TEC distribution reconstruction method and device based on diffusion model

Abstract

The invention discloses a TEC distribution reconstruction method and device based on a diffusion model, and the method comprises the steps: preprocessing TEC data, constructing a diffusion model, inputting the TEC data into the diffusion model, and carrying out the forward diffusion and reverse denoising training; after training is completed, random noise is input into a diffusion model for reverse denoising to obtain an unknown area image, TEC observation data with missing are input into the diffusion model for forward diffusion, random noise is added to obtain a known area image, and the unknown area image and the known area image are combined to obtain a first intermediate image; and inputting the first intermediate image and the missing TEC observation data into the diffusion model, performing forward diffusion and reverse denoising again, circularly combining the unknown region image and the known region image, and performing iteration for limited times to obtain TEC reconstruction data. According to the method, the TEC data coverage rate is increased, full coverage in the global range is achieved, the TEC data generation precision and reliability are improved, and TEC distribution is accurately reconstructed.

Description

Technical Field

[0001] The present invention belongs to the field of space models, and more specifically, relates to a TEC distribution reconstruction method and device based on a diffusion model. Background Art

[0002] Total electron content (TEC) is an important parameter in the study of the Earth's ionosphere, which directly affects the accuracy of GPS navigation and communication systems. At present, global TEC monitoring mainly relies on the following technical means: (1) Global Navigation Satellite System (GNSS) observations: GNSS is one of the main sources for obtaining TEC data. By measuring the delay of GNSS signals, the TEC value along the path can be calculated. The advantage of this method is its wide coverage, but in areas such as the ocean and the polar regions, ground receiving stations are scarce, resulting in incomplete data. (2) Ionospheric sounders: Ionospheric sounders (such as occultation technology) obtain TEC data by monitoring the changes in satellite signals as they pass through the ionosphere. This method has high accuracy, but is limited by observation conditions and equipment layout. (3) Ground-based radar: High-frequency radar can measure the characteristics of the ionosphere through reflected signals and indirectly infer the TEC value. However, this method requires complex equipment and fixed observation stations, resulting in limited data coverage.

[0003] Although the above technologies have played an important role in global TEC monitoring, there are still some shortcomings. (1) Incomplete data coverage. There is a lack of sufficient observation data in the oceans, polar regions and some remote areas. (2) Dependence on fixed equipment. Many measurement methods require expensive fixed equipment and cannot flexibly meet the needs of different geographical regions. Therefore, some researchers have tried to fill the gaps in observational data through data interpolation and assimilation techniques, but these methods are usually limited by model assumptions and cannot accurately reflect actual ionospheric changes. In recent years, machine learning methods have been applied to the prediction and completion of TEC data. For example, by training neural network models, attempts are made to infer TEC values ​​in unknown areas from existing data. These methods have improved the spatial coverage of data to a certain extent, but there are still problems with accuracy and reliability.

[0004] In summary, the existing TEC observation technology and data completion methods have deficiencies in spatial and temporal coverage. How to improve the temporal and spatial coverage of TEC data while further improving accuracy and reliability is an urgent problem to be solved. In view of this, overcoming the technical defects of the above-mentioned existing technologies is an urgent problem to be solved in this technical field. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a TEC distribution reconstruction method and device based on a diffusion model, which aims to solve the shortcomings of the prior art in terms of temporal and spatial coverage and the technical problem of relying on fixed equipment.

[0006] To achieve the above object, according to one aspect of the present invention, a TEC distribution reconstruction method based on a diffusion model is provided, the method comprising:

[0007] Preprocessing TEC data, building a diffusion model, and inputting the TEC data into the diffusion model for forward diffusion and reverse denoising training;

[0008] After the training is completed, random noise is input into the diffusion model for reverse denoising to obtain an unknown region image, missing TEC observation data is input into the diffusion model for forward diffusion to add random noise to obtain a known region image, and the unknown region image and the known region image are combined to obtain a first intermediate image;

[0009] The first intermediate image and the missing TEC observation data are respectively input into the diffusion model for forward diffusion and reverse denoising again, and the unknown region image and the known region image are cyclically combined, and TEC reconstruction data is obtained after a limited number of iterations.

[0010] As a further improvement and supplement to the above solution, the present invention also includes the following additional technical features.

