Sea temperature complementing method and system based on asynchronous diffusion Schrodinger bridge

Abstract

The invention belongs to the technical field of sea temperature complementation, and discloses a sea temperature complementation method and system based on an asynchronous diffusion Schrodinger bridge, and the method comprises the steps: firstly, generating a weight anomal which reflects the abnormal degree of a pixel through a preprocessing step S1, so as to guide a subsequent diffusion process; s2, establishing a bidirectional diffusion path between the initial complementation image and the real image based on a diffusion Schrodinger bridge theory, and dynamically adjusting a diffusion coefficient according to anomay to generate an intermediate state xt; predicting a score function pred through a U-Net network S3, and reconstructing a current image x0 for updating a state or calculating loss; model parameters are optimized through iteration during training, multi-round denoising reconstruction is carried out during inference, and finally a complete high-quality sea surface temperature image SSTrecon is output. According to the invention, local details are fully reserved, and the accuracy of image completion is improved.

Description

Technical Field

[0001] This invention belongs to the field of sea surface temperature (SST) completion technology, and specifically relates to a SST completion method and system based on an asynchronous diffusion Schrödinger bridge. Background Technology

[0002] Currently, cutting-edge methods in deep learning-based sea surface temperature (SST) completion employ an image completion mechanism based on a "diffusion model with multi-scale physical constraints." The first stage uses a diffusion denoising model to reconstruct the weekly mean SST as a coarse prediction of the missing daily SST field, providing global physical constraints. The second stage learns the difference between the weekly mean and the daily SST field, using another diffusion denoising model to repair the daily-scale anomaly, providing local physical constraints. The third stage uses a multi-scale decoupling strategy to fuse global and local constraints to complete the completion. The advantages of this method lie in combining the physical constraints of the weekly and daily mean deviations, the stable generation capability of the DDPM (Divergence Divergence Model), and multi-scale feature fusion to achieve high-precision, physically consistent SST data completion.

[0003] However, this method has the following problems: First, relying solely on one-way reverse denoising while neglecting forward diffusion modeling makes it impossible to explicitly learn the data distribution, making it difficult to fully utilize the original information and spatial correlations, resulting in loss of details or over-smoothing. This leads to a decrease in physical consistency, especially when dealing with complex ocean phenomena (such as mesoscale eddies and sudden frontal changes). At the same time, the lack of effective control over the balance between noise and signal can easily lead to information loss.

[0004] Second, the uniform denoising intensity strategy fails to consider the regional heterogeneity of sea surface temperature (SST) data. The model applies the same denoising intensity to all pixels in the image. This approach fails to adequately consider the unique characteristics of different regions within the SST data and cannot dynamically adjust the denoising process according to the actual conditions of each region. This results in some regions being overly smoothed, destroying details (such as local temperature gradient changes or spatial texture structures), while other regions are under-denoised, affecting reconstruction accuracy and robustness, and limiting practical application effectiveness. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a sea surface temperature completion method and system based on an asynchronous diffusion Schrödinger bridge.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: The sea surface temperature completion method based on the asynchronous diffusion Schrödinger bridge includes the following steps: Step S1, Preprocessing: Input data includes images missing from that day. Weekly mean image And a mask, using the weekly mean image. Fill in the missing images of the day The missing regions in the image are used to generate an initial completed image. Then, the initial completed image was calculated. Image of weekly average The normalized difference between pixels yields the anomaly weight, which reflects the degree of anomaly in each pixel. This provides guidance for the subsequent asynchronous diffusion process; Step S2, Asynchronous Diffusion: Based on the diffusion Schrödinger bridge theory, in the initial image completion... A bidirectional diffusion path is established between the image and the actual SST image of the day, comprising two dual processes: forward asynchronous diffusion sampling and backward asynchronous diffusion sampling; based on pixel-level anomaly weights. Generate diffusion time offset This generates pixel-level offset time steps. ,based on Perform forward asynchronous diffusion sampling or backward asynchronous diffusion sampling, dynamically adjust the diffusion coefficients for noise addition and denoising processes, and finally generate the current time step in the diffusion process. intermediate state ; Step S3, U-Net prediction score: Set the current time step intermediate state And weekly mean images that provide spatial and physical constraints. Input a U-Net network and extract using the U-Net network's encoder-decoder structure. and The spatial features are fused with temporal embedding to achieve region-adaptive denoising prediction, outputting a prediction score function `pred`. Based on this score function `pred`, the reconstructed SST image of the current prediction is calculated. Backward asynchronous diffusion sampling utilizes Update the intermediate state; During the training phase, The initial state is used to calculate the loss function to optimize the model parameters; during the inference phase, the initial state is progressively denoised and reconstructed by iteratively performing U-Net network score prediction and backward asynchronous diffusion sampling, and the prediction result of the last iteration is used. As the final reconstructed complete sea surface temperature image Output.

[0007] Furthermore, step S1 specifically includes: extracting the missing images from the current day. The missing regions were identified using the weekly mean image. Fill in the corresponding pixel values ​​to generate the initial completed image. The calculation formula is as follows: (1); in, for binary mask: (2); Subsequently, through comparison and The differences generate normalized anomaly weights. This is used to reflect the degree of abnormality of each pixel in the non-missing region relative to the weekly mean, and the calculation formula is as follows: (3); in, express operate, It is a scaling factor that defines the threshold for the significance of temperature differences.

