Sea surface temperature completion method and system based on asynchronous diffusion schrodinger bridge

Abstract

The application belongs to the technical field of sea surface temperature completion, and discloses a sea surface temperature completion method and system based on an asynchronous diffusion Schrodinger bridge. First, a weight anomaly reflecting the abnormal degree of pixels is generated through a preprocessing step S1 to guide the subsequent diffusion process. Then, an asynchronous diffusion S2 is performed. Based on the diffusion Schrodinger bridge theory, a bidirectional diffusion path is established between the initial completion image and the real image, and the diffusion coefficient is dynamically adjusted according to the anomaly to generate an intermediate state xt. Next, a U-Net network S3 is used to predict a score function pred, and the current image x0 is reconstructed to update the state or calculate the loss. During training, the model parameters are iteratively optimized, and during inference, multiple rounds of denoising reconstruction are performed to finally output a complete high-quality sea surface temperature image SSTrecon. The application fully retains local details and improves the accuracy of image completion.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of sea surface temperature completion, and particularly relates to a sea surface temperature completion method and system based on an asynchronous diffusion Schrodinger bridge. BACKGROUND

[0002] At present, the frontier method in the field of sea surface temperature completion based on deep learning adopts an image completion mechanism of a diffusion model based on multi-scale physical constraints. A weekly mean value of sea surface temperature reconstructed through a diffusion denoising model is used as a rough prediction of a missing daily sea surface temperature field in the first stage, to provide global physical constraints. A difference relationship between the weekly mean value and the daily sea surface temperature field is learned in the second stage, to repair a daily scale abnormal deviation by using another diffusion denoising model, to provide local physical constraints. A multi-scale decoupling strategy is adopted in the third stage to fuse the global and local constraints to complete the completion. The method has the advantages of combining the physical constraints of the weekly mean value and the daily mean value deviation, the stable generation capability of the DDPM, and the multi-scale feature fusion, to realize high-precision, physically consistent sea surface temperature data completion.

[0003] However, the method has the following problems:

[0004] Firstly, only one-way reverse denoising is relied on, and forward diffusion modeling is ignored, so that the data distribution cannot be explicitly learned, the original information and spatial correlation cannot be fully utilized, details are lost or excessively smoothed, and especially when complex ocean phenomena (such as mesoscale eddies, frontal mutations, etc.) are processed, the physical consistency decreases; meanwhile, the noise and signal balance cannot be effectively controlled, and information loss is prone to occur.

[0005] Secondly, a unified denoising intensity strategy is adopted, and the regional heterogeneity of sea surface temperature data is not considered. The same denoising intensity is applied to all pixel points in the image by the model. This method fails to fully consider the unique characteristics of different regions in the sea surface temperature data, and cannot dynamically adjust the denoising process according to the actual situation of each region, resulting in excessive smoothing and damage to details (such as local temperature gradient changes or spatial texture structures) in some regions, and insufficient denoising in other regions, which affects the reconstruction accuracy and robustness and limits the actual application effect. SUMMARY

[0006] In view of the deficiencies in the prior art, the application provides a sea surface temperature completion method and system based on an asynchronous diffusion Schrodinger bridge.

[0007] To solve the above technical problems, the technical scheme adopted by the application is as follows:

[0008] The sea surface temperature completion method based on the asynchronous diffusion Schrodinger bridge comprises the following steps:

[0009] Step S1, preprocessing:

[0010] The input data includes a missing image of the day , the weekly mean image and the mask, the weekly mean image is used to fill in the missing regions in the daily missing image to generate an initial completed image , and then by calculating the normalized difference between the initial completed image and the weekly mean image , the abnormality weight reflecting the abnormality degree of each pixel is obtained , which provides guidance for the subsequent asynchronous diffusion process;

[0011] Step S2, asynchronous diffusion:

[0012] Based on the diffusion Schrödinger bridge theory, a bidirectional diffusion path is established between the initial completed image and the real daily SST image, including two dual processes of forward asynchronous diffusion sampling and backward asynchronous diffusion sampling; according to the abnormality weight at the pixel level , the diffusion time offset is generated , and then the pixel-level offset time step is generated, based on , the forward asynchronous diffusion sampling or the backward asynchronous diffusion sampling is executed, the diffusion coefficient of the noise adding and the noise removing process is dynamically adjusted, and finally the intermediate state of the current time step in the diffusion process is generated;

[0013] Step S3, U-Net prediction score:

[0014] The current time step , the intermediate state and the weekly mean image providing spatial and physical constraints are input into the U-Net network, the spatial features of and are extracted using the encoder-decoder structure of the U-Net network, and the time embedding is fused, the region-adaptive denoising prediction is realized, and the predicted score function pred is output; based on the score function pred, the current predicted reconstructed SST image is calculated, and the backward asynchronous diffusion sampling updates the intermediate state ;

[0015] In the training stage, the loss function is calculated to optimize the model parameters; in the inference stage, the initial state is iteratively executed by the U-Net network score prediction and the backward asynchronous diffusion sampling, the denoising reconstruction is gradually performed, and the prediction result of the last iteration is taken as the final reconstructed complete sea surface temperature image output.