[0011] Preferably, the TEC distribution reconstruction method based on the diffusion model as described in claim 1 is characterized in that the preprocessing of the TEC data includes: using linear interpolation method to expand the data resolution of TEC data with no missing data and a resolution of 64*64 to 180*360.

[0012] Preferably, the method of inputting the TEC data into the diffusion model for forward diffusion and reverse denoising training comprises:

[0013] The TEC data is input into the diffusion model for forward diffusion and reverse denoising respectively, wherein the forward denoising converts the input TEC data into pure noise; and the reverse denoising converts random noise into TEC data;

[0014] The difference between the added noise and the denoised noise at the corresponding moment is used for comparison, and the training of the diffusion model is stopped when the noise difference between the added noise and the denoised noise reaches a preset threshold.

[0015] Preferably, the forward noising is performed by using a Markov chain and a Bayesian formula to derive the noisy TEC data from the original TEC data after adding any number of noises.

[0016] Preferably, the reverse denoising utilizes a U-net neural network to predict and remove noise.

[0017] Preferably, the method of inputting missing TEC observation data into the diffusion model for forward diffusion and adding random noise to obtain a known area image comprises:

[0018] Inputting the missing TEC observation data into the diffusion model, performing forward noise addition, wherein the noise is random noise, to obtain a first image;

[0019] The first image is combined with the mask to obtain an image of the known area.

[0020] Preferably, the method of inputting random noise into the diffusion model for reverse denoising to obtain an unknown area image comprises:

[0021] The image of the known area is combined with the inverse mask to mark it as an unknown area, and the known area information is retained as a conditional loop to iteratively guide the generation of unknown area data.

[0022] According to another aspect of the present invention, a TEC distribution reconstruction device based on a diffusion model is provided, the device comprising:

[0023] one or more processors;

[0024] A storage device is used to store one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors implement the TEC distribution reconstruction method based on the diffusion model as described in the first aspect.

[0025] In general, the above technical solution conceived by the present invention has the following beneficial effects compared with the prior art:

[0026] The present invention achieves the following goals by applying diffusion generation technology: (1) improving data coverage by using the diffusion model to learn the known TEC data distribution and generate high-precision data of unknown areas to achieve comprehensive coverage on a global scale. (2) improving data generation accuracy and reliability, providing a more accurate data generation method, accurately reconstructing the missing TEC distribution, and improving the overall data quality.

[0027] The TEC distribution reconstruction method based on the diffusion model provided by the present invention solves the shortcomings of the existing technology in terms of temporal and spatial coverage. In addition to being able to provide continuous high-temporal resolution data and accurately capture the dynamic changes of the ionosphere, the diffusion model greatly reduces the dependence on expensive equipment, making the technology more flexible and scalable. Through conditional input and model optimization, the accuracy and reliability of generated data are significantly improved, ensuring accurate modeling of complex data distribution. These advantages make this method more efficient and reliable in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0029] Figure 1 is a flowchart of a TEC distribution reconstruction method based on a diffusion model provided in the first embodiment;

[0030] Figure 2 is a high-precision reconstruction flow chart of global ionospheric TEC distribution provided in the first embodiment;

[0031] Figure 3 This is a diagram of the internal structure framework based on the diffusion model technology provided in the first embodiment;

[0032] Figure 4 is a schematic diagram of the conditional reasoning process of the diffusion model provided in the first embodiment;

[0033] Figure 5 This is a schematic diagram of a TEC distribution reconstruction device based on a diffusion model provided in the second embodiment. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0035] The TEC data reconstruction method based on traditional data assimilation is limited by the model parameterization and uncertainty of observation data, and it is difficult to accurately reflect the actual ionospheric changes, which leads to challenges to its applicability in complex space weather systems. At the same time, the TEC data reconstruction method based on machine learning has improved the spatial coverage of data to a certain extent, but there are still problems with accuracy and reliability. At the same time, the neural network model requires a large amount of training data, and has high requirements on the generalization ability and robustness of the model. Therefore, this embodiment aims to solve the problem of high-precision reconstruction of TEC data, and further improve the data accuracy and reliability while improving the spatiotemporal coverage of TEC data.

[0036] In order to solve the above problems, this embodiment achieves the following goals by applying diffusion generation technology: (1) Improve data coverage, use the diffusion model to learn the distribution of known TEC data, generate high-precision data of unknown areas, and achieve comprehensive coverage on a global scale. (2) Improve data generation accuracy and reliability, provide a more accurate data generation method, accurately reconstruct the missing TEC distribution, and improve the overall data quality.