[0008] Furthermore, in step S2, the abnormality degree weights are first determined. Calculate the diffusion time offset for each pixel Used to adjust the time step to generate pixel-level offset time steps. Then based on pixel-level offset time steps It extracts independent forward and backward diffusion coefficients for each pixel from a predefined noise schedule and performs a non-uniform asynchronous diffusion process to generate an intermediate state connecting the initial data and the target data. The entire asynchronous diffusion process achieves differentiated reconstruction of heterogeneous regions through pixel-level diffusion coefficients, where: In forward asynchronous diffusion sampling, intermediate states From initial data With target data The noise is obtained by linearly superimposing the diffusion coefficient, and the noise intensity is controlled by the pixel-level forward diffusion coefficient: low outlier regions have small offsets, are close to the target data, have high confidence during reconstruction, and the intermediate state after forward asynchronous diffusion sampling is closer to the target data. The high outlier regions have large offsets, closely resembling the initial data, and the intermediate state after forward asynchronous diffusion sampling is even closer to the initial data. To protect the original information; In backward asynchronous diffusion sampling, the U-Net network predicts the score function and calculates the target data prediction value, i.e., the currently predicted reconstructed SST image. Backward asynchronous diffusion sampling utilizes and initial data The intermediate state is updated step by step by denoising based on the pixel-level back diffusion coefficient. For regions with low outliers, the offset is small, the diffusion process is fast, and the denoising process relies more on the target data predicted by the neural network to achieve rapid convergence; for regions with high outliers, the offset is large, the diffusion process is slow, and the denoising process preserves the current intermediate state more. This information enables progressive detail repair.

[0009] Further, in step S2, the initially completed image is... Recorded as As initial data, the actual SST image of that day is recorded as... Using the initial data as the target data, the diffusion Schrödinger bridge theory is employed to achieve bidirectional optimization between the initial data and the target data. The specific steps are as follows: Step S21: Based on the anomaly degree weight Calculate the diffusion time offset for each pixel This is mapped to the effective range, thereby generating pixel-level offset time steps. The calculation formula is as follows: (4); in, and These are predefined time offset ranges, namely the minimum and maximum values; (5); in, The function is used to limit the input value to a specified range, ensuring Within the valid range of 0 to within, Represents the current time step. Represents the total number of steps; Step S22: Pixel-level offset time step The system calculates the corresponding independent diffusion coefficient for each pixel from a predefined noise schedule and performs a non-uniform asynchronous diffusion process to generate an intermediate state that connects the initial data and the target data. The formula for generating intermediate states through forward diffusion sampling is as follows: (6); in, For standard normal noise, The diffusion coefficient is the diffusion coefficient for all time steps of the forward diffusion sampling. Based on predefined noise scheduling calculate: (7); ; ; in, For time step The noise variance, For time step The noise variance, It is a time step Forward noise cumulative standard deviation It is a time step Backward noise cumulative standard deviation; Pre-calculate the diffusion coefficients for all time steps of forward diffusion sampling. And stored in three arrays respectively. , , The calculation formula is as follows: ; ; in, Store the corresponding target data diffusion coefficient , Store the corresponding initial data diffusion coefficient , Store corresponding noise diffusion coefficient , Represents the current time step ; based on Generate independent diffusion coefficients for each pixel from predefined noise scheduling and pre-computed diffusion coefficients. This enables forward asynchronous diffusion sampling, and the calculation formula is as follows: (12); (13); The formula for updating intermediate states via backdiffusion sampling is as follows: (14); in This is the currently predicted reconstructed SST image. Represents the current time step The intermediate state, The diffusion coefficient representing the previous state across all time steps of backward sampling. , , The calculation is as follows: (15); ; ; Backward diffusion sampling also uses pixel-level offset time steps. Generate an independent diffusion coefficient for each pixel , , This achieves backward asynchronous diffusion sampling, maintaining duality with forward asynchronous diffusion sampling, and realizes a region-adaptive diffusion process: due to the low outlier region Small, in backsampling Power is significant. Small weights enable fast convergence. Due to high outlier regions Large, backsampling Small weight, With significant weight, slow repair can be achieved. .

[0010] Furthermore, in step S3, firstly, the current time step... intermediate state and the weekly mean image as a physical constraint Channel dimensions are concatenated to form a two-channel tensor input; simultaneously, the time step representing the diffusion process is... The two-channel tensor input is converted into a high-dimensional temporal embedding vector through sine-cosine position encoding. Then, the two-channel tensor input and the temporal embedding vector are input into the encoder-decoder architecture of the U-Net network. Spatial features are extracted and temporal context information is fused through multi-level convolution operations. Finally, the predicted score function pred is output to represent the direction of the denoising gradient.

[0011] Furthermore, in step S3, the scoring function formula is defined as follows: ; in, Represents the current time step The intermediate state, Represents the actual SST image of that day. represent The corresponding pixel-level forward noise accumulation standard deviation; Predict the score function using the U-Net network. Its output is denoted as pred, and the predicted score function pred is used to replace the inference phase. Perform denoising operations to calculate the predicted value of the target data, i.e., the currently predicted reconstructed SST image. The calculation formula is as follows: ; in, It is the score function predicted by the U-Net network.

[0012] Furthermore, during the training phase, the intermediate states obtained through forward asynchronous diffusion sampling... The score function predicted by the U-Net network Calculate the target data prediction value, i.e., the currently predicted reconstructed SST image. This is used to calculate the loss function to optimize model parameters and achieve region-adaptive denoising learning; in the inference phase, the initial completed image is used. Using the initial data, U-Net network score prediction and backward asynchronous diffusion sampling are iteratively performed, gradually denoising and reconstructing the data, and the prediction result of the last sampling is used. As the final reconstructed complete sea surface temperature image .