[0016] Further, step S1 specifically comprises: filling the missing area of the missing image of the day with the corresponding pixel value of the weekly mean image to generate an initial completion image , the calculation formula is as follows:

[0017] (1);

[0018] wherein, is a binary mask of

[0019] (2);

[0020] Subsequently, by comparing the difference between and , a normalized abnormality weight is generated, which is used to reflect the abnormality degree of each pixel in the non-missing area relative to the weekly mean value, and the calculation formula is as follows:

[0021] (3);

[0022] wherein, represents operation, is a scaling factor, which defines the significance threshold of temperature difference.

[0023] Further, in step S2, first, the diffusion time offset is calculated for each pixel according to the abnormality weight , which is used to adjust the time step to generate a pixel-level offset time step ; then based on the pixel-level offset time step , the corresponding independent forward and backward diffusion coefficients are extracted for each pixel from the predefined noise scheduling, and a non-uniform asynchronous diffusion process is performed to generate an intermediate state connecting the initial data and the target data; the entire asynchronous diffusion process realizes the differential reconstruction of the heterogeneous area through the pixel-level diffusion coefficient, wherein:

[0024] In the forward asynchronous diffusion sampling, the intermediate state is obtained by linearly superimposing noise on the initial data and the target data based on the diffusion coefficient, and the noise intensity is controlled by the pixel-level forward diffusion coefficient: the low abnormal value area has a small offset, which is close to the target data, and the confidence is high during reconstruction, and the intermediate state after forward asynchronous diffusion sampling is closer to ; the high abnormal value area has a large offset, which is close to the initial data, and the intermediate state after forward asynchronous diffusion sampling is closer to​​ To protect the original information;

[0025] 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.

[0026] 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:

[0027] 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:

[0028] (4);

[0029] in, and These are predefined time offset ranges, namely the minimum and maximum values;

[0030] (5);

[0031] 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;

[0032] 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.

[0033] where the forward diffusion sampling generates the intermediate state formula as follows:

[0034] (6);

[0035] where, is the standard normal noise, is the diffusion coefficient of all time steps of the forward diffusion sampling, based on the predefined noise schedule

[0036] (7);

[0037] ;

[0038] ;

[0039] where, is the noise variance of time step , is the noise variance of time step , is the forward noise cumulative standard deviation at time step , is the backward noise cumulative standard deviation at time step ;

[0040] The diffusion coefficients of all time steps of the forward diffusion sampling are pre-computed and stored in three arrays , , respectively, with the following calculation formula:

[0041] ;

[0042] ;

[0043] where, stores the diffusion coefficient corresponding to the target data , stores the diffusion coefficient corresponding to the initial data , stores the diffusion coefficient corresponding to the noise , represents the current time step ;

[0044] Based on , an independent diffusion coefficient is generated for each pixel from the predefined noise schedule and the pre-computed diffusion coefficients​ Thus, the forward asynchronous diffusion sampling is realized, and the calculation formula is as follows:

[0045] (12);

[0046] (13);

[0047] The intermediate state formula in the backward diffusion sampling update is as follows:

[0048] (14);

[0049] wherein is the current predicted reconstructed SST image, represents the intermediate state at the current time step , and represents the previous state, and the diffusion coefficient of all time steps in the backward sampling , , is calculated as follows:

[0050] (15);

[0051] ;

[0052] ;

[0053] The backward diffusion sampling also generates an independent diffusion coefficient for each pixel by pixel-level offsetting the time step , , , realizes the backward asynchronous diffusion sampling, maintains the duality with the forward asynchronous diffusion sampling, and realizes the region-adaptive diffusion process: since the of the low abnormal value region is small, the weight is large in the backward sampling, the weight is small, and fast convergence to is realized; since the of the high abnormal value region is large, the weight is small in the backward sampling, the weight is large, and slow repair to is realized.

[0054] Further, in step S3, first, the intermediate state at the current time step and the weekly mean image as the physical constraint are spliced in the channel dimension to form a two-channel tensor input; meanwhile, the time step The high-dimensional time embedding vector is converted through a sine-cosine position encoding; then, the two-channel tensor input and the time embedding vector are jointly input into an encoder-decoder architecture of a U-Net network, spatial features are extracted through multi-level convolution operations, and time context information is fused; finally, a predicted score function pred is output, which is used to represent the direction of the denoising gradient.

[0055] Further, in step S3, the score function is defined as follows:

[0056] ;

[0057] wherein, represents the intermediate state at the current time step, represents the real daily SST image, represents the corresponding pixel-level forward noise cumulative standard deviation. The score function is predicted by the U-Net network , and the output is denoted as pred. The predicted score function pred is used to replace

[0058] in the inference stage to perform a denoising operation to calculate the target data prediction value, i.e., the current predicted reconstructed SST image , and the calculation formula is as follows:

[0059] ;

[0060] wherein, is the score function predicted by the U-Net network.