[0037] Embodiment 1

[0038] This embodiment 1 provides a TEC distribution reconstruction method based on a diffusion model, such as Figure 1 As shown, the method includes:

[0039] S101: pre-processing TEC data, constructing a diffusion model, and inputting the TEC data into the diffusion model for forward diffusion and reverse denoising training.

[0040] The preprocessing of TEC data is to process the grid data. The TEC data (resolution 64*64) provided by The International GNSS Service (IGS) without missing data is expanded to a resolution of 180*360 using the linear interpolation method to train the high-precision diffusion model.

[0041] The diffusion model consists of two main parts: the forward diffusion part and the backward denoising part.

[0042] Forward diffusion part: During the forward diffusion process, the model gradually adds noise to the TEC data. This is a step-by-step transformation process, usually performed through a predefined noise characterization function. This process transforms the original data into pure noise over multiple time steps, allowing the model to learn the data distribution under different noise levels.

[0043] Reverse denoising: The reverse denoising process is the process of gradually removing noise. The diffusion model gradually restores the original data distribution by learning how to recover TEC data from noise. This part is usually implemented by a deep neural network, which uses known conditional information to guide data generation.

[0044] These two parts work together, with forward diffusion providing a path for data to be transformed into noise, and reverse denoising generating new data by learning the inverse process. This collaboration enables the model to generate high-quality samples under given conditions and achieve effective modeling of complex data distributions.

[0045] S102: After the training is completed, random noise is input into the diffusion model for reverse denoising to obtain an unknown region image, missing TEC observation data is input into the diffusion model for forward diffusion to add random noise to obtain a known region image, and the unknown region image and the known region image are combined to obtain a first intermediate image.

[0046] A large amount of high-precision IGS data is fed into the diffusion model for training, and the difference between the noise during denoising and the noise predicted by the model during denoising at the corresponding moment is compared to evaluate and optimize the model.

[0047] S103: Input the first intermediate image and the missing TEC observation data into the diffusion model respectively to perform forward diffusion and reverse denoising again, cyclically combine the unknown area image and the known area image, and obtain TEC reconstructed data after a limited number of iterations.

[0048] The number of iterations has been learned during the training process, and the number of iterations is determined after the training is completed.

[0049] In order to improve the reconstruction accuracy of TEC data, high-precision observation data with a large number of missing parts are used as inference conditions for the trained diffusion model. Figure 4 As shown, the noise and high-precision observation data with a large number of missing parts are used as the input of the conditional reasoning model, where the input noise is denoised once through the reverse process of the diffusion model, and the input high-precision observation data with a large number of missing parts is added with random noise through the forward process of the diffusion model. Then, the missing area image of the reverse process and the known area image result of the forward process are combined to obtain the intermediate result Xt. Then, Xt and the high-precision observation data with a large number of missing parts are used as the input of the conditional reasoning model, and the known area information is used as the reasoning condition of the diffusion model. Xt-1 is obtained in the same way, as shown in Figure 4 As shown. Xt-1 is used as Xt of the next cycle, and after iteration, the final X0 is obtained, which is the reconstructed TEC data.

[0050] In order to train a high-precision diffusion model, in combination with this embodiment, there is also a preferred implementation scheme, specifically, as follows: Figure 2 As shown, the preprocessing of TEC data includes: using linear interpolation method to expand the data resolution of TEC data with no missing data and a resolution of 64*64 to 180*360. After the expansion, the accuracy of the TEC data is improved.

[0051] In order to effectively model the model, there is also a preferred implementation scheme in combination with the present embodiment, specifically, as follows: Figure 2 As shown, the method of inputting the TEC data into the diffusion model for forward diffusion and reverse denoising training includes:

[0052] The TEC data is input into the diffusion model for forward diffusion and reverse denoising respectively, wherein the forward denoising converts the input TEC data into pure noise; and the reverse denoising converts random noise into TEC data;

[0053] The difference between the added noise and the denoised noise at the corresponding moment is used for comparison, and the training of the diffusion model is stopped when the noise difference between the added noise and the denoised noise reaches a preset threshold.

[0054] Random noise is a pure noise image randomly sampled from a normal distribution, and its size is consistent with the input TEC data image size.