[0013] Furthermore, the loss function is as follows: (20); It is divided into two parts: This represents the reconstruction loss between the original label and the actual label. yes The weight, This represents the currently predicted reconstructed SST image. Image of weekly average The loss between the difference and the true difference, yes The weights; Reconstruction losses Calculate the score function of the U-Net network prediction With real labels Mean square error between The loss function is as follows: ; Outlier constraint loss as follows: (twenty two); in, For the currently predicted reconstructed SST image, This is a real SST image from that day. Weekly mean image .

[0014] The present invention also provides a sea surface temperature completion system based on an asynchronous diffusion Schrödinger bridge, for implementing the sea surface temperature completion method based on an asynchronous diffusion Schrödinger bridge as described above. The system includes a preprocessing module, an asynchronous diffusion Schrödinger module, and a U-Net prediction score function module. The preprocessing module takes the missing images of the day as input. and weekly mean image The missing regions were represented by the weekly mean image. Initialization yields the initial completed image. Then utilize and weekly mean image The anomaly weights are obtained based on the normalization formula. This is used to guide asynchronous diffusion processes; The asynchronous diffusion Schrödinger bridge module, through input... Actual SST image from that day and abnormality weight Forward asynchronous diffusion sampling and backward asynchronous diffusion sampling are performed; during training, the asynchronous diffusion Schrödinger module is constructed through forward asynchronous diffusion sampling. and The joint distribution path between them outputs intermediate states. During the inference process, utilize The scores calculated by the U-Net prediction score function module The intermediate state is updated iteratively through backward asynchronous diffusion sampling. ; The U-Net prediction scoring function module takes a time step as input. At the current time step intermediate state and the weekly mean image as a physical constraint The prediction score function is used to calculate the currently predicted reconstructed SST image. During training, intermediate states generated by forward diffusion sampling The U-Net network is used to predict the score function and calculate the target data for the current prediction, i.e., the reconstructed SST image for the current prediction. During the inference process, the initial completed image is input. The initial data was used to obtain the final reconstructed complete sea surface temperature image through iterative network score prediction and backward asynchronous diffusion sampling. .

[0015] Compared with the prior art, the advantages of this invention are: (1) Significantly improves training efficiency and stability. Existing traditional denoising diffusion probability models rely on a large number of sampling steps (usually hundreds to thousands of steps) for implicit fitting, which is complex to train and prone to instability due to parameter fluctuations. This invention achieves symmetric bidirectional diffusion optimization through the Schrödinger bridge framework, explicitly models the joint probability distribution from missing data to target data, generates intermediate states through forward sampling, and uses U-Net to predict target data through backward sampling, achieving high-quality completion with fewer steps (20 iterations in this method), significantly reducing computational overhead. In addition, the loss function uses dynamic weights to optimize the denoising direction in the early stage and stabilize training in the later stage. Combined with exponential moving average (EMA), it further enhances parameter consistency, thereby improving training efficiency and stability.

[0016] (2) Ensuring sufficient local details to improve the accuracy of image completion. Existing methods use uniform denoising intensity, ignoring the heterogeneity of sea surface temperature data regions, thus limiting the accuracy of image completion. This method introduces an asynchronous diffusion strategy, dynamically adjusting the denoising intensity through pixel-level time-step offsets. Specifically, low outlier regions use diffusion parameters corresponding to small time-step offsets for rapid convergence to preserve details and provide contextual constraints; high outlier regions use diffusion parameters corresponding to large time-step offsets for gradual repair to improve accuracy. Simultaneously, the model utilizes conditional images (weekly averages)... It provides spatial and physical constraints, enhances the spatial correlation of U-Net predictions, ensures the preservation of details of complex ocean features, and effectively solves the problem of detail loss or over-smoothing caused by synchronous denoising. Attached Figure Description

[0017] 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.

[0018] Figure 1 This is a schematic diagram of the system structure of the present invention; Figure 2 The visualization results of the present invention and existing methods at a missing rate of 68% are compared, wherein (a) is a damaged SST image; (b) is a real SST image; (c) is the AIN result; (d) is the DINEOF result; (e) is the Phy_INN result; (f) is the I2SB result; (g) is the DINFNN result; (h) is the SVIFNN result; and (i) is the result of the method of the present invention. Detailed Implementation

[0019] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0020] Example 1 This embodiment designs a sea surface temperature completion method based on an asynchronous diffusion Schrödinger bridge, including the following steps: Step S1, Preprocessing: Input data includes images missing from that day. Weekly mean image And a mask, using the weekly mean image. Fill in the missing images of the day The missing regions in the image are used to generate an initial completed image. Then, the initial completed image was calculated. Image of weekly average The normalized difference between pixels yields the anomaly weight, which reflects the degree of anomaly in each pixel. This provides guidance for the subsequent asynchronous diffusion process.

[0021] Step S1 specifically includes: extracting the missing images from the current day. The missing regions were identified using the weekly mean image. Fill in the corresponding pixel values ​​to generate the initial completed image. The calculation formula is as follows: (1); in, for binary mask: (2); Subsequently, through comparison and The differences generate normalized anomaly weights. This is used to reflect the degree of abnormality of each pixel in the non-missing region relative to the weekly mean, and the calculation formula is as follows: (3); in, express operate, It is a scaling factor that defines the threshold for the significance of temperature differences.

[0022] Step S2, Asynchronous Diffusion: Based on the diffusion Schrödinger bridge theory, in the initial image completion... A bidirectional diffusion path is established between the image and the actual SST image of the day, comprising two dual processes: forward asynchronous diffusion sampling and backward asynchronous diffusion sampling; based on pixel-level anomaly weights. Generate diffusion time offset This generates pixel-level offset time steps. ,based on Perform forward asynchronous diffusion sampling or backward asynchronous diffusion sampling, dynamically adjust the diffusion coefficients for noise addition and denoising processes, and finally generate the current time step in the diffusion process. intermediate state .

