shown, the platform consists of core components such as a programmable DC power supply DP800, a digitally controlled DC power supply SPE3102, two 8-channel MR2103 magnetic sensor chips, two stepper motors, an NIUSB-6289 data acquisition card, and a computer. The MR2103 magnetic sensor boasts a high sensitivity of 5 mV / GS, enabling it to accurately capture changes in magnetic field strength, laying the foundation for subsequent data acquisition.

[0124] In terms of the data acquisition circuit design, two 8-channel magnetic sensor chips are mounted side-by-side on a non-magnetic material base. This special non-magnetic base design effectively avoids interference from external magnetic fields, ensuring the stability and accuracy of the detection data. During the experiment, the circuit for the magnetic field under test is securely mounted on the base surface and moved along the x-axis and y-axis directions by two stepper motors, respectively, to achieve coverage of the entire acquisition area. The scanning path is as follows: Figure 1 As shown. These two stepper motors can drive the base to move back and forth in the x and y directions respectively, gradually scanning the entire magnetic field area to ensure that no data is missed during the acquisition process.

[0125] During the experiment, the stepper motor moved segment by segment strictly according to the preset path. After each step forward, it paused briefly. During these pauses, the NI USB-6289 data acquisition card immediately activated, recording the magnetic field strength data at the current location in real time. Because the adjacent channels of the two sensor chips are vertically arranged, they can sense magnetic field components in different directions, thus obtaining more accurate multidimensional magnetic field information. This acquired data is automatically stored in a spreadsheet, facilitating data organization and providing convenience for subsequent in-depth analysis and processing. The entire movement and data acquisition process continues until the entire circuit layout is fully covered, ensuring comprehensive and complete magnetic field sampling data, providing reliable data support for research. Furthermore, the stepper motor's step size is flexibly adjustable. By setting different step sizes, magnetic field image data acquisition at different resolutions can be achieved; specific parameters can be found in Table 3. This function allows for flexible control of acquisition accuracy according to different experimental needs, greatly improving the platform's applicability and practicality.

[0126] Table 3

[0127]

[0128] Because other electronic devices are present in the experimental environment, their magnetic fields can interfere with the acquired signals. To reduce the impact of this noise, the circuit was powered off before the experiment, and background magnetic field data was collected as a noise reference. Subsequently, the circuit under test was powered on again, and the magnetic field strength was collected. During data processing, the magnetic field data collected under power was subtracted from the background noise to obtain a relatively clean circuit magnetic field signal map, thus enhancing the accuracy of the experimental results.

[0129] Experimental procedure:

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

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

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

[0133] (4) After the background noise is collected, 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 to move along the predetermined path and collect the magnetic field signal strength data at this time.

[0135] All circuit boards were connected to a 3A current, and low-resolution and high-resolution magnetic field images were acquired using the experimental setup. The low-resolution magnetic field image was then input into the network, and the images were magnified by 4x and 8x respectively. The effects of various methods are shown below. Figure 5 As shown, an experimental circuit board consisting of four wire loops was designed, with the spacing between each loop being 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 lighter-colored areas in the magnetic field image. In other words, when the wire spacing is close, the magnetic field distribution becomes more complex, and it is difficult to accurately distinguish the boundaries between the loops. This situation also includes... Figure 5 The star and pine tree shapes shown.

[0136] Table 4

[0137]

[0138] Table 4 lists the corresponding PSNR and SSIM values. As can be seen from Table 4, the performance of many models deteriorates under these conditions, especially when the loop spacing is close. The models often fail to clearly identify subtle differences between loops, resulting in blurred loop intervals and affecting the model's accuracy and resolution. However, the model of this invention, by introducing physical information, not only achieves good recognition results even with large loop spacing but also maintains high resolution and clearly identifies the boundaries of each loop even with small loop spacing.

[0139] This invention proposes a novel physical information neural network to achieve high-precision super-resolution imaging of magnetic fields; by embedding the Biot-Savart law into the neural network, the network's requirement for training data is reduced, while the network's stability is improved.