[0055] The cross entropy loss function is used to measure the noise difference. The cross entropy can measure the difference between two different probability distributions in the same random variable. The smaller the value, the better the model prediction effect.

[0056] In combination with the present embodiment, there is also a preferred implementation scheme. Specifically, the forward noise addition derives the noisy TEC data from the original TEC data to the noisy TEC data after adding any number of noises through the Markov chain and the Bayesian formula.

[0057] In combination with this embodiment, there is also a preferred implementation scheme, specifically, as follows Figure 3 As shown, the reverse denoising utilizes a U-net neural network to predict and remove noise.

[0058] In combination with this embodiment, there is also a preferred implementation scheme, specifically, as follows Figure 3 As shown, the method of inputting missing TEC observation data into the diffusion model for forward diffusion and adding random noise to obtain a known area image includes:

[0059] Inputting the missing TEC observation data into the diffusion model, performing forward noise addition, wherein the noise is random noise, to obtain a first image;

[0060] The first image is combined with the mask to obtain an image of the known area.

[0061] like Figure 3As shown, the original data image is input into the diffusion model and firstly subjected to the forward denoising process to obtain the image after denoising T times. The image after denoising T times is then subjected to reverse denoising, and the noise is removed by using the U-net neural network prediction. The image after denoising T times is subjected to a finite number of downsampling and a finite number of upsampling of the U-net neural network to obtain the image after passing through the U-net neural network once. The image after passing through the U-net neural network once is then subjected to a finite number of downsampling and a finite number of upsampling of the U-net neural network to generate the final data. Compared with the original data image, the final image is the same as the original image, indicating that the U-net neural network is used to predict and remove noise.

[0062] In combination with this embodiment, there is also a preferred implementation scheme, specifically, as follows Figure 4 As shown, the method of inputting random noise into the diffusion model for reverse denoising to obtain an unknown area image includes:

[0063] The image of the known area is combined with the inverse mask to mark it as an unknown area, and the known area information is retained as a conditional loop to iteratively guide the generation of unknown area data.

[0064] The diffusion model is selected for high-precision reconstruction of global ionospheric TEC distribution because the diffusion model has strong nonlinear modeling capabilities and has begun to show its unique potential in many other fields, especially in image processing and natural language processing. In this embodiment, the diffusion model is applied to the field of high-precision reconstruction of ionospheric TEC data to better capture the complex dynamic process of ionospheric TEC and improve the accuracy of data generation.

[0065] First, the original TEC data (64*64 resolution) is expanded to 180*360 resolution through interpolation. Then, the diffusion model is trained to learn the characteristic distribution of TEC data. Among them, the forward diffusion uses the Markov chain and Bayesian formula to derive the TEC data after adding any number of noises from the original TEC data in one step, which greatly reduces the resources and time consumed by slowly adding noise step by step. The reverse denoising uses the U-net neural network to predict and remove noise, gradually approaching the original image. Finally, the information of the known area is used as a condition to infer the missing part of the TEC data information using the trained diffusion model, thereby achieving high-precision reconstruction of the TEC data.

[0066] like Figure 4 As shown, when the information of the known area is used as a condition to infer the TEC data information of the missing part using the trained diffusion model, the ionospheric TEC data of the missing area is combined with the mask Mask to mark the known and unknown areas, and the known area information is retained as a condition to iteratively guide the generation of unknown area data.

[0067] Regarding the conditional reasoning part, the forward process of the diffusion model randomly adds Gaussian noise. After the input image is added with random noise, the known area is continuously used as a condition to control the generation of missing areas. The Xt-1 image obtained by adding noise is combined with the mask Mask to obtain the Xt-1 image of the known area. The Xt image (the X(t+1) image is inferred by the diffusion model to obtain the Xt image) is then reversely denoised to obtain the Xt-1 image. The Xt-1 image is combined with the inverse mask Mask Inv to obtain the Xt-1 image of the unknown area. The Xt-1 image obtained by combining the known area and the unknown area is used as the Xt of the next cycle, and the cycle is iterated until the final X0 is obtained.