[0023] In step S2, firstly, based on the anomaly degree weight... Calculate the diffusion time offset for each pixel Used to adjust the time step to generate pixel-level offset time steps. Then based on pixel-level offset time steps It extracts independent forward and backward diffusion coefficients for each pixel from a predefined noise schedule and performs a non-uniform asynchronous diffusion process to generate an intermediate state connecting the initial data and the target data. The entire asynchronous diffusion process achieves differentiated reconstruction of heterogeneous regions through pixel-level diffusion coefficients, where: In forward asynchronous diffusion sampling, intermediate states From initial data With target data The noise is obtained by linearly superimposing the diffusion coefficient, and the noise intensity is controlled by the pixel-level forward diffusion coefficient: low outlier regions have small offsets, are close to the target data, have high confidence during reconstruction, and the intermediate state after forward asynchronous diffusion sampling is closer to the target data. The high outlier regions have large offsets, closely resembling the initial data, and the intermediate state after forward asynchronous diffusion sampling is even closer to the initial data. To protect the original information; In backward asynchronous diffusion sampling, the U-Net network predicts the score function and calculates the target data prediction value, i.e., the currently predicted reconstructed SST image. Backward asynchronous diffusion sampling utilizes and initial data The intermediate state is updated step by step by denoising based on the pixel-level back diffusion coefficient. For regions with low outliers, the offset is small, the diffusion process is fast, and the denoising process relies more on the target data predicted by the neural network to achieve rapid convergence; for regions with high outliers, the offset is large, the diffusion process is slow, and the denoising process preserves the current intermediate state more. This information enables progressive detail repair.

[0024] In a preferred embodiment, step S2 involves initially completing the image. Recorded as As initial data, the actual SST image of that day is recorded as... Using the initial data as the target data, the diffusion Schrödinger bridge theory is employed to achieve bidirectional optimization between the initial data and the target data. The specific steps are as follows: Step S21: Based on the anomaly degree weight Calculate the diffusion time offset for each pixel This is mapped to the effective range, thereby generating pixel-level offset time steps. The calculation formula is as follows: (4); in, and These are predefined time offset ranges, namely the minimum and maximum values; (5); in, The function is used to limit the input value to a specified range, ensuring Within the valid range of 0 to within, Represents the current time step. Represents the total number of steps; Step S22: Pixel-level offset time step The system calculates the corresponding independent diffusion coefficient for each pixel from a predefined noise schedule and performs a non-uniform asynchronous diffusion process to generate an intermediate state that connects the initial data and the target data. The formula for generating intermediate states through forward diffusion sampling is as follows: (6); in, For standard normal noise, The diffusion coefficient is the diffusion coefficient for all time steps of the forward diffusion sampling. Based on predefined noise scheduling calculate: (7); ; ; in, For time step The noise variance, For time step The noise variance, It is a time step Forward noise cumulative standard deviation It is a time step Backward noise cumulative standard deviation; Pre-calculate the diffusion coefficients for all time steps of forward diffusion sampling. And stored in three arrays respectively. , , The calculation formula is as follows: ; ; in, Store the corresponding target data diffusion coefficient , Store the corresponding initial data diffusion coefficient , Store corresponding noise diffusion coefficient , Represents the current time step ; based on Generate independent diffusion coefficients for each pixel from predefined noise scheduling and pre-computed diffusion coefficients. This enables forward asynchronous diffusion sampling, and the calculation formula is as follows: (12); (13); The formula for updating intermediate states via backdiffusion sampling is as follows: (14); in This is the currently predicted reconstructed SST image. Represents the current time step The intermediate state, The diffusion coefficient representing the previous state across all time steps of backward sampling. , , The calculation is as follows: (15); ; ; Backward diffusion sampling also uses pixel-level offset time steps. Generate an independent diffusion coefficient for each pixel , , This achieves backward asynchronous diffusion sampling, maintaining duality with forward asynchronous diffusion sampling, and realizes a region-adaptive diffusion process: due to the low outlier region Small, in backsampling Power is significant. Small weights enable fast convergence. Due to high outlier regions Large, backsampling Small weight, With significant weight, slow repair can be achieved. .

[0025] Step S3, U-Net prediction score: Set the current time step intermediate state And weekly mean images that provide spatial and physical constraints. Input a U-Net network and extract using the U-Net network's encoder-decoder structure. and The spatial features are fused with temporal embedding to achieve region-adaptive denoising prediction, outputting a prediction score function `pred`. Based on this score function `pred`, the reconstructed SST image of the current prediction is calculated. Backward asynchronous diffusion sampling utilizes Update the intermediate state.

[0026] During the training phase, The initial state is used to calculate the loss function to optimize the model parameters; during the inference phase, the initial state is progressively denoised and reconstructed by iteratively performing U-Net network score prediction and backward asynchronous diffusion sampling, and the prediction result of the last iteration is used. As the final reconstructed complete sea surface temperature image Output.

[0027] In a preferred implementation, in step S3, firstly, the current time step... intermediate state and the weekly mean image as a physical constraint Channel dimensions are concatenated to form a two-channel tensor input; simultaneously, the time step representing the diffusion process is... The two-channel tensor input is converted into a high-dimensional temporal embedding vector through sine-cosine position encoding. Then, the two-channel tensor input and the temporal embedding vector are input into the encoder-decoder architecture of the U-Net network. Spatial features are extracted and temporal context information is fused through multi-level convolution operations. Finally, the predicted score function pred is output to represent the direction of the denoising gradient.