[0140] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A magnetic field super-resolution imaging training method based on physical information, characterized in that: include, A first image sample and a second image sample are provided; 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; The second image sample is input into the super-resolution network, and the network outputs a predicted high-resolution image of the magnetic field distribution. Extract the corresponding current density distribution from the predicted high-resolution magnetic field distribution image, and use the obtained current density to calculate the magnetic field distribution in reverse, thereby generating the calculated high-resolution magnetic field distribution image. The calculated high-resolution magnetic field distribution image is compared with the corresponding high-resolution magnetic field distribution image in the first image sample, and the data loss value is calculated. The super-resolution network is optimized by calculating the data loss value.

2. The magnetic field super-resolution imaging training method based on physical information as described in claim 1, characterized in that: The extraction of the corresponding current density distribution, specifically... Preparing high-resolution magnetic field distribution images from the output of a super-resolution network The resolution is x×y, and the pixel value represents the magnetic field strength. right Perform two-dimensional Fourier transforms on the x and y magnetic field components respectively to obtain the frequency domain magnetic field strength. Combined with formula (1), the frequency domain current density is calculated; Performing a two-dimensional inverse Fourier transform on the frequency domain current density yields the spatial current density distribution in the x×y domain. ; Among them, in position Current density at It can be represented as: ； In the formula, and These are the spatial frequencies in the x and y directions of the magnetic field distribution image; The height of the magnetometer; For in position The magnetic field strength measured at the location; The permeability of free space, 4 ; It is a constant.​ 3. The magnetic field super-resolution imaging training method based on physical information as described in claim 2, characterized in that: Noise is filtered using a Gaussian low-pass filter during the extraction of the corresponding current density distribution. The Gaussian low-pass filter is calculated according to formula (2): ； The value of σ ranges from 400 to 600.

4. The magnetic field super-resolution imaging training method based on physical information as described in claim 2, characterized in that: The generated high-resolution magnetic field distribution image, specifically, Will Discretize the current element into x×y current elements, and calculate the small magnetic field of each current element at the corresponding observation point according to the Biot-Savart law. For each current element... In position The tiny magnetic field generated at that location Represented as: ； In the formula, For current intensity, The direction vector of the current element. It is the unit vector pointing from the current element to the observation point. It is the distance between the observation point and the current element; Summing the minute magnetic field components of all current elements and iterating through the x×y observation points generates a calculated high-resolution image of the magnetic field distribution. .

5. The magnetic field super-resolution imaging training method based on physical information as described in claim 1, characterized in that: The calculated data loss value, specifically, Determine the calculated high-resolution magnetic field distribution image With the first image sample ; ensure and The pixel spatial positions correspond one-to-one; The loss is calculated using the mean square error formula, which is: ； in, They are respectively and Image length and width.

6. The magnetic field super-resolution imaging training method based on physical information as described in claim 1, characterized in that: The optimization of the super-resolution network by calculating data loss values, specifically... The calculated physical loss With data loss Construct a comprehensive loss value , Represented as: ； in, The coefficient for physical loss. The value range is 0 to 50.

7. A magnetic field super-resolution imaging system based on physical information, characterized in that: include, A magnetic field image sample generation and preprocessing module is used to generate or acquire a first image sample and preprocess 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 downsampling the corresponding first image sample; A super-resolution network module is used to output a predicted high-resolution magnetic field distribution image from the second image sample through the network. The current density inversion module is used to extract the current density distribution from the predicted high-resolution magnetic field map; The magnetic field inverse calculation module is used to calculate a high-resolution magnetic field map that conforms to physical laws through current density distribution; The loss calculation and network optimization module is used to calculate the loss value and optimize the parameters of the super-resolution network; and, The imaging result output and storage module is used to output the final super-resolution magnetic field image and store the data.

8. The magnetic field super-resolution imaging system based on physical information as described in claim 7, characterized in that: The super-resolution network module is an SRResNet super-resolution network. The input layer receives the preprocessed second image sample, performs initial feature extraction through convolutional and activation layers, enhances feature learning through residual blocks, and then enlarges the feature map to x×y pixels through upsampling blocks. Finally, the output layer outputs the predicted high-resolution magnetic field distribution image.

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