[0068] The TEC data reconstruction method based on traditional data assimilation is limited by the model parameterization and uncertainty of observation data, and it is difficult to accurately reflect the actual ionospheric changes, which leads to challenges to its applicability in complex space weather systems. At the same time, the TEC data reconstruction method based on machine learning has improved the spatial coverage of data to a certain extent, but there are still problems with accuracy and reliability. At the same time, the neural network model requires a large amount of training data, and has high requirements on the generalization ability and robustness of the model. Therefore, this embodiment aims to solve the problem of high-precision reconstruction of TEC data, and further improve the data accuracy and reliability while improving the spatiotemporal coverage of TEC data.

[0069] In order to solve the above problems, this embodiment achieves the following goals by applying diffusion generation technology: (1) Improve data coverage, use the diffusion model to learn the distribution of known TEC data, generate high-precision data of unknown areas, and achieve comprehensive coverage on a global scale. (2) Improve data generation accuracy and reliability, provide a more accurate data generation method, accurately reconstruct the missing TEC distribution, and improve the overall data quality.

[0070] This embodiment generates missing ionospheric TEC data on a global scale, solving the deficiencies of existing technologies in terms of temporal and spatial coverage. This embodiment can provide continuous high-temporal resolution data to accurately capture the dynamic changes of the ionosphere. In addition, the diffusion model in this embodiment greatly reduces the reliance on expensive equipment, making the technology more flexible and scalable. Through conditional input and model optimization, the accuracy and reliability of generated data are significantly improved, ensuring accurate modeling of complex data distribution. These advantages make the technology more efficient and reliable in practical applications.

[0071] Embodiment 2:

[0072] A TEC distribution reconstruction device based on a diffusion model, such as Figure 5 As shown, the device includes:

[0073] one or more processors;

[0074] A storage device is used to store one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors implement the TEC distribution reconstruction method based on the diffusion model as described in any one of the first embodiments.

[0075] Figure 5 This is a schematic diagram of the structure of the TEC distribution reconstruction device based on the diffusion model provided in the third embodiment. Figure 5 A block diagram of an exemplary diffusion model-based TEC distribution reconstruction device suitable for implementing the embodiments of the present invention is shown. Figure 5 The TEC distribution reconstruction device based on the diffusion model shown is only an example and should not bring any limitation to the function and scope of use of this embodiment.

[0076] like Figure 5 As shown, the TEC distribution reconstruction device based on the diffusion model is presented in the form of a general device. The components of the TEC distribution reconstruction device based on the diffusion model may include but are not limited to: one or more processors or processing units, memory, and a bus connecting different system components (including memory and processing units).

[0077] The term "bus" refers to one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processor or a local bus using any of a variety of bus architectures. For example, these architectures include, but are not limited to, the Industry Standard Architecture (ISA) bus, the Micro Channel Architecture (MAC) bus, the Enhanced ISA bus, the Video Electronics Standards Association (VESA) local bus, and the Peripheral Component Interconnect (PCI) bus.

[0078] The TEC distribution reconstruction device based on the diffusion model typically includes a variety of computer system readable media. These media can be any available media that can be accessed by the device for correcting the intelligent well logging interpretation model, including volatile and non-volatile media, removable and non-removable media.

[0079] The memory may include a computer system readable medium in the form of a volatile memory, such as a random access memory (RAM) 30 and / or a cache memory. The diffusion model-based TEC distribution reconstruction device may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, the storage system may be used to read and write non-removable, non-volatile magnetic media ( Figure 5 not shown, usually called a "hard drive"). Although Figure 5Not shown, a disk drive for reading and writing to a removable non-volatile disk (e.g., a "floppy disk"), and an optical drive for reading and writing to a removable non-volatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical medium) may be provided. In these cases, each drive may be connected to the bus via one or more data medium interfaces. The memory may include at least one program product having a set (e.g., at least one) of program modules that are configured to perform the functions of each embodiment of the present embodiment.

[0080] A program / utility having a set (at least one) of program modules may be stored in, for example, a memory, such program modules including but not limited to an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment. The program modules generally perform the functions and / or methods of the embodiments described in this embodiment.