[0028] In step S3, the scoring function formula is defined as follows: ; in, Represents the current time step The intermediate state, Represents the actual SST image of that day. represent The corresponding pixel-level forward noise accumulation standard deviation; Predict the score function using the U-Net network. Its output is denoted as pred, and the predicted score function pred is used to replace the inference phase. Perform denoising operations to calculate the predicted value of the target data, i.e., the currently predicted reconstructed SST image. The calculation formula is as follows: ; in, It is the score function predicted by the U-Net network.

[0029] During the training phase, intermediate states are obtained through forward asynchronous diffusion sampling. The score function predicted by the U-Net network Calculate the target data prediction value, i.e., the currently predicted reconstructed SST image. This is used to calculate the loss function to optimize model parameters and achieve region-adaptive denoising learning; in the inference phase, the initial completed image is used. Using the initial data, U-Net network score prediction and backward asynchronous diffusion sampling are iteratively performed, gradually denoising and reconstructing the data, and the prediction result of the last sampling is used. As the final reconstructed complete sea surface temperature image .

[0030] The loss function of this invention is as follows: (20); It is divided into two parts: This represents the reconstruction loss between the original label and the actual label. yes The weight, This represents the currently predicted reconstructed SST image. Image of weekly average The loss between the difference and the true difference, yes The weights; Reconstruction losses Calculate the score function of the U-Net network prediction With real labels Mean square error between The loss function is as follows: ; Outlier constraint loss as follows: (twenty two); in, For the currently predicted reconstructed SST image, This is a real SST image from that day. Weekly mean image .

[0031] This invention introduces the Schrödinger bridge theoretical framework into the sea surface temperature image completion task, realizing bidirectional diffusion for sea surface temperature image completion. The Schrödinger bridge module is designed with symmetrical forward and backward diffusion processes, explicitly modeling the joint probability distribution. Forward sampling uses initial data and conditional images (weekly averages) Intermediate states are generated, backsampling is performed using the U-Net prediction score function, and then the predicted target data is generated. and iteratively update the state. Two-way diffusion can make full use of initial data information, combined with... Enhancing spatial correlation ensures the preservation of details and physical consistency of complex ocean features. This solves the problem that the original method, which reconstructs data through implicit fitting, struggles to explicitly model the joint probability distribution from missing data to target data, resulting in insufficient utilization of initial data information and weak spatial correlation.

[0032] In the diffusion model, an asynchronous diffusion strategy is proposed, controlling the denoising intensity through pixel-level offset time steps. This method utilizes outlier weights to calculate pixel-level offset time steps. For low outlier regions, the offset time steps are smaller, and the diffusion parameters used are those corresponding to earlier time steps, resulting in rapid convergence and providing spatial context constraints. For high outlier regions, the offset time steps are larger, and the diffusion parameters used are those corresponding to mid-to-late time steps, providing gradual repair to improve accuracy. This addresses the problem of the original method applying a uniform denoising intensity to all pixels, which may lead to over-smoothing in some areas, destroying detailed features (such as local temperature gradients), or insufficient repair in some areas, affecting the image completion effect.

[0033] Example 2 like Figure 1 As shown, this embodiment designs a sea surface temperature (SST) completion system based on an asynchronous diffusion Schrödinger bridge to implement the SST completion method based on an asynchronous diffusion Schrödinger bridge as described in Embodiment 1.

[0034] The system includes a preprocessing module, an asynchronous diffusion Schrödinger module, and a U-Net prediction score function module; The preprocessing module takes the missing images of the day as input. and weekly mean image The missing regions were represented by the weekly mean image. Initialization yields the initial completed image. Then utilize and weekly mean image The anomaly weights are obtained based on the normalization formula. It is used to guide asynchronous diffusion processes.

[0035] The asynchronous diffusion Schrödinger bridge module, through input... Actual SST image from that day and abnormality weight Forward asynchronous diffusion sampling and backward asynchronous diffusion sampling are performed; during training, the asynchronous diffusion Schrödinger module is constructed through forward asynchronous diffusion sampling. and The joint distribution path between them outputs intermediate states. During the inference process, utilize The scores calculated by the U-Net prediction score function module The intermediate state is updated iteratively through backward asynchronous diffusion sampling. .

[0036] The U-Net prediction scoring function module takes a time step as input. At the current time step intermediate state and the weekly mean image as a physical constraint The prediction score function is used to calculate the currently predicted reconstructed SST image. During training, intermediate states generated by forward diffusion sampling The U-Net network is used to predict the score function and calculate the target data for the current prediction, i.e., the reconstructed SST image for the current prediction. During the inference process, the initial completed image is input. The initial data was used to obtain the final reconstructed complete sea surface temperature image through iterative network score prediction and backward asynchronous diffusion sampling. .

[0037] Example 3 As another embodiment of the present invention, a computer-readable storage medium is also provided, storing a computer program, which, when executed by a processor, is used to implement the sea surface temperature completion method based on the asynchronous diffusion Schrödinger bridge as described in Embodiment 1 above.

[0038] Computer-readable storage media can be non-volatile computer-readable storage media. Examples include, but are not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0039] Experimental results: Dataset and Preprocessing: To verify the technical effectiveness, this embodiment selected Level 4 SST products from the National Satellite Ocean Application Service from January 2022 to April 2023. Subsequently, to simulate realistic cloud coverage, a real cloud mask was selected from WHU cloud data for data preprocessing, with cloud coverage rates set to 8%, 25%, 46%, and 68%, respectively. Furthermore, a signal-to-noise ratio (SNR) of 0.1 was added to simulate information loss during data acquisition. Finally, the image size was cropped to 64×64, and the data range was normalized to the (-1, 1) interval for experimental testing.

[0040] Evaluation index: Root mean square error (RMSE) was used. ), coefficient of determination ( () is used as an evaluation indicator to assess the reconstruction results.

[0041] Baseline Selection: To demonstrate the effectiveness and advancement of the proposed solution, classic and cutting-edge methods in the field were selected for comparative experiments: AIN, DINEOF, Phy_INN, I2SB, DINFNN, and SVIFNN. DINEOF is a classic method in this field, using statistical interpolation to complete missing data in a spatiotemporal manner. AIN, Phy_INN, DINFNN, and SVIFNN are all cutting-edge methods based on deep neural networks in this field, while I²SB is a cutting-edge deep learning method for common image restoration tasks, also applying the Schrödinger bridge theory framework. Details are as follows: AIN: A GAN-based SST completion method that employs a "coarse-to-fine" strategy in the image domain. First, it predicts the weekly average using the monthly average, then predicts daily outliers based on the predicted weekly average. Finally, the reconstructed SST image is obtained by directly adding the weekly average and the daily outliers.

[0042] DINEOF: A classic missing data completion method based on empirical orthogonal functions (EOF), widely used in geophysics. It combines EOF analysis with spatial interpolation, using the identification of spatial patterns that best represent the main changes or structures in the dataset to aid in interpolation and fill in missing data.

[0043] Phy_INN: A cutting-edge SST inpainting method based on GAN. This method uses the ASPP (Spatial Pyramid Pooling with Hollows) module to learn information at different scales of weekly mean and daily anomalies in the image domain, and then performs deep fusion of feature embeddings at different scales to achieve the inpainting task of SST images.

[0044] I²SB: This method is a cutting-edge image inpainting approach based on a nonlinear diffusion model. Its core idea is to directly learn the mapping relationship between clean and degraded image distributions by constructing a nonlinear diffusion Schrödinger bridge between them. Unlike traditional diffusion models that start with random noise, I²SB uses the degraded image as the initial condition and gradually recovers a high-quality image through a more efficient diffusion path.

[0045] DINFNN: A cutting-edge SST completion method based on GAN. It employs a three-stream architecture, simultaneously inputting weekly averages, historical data, and current day's damaged data, and learns periodic stability information, temporal historical information, and contextual information of the current day's completed image, respectively. The three are then fused to complete the completion.

[0046] SVIFNN: A cutting-edge SST completion method based on GAN. It adopts a two-stream structure and uses a designed anomaly attention mechanism to fully preserve the anomalous patterns of negative correlation between the daily SST data and the weekly mean, while stabilizing attention focuses on the stable patterns of positive correlation between the daily SST data and the weekly mean.

[0047] The results are shown in Tables 1 and 2 below: Table 1. Comparison of RMSE indicators between the present invention and existing methods Cover Ratio AIN DINEOF Phy_INN <![CDATA[I 2 SB]]> DINFNN SVIFNN Ours 8% 0.1005 0.1287 0.0802 0.0660 0.0678 0.0625 0.0393 25% 0.1161 0.1427 0.1015 0.0747 0.0616 0.0697 0.0453 46% 0.1220 0.1513 0.1030 0.1160 0.0987 0.1045 0.0539 68% 0.1292 0.1911 0.1223 0.1324 0.0951 0.1299 0.0573 Table 2. Comparison of R² index between the present invention and existing methods Cover Ratio AIN DINEOF Phy_INN <![CDATA[I 2 SB]]> DINFNN SVIFNN Ours 8% 0.7759 0.9441 0.9901 0.9931 0.9936 0.9949 0.9977 25% 0.7498 0.8570 0.9227 0.9690 0.9825 0.9801 0.9905 46% 0.7341 0.7834 0.8620 0.8678 0.9254 0.9038 0.9751 68% 0.6455 0.2241 0.7598 0.5687 0.8896 0.7761 0.9496 Secondly, some experimental results at a 68% missing rate were selected and visualized, as shown below. Figure 2 As shown, Figure 2 For the visualization comparison of the present invention and existing methods at a 68% missing rate, (a) the damaged SST image; (b) the real SST image; (c) the AIN result; (d) the DINEOF result; (e) the Phy_INN result; (f) the I 2 SB results; (g) DINFNN results; (h) SVIFNN results; (i) Results of the method of the present invention.

[0048] The results, as shown in Tables 1-2, demonstrate that the method of this invention consistently exhibits superior results in sea surface temperature image completion tasks under four different missing rates. This proves the effectiveness of this invention in improving completion performance. Furthermore, in cases of large-area missing data (46% and 68% missing rates, especially 68% missing rate), the completion results significantly outperform other methods. In addition, the visualization results (such as...) Figure 2The comparison further demonstrates the robustness of the completion effect of this invention under large-area missing data. In summary, the experimental results prove the superiority of this method compared with other cutting-edge methods, as well as the robustness of the model under large-area missing data.

[0049] In summary, the innovations of this invention are: 1) The U-Net prediction module combines bidirectional sampling to explicitly model the joint probability distribution from missing data to target data, solving the shortcomings of insufficient utilization of initial data information and weak spatial correlation caused by the implicit fitting of the original method, and avoiding loss of details or over-smoothing. 2) A pixel-level offset time step is introduced into the asynchronous diffusion Schrödinger bridge module, and the denoising intensity is dynamically adjusted according to the outlier weights, solving the shortcomings of the synchronous denoising strategy of the original method that ignores the heterogeneity of the sea surface temperature region. Low outlier regions converge quickly to provide spatial context constraints, and high outlier regions are progressively repaired to ensure integrity and avoid over-smoothing.