[0081] The TEC distribution reconstruction device based on the diffusion model can also communicate with one or more external devices (such as keyboards, pointing devices, displays, etc.), and can also communicate with one or more devices that enable users to interact with the TEC distribution reconstruction device based on the diffusion model, and / or communicate with any device that enables the TEC distribution reconstruction device based on the diffusion model to communicate with one or more other devices (such as network cards, modems, etc.). Such communication can be carried out through an input / output (I / O) interface. In addition, the device for correcting the intelligent logging interpretation model can also communicate with one or more networks (such as a local area network (LAN), a wide area network (WAN) and / or a public network, such as the Internet) through a network adapter. Figure 5 As shown, the network adapter communicates with other modules of the TEC distribution reconstruction device based on the diffusion model through the bus. It should be understood that, although not shown in the figure, other hardware and / or software modules can be used in conjunction with the TEC distribution reconstruction device based on the diffusion model, including but not limited to: microcode, device driver, redundant processing unit, external disk drive array, RAID system, tape drive and data backup storage system, etc.

[0082] The processing unit executes various functional applications and data processing by running the program stored in the memory, for example, realizing the TEC distribution reconstruction method based on the diffusion model provided in any embodiment of the present embodiment. That is: pre-processing TEC data, constructing a diffusion model, inputting the TEC data into the diffusion model for forward diffusion and reverse denoising training; after the training is completed, inputting random noise into the diffusion model for reverse denoising to obtain an unknown region image, inputting missing TEC observation data into the diffusion model for forward diffusion and adding random noise to obtain a known region image, combining the unknown region image with the known region image to obtain a first intermediate image; respectively inputting the first intermediate image and the missing TEC observation data into the diffusion model for forward diffusion and reverse denoising again, cyclically combining the unknown region image with the known region image, and obtaining TEC reconstruction data after a limited number of iterations.

[0083] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A TEC distribution reconstruction method based on a diffusion model, characterized in that: The method comprises: Preprocessing TEC data, building a diffusion model, and inputting the TEC data into the diffusion model for forward diffusion and reverse denoising training; After the training is completed, random noise is input into the diffusion model for reverse denoising to obtain an unknown region image, missing TEC observation data is input into the diffusion model for forward diffusion to add random noise to obtain a known region image, and the unknown region image and the known region image are combined to obtain a first intermediate image; The first intermediate image and the missing TEC observation data are respectively input into the diffusion model for forward diffusion and reverse denoising again, and the unknown region image and the known region image are cyclically combined, and TEC reconstruction data is obtained after a limited number of iterations.

2. The TEC distribution reconstruction method based on the diffusion model according to claim 1, characterized in that: The preprocessing of TEC data includes: using linear interpolation method to expand the resolution of TEC data with no missing data and a resolution of 64*64 to 180*360.

3. The TEC distribution reconstruction method based on the diffusion model according to claim 1, characterized in that: The method of inputting the TEC data into the diffusion model for forward diffusion and reverse denoising training includes: The TEC data is input into the diffusion model for forward diffusion and reverse denoising respectively, wherein the forward denoising converts the input TEC data into pure noise; and the reverse denoising converts random noise into TEC data; The difference between the added noise and the denoised noise at the corresponding moment is used for comparison, and the training of the diffusion model is stopped when the noise difference between the added noise and the denoised noise reaches a preset threshold.

4. The TEC distribution reconstruction method based on the diffusion model according to claim 3, characterized in that: The forward noise addition derives the noise-added TEC data from the original TEC data to the noise-added TEC data after adding any number of noises through the Markov chain and the Bayesian formula.

5. The TEC distribution reconstruction method based on the diffusion model according to claim 3, characterized in that: The reverse denoising utilizes a U-net neural network to predict and remove noise.

6. The TEC distribution reconstruction method based on the diffusion model according to claim 3, characterized in that: The method of inputting missing TEC observation data into the diffusion model for forward diffusion and adding random noise to obtain a known area image comprises: Inputting the missing TEC observation data into the diffusion model, performing forward noise addition, wherein the noise is random noise, to obtain a first image; The first image is combined with the mask to obtain an image of the known area.

7. The TEC distribution reconstruction method based on the diffusion model according to claim 3, characterized in that: The method of inputting random noise into the diffusion model for reverse denoising to obtain an unknown area image comprises: The image of the known area is combined with the inverse mask to mark it as an unknown area, and the known area information is retained as a conditional loop to iteratively guide the generation of unknown area data.

8. A TEC distribution reconstruction device based on a diffusion model, characterized in that the device include: one or more processors; A storage device for storing one or more programs, when the one or more programs are executed by the one or more processors, the one or more processors implement the TEC distribution reconstruction method based on the diffusion model as described in any one of claims 1-7.

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