[0050] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should be protected by the present invention.

Claims

1. A sea surface temperature completion method based on an asynchronous diffusion Schrödinger bridge, characterized in that, Includes the following steps: Step S1, Preprocessing: Input data includes images missing from that day. Weekly mean image And a mask, using the weekly mean image. Fill in the missing images of the day The missing regions in the image are used to generate an initial completed image. Then, the initial completed image was calculated. Image of weekly mean The normalized difference between pixels yields the anomaly weight, which reflects the degree of anomaly in each pixel. This provides guidance for the subsequent asynchronous diffusion process; Step S2, Asynchronous Diffusion: Based on the diffusion Schrödinger bridge theory, in the initial image completion... A bidirectional diffusion path is established between the image and the actual SST image of the day, comprising two dual processes: forward asynchronous diffusion sampling and backward asynchronous diffusion sampling; based on pixel-level anomaly weights. Generate diffusion time offset This generates pixel-level offset time steps. ,based on Perform forward asynchronous diffusion sampling or backward asynchronous diffusion sampling, dynamically adjust the diffusion coefficients for noise addition and denoising processes, and finally generate the current time step in the diffusion process. intermediate state ; Step S3, U-Net prediction score: Set the current time step intermediate state And weekly mean images that provide spatial and physical constraints. Input a U-Net network and extract using the U-Net network's encoder-decoder structure. and The spatial features are fused with temporal embedding to achieve region-adaptive denoising prediction, outputting a prediction score function `pred`. Based on this score function `pred`, the reconstructed SST image of the current prediction is calculated. Backward asynchronous diffusion sampling utilizes Update the intermediate state; During the training phase, The initial state is used to calculate the loss function to optimize the model parameters; during the inference phase, the initial state is progressively denoised and reconstructed by iteratively performing U-Net network score prediction and backward asynchronous diffusion sampling, and the prediction result of the last iteration is used. As the final reconstructed complete sea surface temperature image Output.

2. The sea surface temperature completion method based on an asynchronous diffusion Schrödinger bridge according to claim 1, characterized in that, Step S1 specifically includes: extracting the missing images from the current day. The missing regions were identified using the weekly mean image. Fill in the corresponding pixel values ​​to generate the initial completed image. The calculation formula is as follows: （1）； in, for binary mask: （2）； Subsequently, through comparison and The differences generate normalized anomaly weights. This is used to reflect the degree of abnormality of each pixel in the non-missing region relative to the weekly mean, and the calculation formula is as follows: （3）； in, express operate, It is a scaling factor that defines the threshold for the significance of temperature differences.

3. The sea surface temperature completion method based on an asynchronous diffusion Schrödinger bridge according to claim 1, characterized in that, In step S2, firstly, based on the anomaly degree weight... Calculate the diffusion time offset for each pixel Used to adjust the time step to generate pixel-level offset time steps. Then based on pixel-level offset time steps It extracts independent forward and backward diffusion coefficients for each pixel from a predefined noise schedule and performs a non-uniform asynchronous diffusion process to generate an intermediate state connecting the initial data and the target data. The entire asynchronous diffusion process achieves differentiated reconstruction of heterogeneous regions through pixel-level diffusion coefficients, where: In forward asynchronous diffusion sampling, intermediate states From initial data With target data The noise is obtained by linearly superimposing the diffusion coefficient, and the noise intensity is controlled by the pixel-level forward diffusion coefficient: low outlier regions have small offsets, are close to the target data, have high confidence during reconstruction, and the intermediate state after forward asynchronous diffusion sampling is closer to the target data. The high outlier regions have large offsets, closely resembling the initial data, and the intermediate state after forward asynchronous diffusion sampling is even closer to the initial data. To protect the original information; In backward asynchronous diffusion sampling, the U-Net network predicts the score function and calculates the target data prediction value, i.e., the currently predicted reconstructed SST image. Backward asynchronous diffusion sampling utilizes and initial data The intermediate state is updated step by step by denoising based on the pixel-level back diffusion coefficient. For regions with low outliers, the offset is small, the diffusion process is fast, and the denoising process relies more on the target data predicted by the neural network to achieve rapid convergence; for regions with high outliers, the offset is large, the diffusion process is slow, and the denoising process preserves the current intermediate state more. This information enables progressive detail repair.

4. The sea surface temperature completion method based on an asynchronous diffusion Schrödinger bridge according to claim 1, characterized in that, Step S2, the initial completed image Recorded as As initial data, the actual SST image of that day is recorded as... Using the initial data as the target data, the diffusion Schrödinger bridge theory is employed to achieve bidirectional optimization between the initial data and the target data. The specific steps are as follows: Step S21: Based on the anomaly degree weight Calculate the diffusion time offset for each pixel This is mapped to the effective range, thereby generating pixel-level offset time steps. The calculation formula is as follows: （4）； in, and These are predefined time offset ranges, namely the minimum and maximum values; （5）； in, The function is used to limit the input value to a specified range, ensuring Within the valid range of 0 to within, Represents the current time step. Represents the total number of steps; Step S22: Pixel-level offset time step The system calculates the corresponding independent diffusion coefficient for each pixel from a predefined noise schedule and performs a non-uniform asynchronous diffusion process to generate an intermediate state that connects the initial data and the target data. The formula for generating intermediate states through forward diffusion sampling is as follows: （6）； in, For standard normal noise, The diffusion coefficient is the diffusion coefficient for all time steps of the forward diffusion sampling. Based on predefined noise scheduling calculate: （7）； ； ； in, For time steps The noise variance, For time steps The noise variance, It is a time step Forward noise cumulative standard deviation It is a time step Backward noise cumulative standard deviation; Pre-calculate the diffusion coefficients for all time steps of forward diffusion sampling. And stored in three arrays respectively. , , The calculation formula is as follows: ； ； in, Store the corresponding target data diffusion coefficient , Store the corresponding initial data diffusion coefficient , Store corresponding noise diffusion coefficient , Represents the current time step ; based on Generate independent diffusion coefficients for each pixel from predefined noise scheduling and pre-computed diffusion coefficients. This enables forward asynchronous diffusion sampling, and the calculation formula is as follows: （12）； （13）； The formula for updating intermediate states via backdiffusion sampling is as follows: （14）； in This is the currently predicted reconstructed SST image. Represents the current time step The intermediate state, The diffusion coefficient representing the previous state across all time steps of backward sampling. , , The calculation is as follows: （15）； ； ； Backward diffusion sampling also uses pixel-level offset time steps. Generate an independent diffusion coefficient for each pixel , , This achieves backward asynchronous diffusion sampling, maintaining duality with forward asynchronous diffusion sampling, and realizes a region-adaptive diffusion process: due to the low outlier region Small, in backsampling Power is significant. Small weights enable fast convergence. Due to high outlier regions Large, backsampling Small weight, With significant weight, slow repair can be achieved. .

5. The sea surface temperature completion method based on an asynchronous diffusion Schrödinger bridge according to claim 1, characterized in that, In step S3, firstly, the current time step... intermediate state and the weekly mean image as a physical constraint Channel dimensions are concatenated to form a two-channel tensor input; simultaneously, the time step representing the diffusion process is... The two-channel tensor input is converted into a high-dimensional temporal embedding vector through sine-cosine position encoding. Then, the two-channel tensor input and the temporal embedding vector are input into the encoder-decoder architecture of the U-Net network. Spatial features are extracted and temporal context information is fused through multi-level convolution operations. Finally, the predicted score function pred is output to represent the direction of the denoising gradient.

6. The sea surface temperature completion method based on an asynchronous diffusion Schrödinger bridge according to claim 5, characterized in that, In step S3, the scoring function formula is defined as follows: ； in, Represents the current time step The intermediate state, Represents the actual SST image of that day. represent The corresponding pixel-level forward noise accumulation standard deviation; Predict the score function using the U-Net network. Its output is denoted as pred, and the predicted score function pred is used to replace the inference phase. Perform denoising operations to calculate the predicted value of the target data, i.e., the currently predicted reconstructed SST image. The calculation formula is as follows: ； in, It is the score function predicted by the U-Net network.

7. The sea surface temperature completion method based on an asynchronous diffusion Schrödinger bridge according to claim 1, characterized in that, During the training phase, intermediate states are obtained through forward asynchronous diffusion sampling. The score function predicted by the U-Net network Calculate the target data prediction value, i.e., the currently predicted reconstructed SST image. It is used to calculate the loss function to optimize the model parameters and achieve region-adaptive denoising learning; During the inference phase, the initial completed image is... Using the initial data, U-Net network score prediction and backward asynchronous diffusion sampling are iteratively performed, gradually denoising and reconstructing the data, and the prediction result of the last sampling is used. As the final reconstructed complete sea surface temperature image .

8. The sea surface temperature completion method based on an asynchronous diffusion Schrödinger bridge according to claim 1, characterized in that, The loss function is as follows: （20）； It is divided into two parts: This represents the reconstruction loss between the original label and the actual label. yes The weight, This represents the currently predicted reconstructed SST image. Image of weekly mean The loss between the difference and the true difference, yes The weights; Reconstruction losses Calculate the score function of the U-Net network prediction With real labels Mean square error between The loss function is as follows: ； Outlier constraint loss as follows: （22）； in, For the currently predicted reconstructed SST image, This is a real SST image from that day. Weekly mean image .

9. A sea surface temperature completion system based on an asynchronous diffusion Schrödinger bridge, characterized in that, To implement the sea surface temperature completion method based on the asynchronous diffusion Schrödinger bridge as described in any one of claims 1-7, the system includes a preprocessing module, an asynchronous diffusion Schrödinger module, and a U-Net prediction score function module; The preprocessing module takes the missing images of the day as input. and weekly mean image The missing regions were represented by the weekly mean image. Initialization yields the initial completed image. Then utilize and weekly mean image The anomaly weights are obtained based on the normalization formula. This is used to guide asynchronous diffusion processes; The asynchronous diffusion Schrödinger bridge module, through input... Actual SST image from that day and abnormality weight Forward asynchronous diffusion sampling and backward asynchronous diffusion sampling are performed; during training, the asynchronous diffusion Schrödinger module is constructed through forward asynchronous diffusion sampling. and The joint distribution path between them outputs intermediate states. ; In the inference process, using The scores calculated by the U-Net prediction score function module The intermediate state is updated iteratively through backward asynchronous diffusion sampling. ; The U-Net prediction scoring function module takes a time step as input. At the current time step intermediate state and the weekly mean image as a physical constraint The prediction score function is used to calculate the currently predicted reconstructed SST image. During training, intermediate states generated by forward diffusion sampling The U-Net network is used to predict the score function and calculate the target data for the current prediction, i.e., the reconstructed SST image for the current prediction. ; During the inference process, the initial completed image is input. The initial data was used to obtain the final reconstructed complete sea surface temperature image through iterative network score prediction and backward asynchronous diffusion sampling. .

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