[0061] Further, in the training stage, the intermediate state predicted by the score function of the U-Net network is used to calculate the target data prediction value, i.e., the current predicted reconstructed SST image , which is used to calculate the loss function to optimize the model parameters and realize the regional adaptive denoising learning; in the inference stage, the initial completed image is used as the initial data, the U-Net network score prediction and backward asynchronous diffusion sampling are iteratively performed, the gradual denoising reconstruction is performed, and the result of the last sampling prediction is used as the final reconstructed complete sea surface temperature image .

[0062] Further, the loss function is as follows:

[0063] (20);

[0064] ​​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;

[0065] 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:

[0066] ;

[0067] Outlier constraint loss as follows:

[0068] (twenty two);

[0069] in, For the currently predicted reconstructed SST image, This is a real SST image from that day. Weekly mean image .

[0070] 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.

[0071] 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 according to the normalization formula. This is used to guide asynchronous diffusion processes;

[0072] The asynchronous diffusion Schrödinger bridge module, through input... Actual SST image from that day and abnormality weight performing forward asynchronous diffusion sampling and backward asynchronous diffusion sampling; during the training process, the asynchronous diffusion Schrödinger module constructs a joint distribution path between and outputs an intermediate state and ; during the inference process, the intermediate state is iteratively updated by backward asynchronous diffusion sampling using and the predicted score function calculated by the U-Net prediction score function module ; ; ;

[0073] The U-Net prediction score function module predicts the score function to calculate the current predicted reconstructed SST image by inputting the time step , the intermediate state at the current time step , and the weekly mean image as a physical constraint ; during the training process, the intermediate state generated by forward diffusion sampling is input into the U-Net network prediction score function to calculate the current predicted target data, i.e., the current predicted reconstructed SST image ; during the inference process, the input initial completed image is input as initial data into the iterative network score prediction and backward asynchronous diffusion sampling to obtain the final reconstructed complete sea surface temperature image . Compared with the prior art, the present application has the following advantages:

[0074] (1) Significantly improve the training efficiency and stability. The existing traditional denoising diffusion probability model relies on a large number of sampling steps (usually hundreds to thousands of steps) for implicit fitting, and the training is complex and unstable due to parameter fluctuations. The present application realizes symmetric bidirectional diffusion optimization through the Schrödinger bridge framework, explicitly models the joint probability distribution from missing data to target data, generates an intermediate state through forward sampling, and uses a U-Net to predict target data through backward sampling, thereby achieving high-quality completion with fewer steps (the number of iteration steps in the present method is 20), significantly reducing the computational overhead. In addition, the loss function uses dynamic weights to optimize the denoising direction in the early stage and stabilize the training in the later stage, and combines the exponential moving average (EMA) to further enhance the parameter consistency, thereby improving the training efficiency and stability.

[0075]

[0076] ​​​(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

[0077] 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.

[0078] Figure 1 This is a schematic diagram of the system structure of the present invention;

[0079] 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

[0080] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0081] Example 1

[0082] This embodiment designs a sea surface temperature completion method based on an asynchronous diffusion Schrödinger bridge, including the following steps:

[0083] Step S1, Preprocessing:

[0084] 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. , and then the abnormality degree weight reflecting the abnormality degree of each pixel is obtained by calculating the normalized difference between the initial completed image and the weekly mean image . , which provides guidance for the subsequent asynchronous diffusion process.

[0085] Step S1 specifically includes: filling the missing area of the missing image of the day with the corresponding pixel value of the weekly mean image to generate an initial completed image , and the calculation formula is as follows:

[0086] (1).

[0087] Among them, is the binary mask of :

[0088] (2).

[0089] Subsequently, by comparing the difference between and , the normalized abnormality degree weight is generated, which is used to reflect the abnormality degree of each pixel in the non-missing area relative to the weekly mean, and the calculation formula is as follows:

[0090] (3).

[0091] Among them, represents operation, is a scaling factor, which defines the significance threshold of temperature difference.

[0092] Step S2, asynchronous diffusion:

[0093] Based on the diffusion Schrödinger bridge theory, a bidirectional diffusion path is established between the initial completed image and the real daily SST image, including two dual processes of forward asynchronous diffusion sampling and backward asynchronous diffusion sampling; according to the pixel-level abnormality degree weight , the diffusion time offset is generated, and then the pixel-level offset time step is generated, based on , the forward asynchronous diffusion sampling or the backward asynchronous diffusion sampling is performed, the diffusion coefficient of the noise adding and noise removing process is dynamically adjusted, and finally the intermediate state of the current time step in the diffusion process is generated. .

[0094] In step S2, first, according to the abnormality degree weight The diffusion time offset is calculated for each pixel , for adjusting the time step to generate a pixel-level offset time step ; then based on the pixel-level offset time step , the corresponding independent forward and backward diffusion coefficients are extracted for each pixel based on the pre-defined noise schedule, and a non-uniform asynchronous diffusion process is performed to generate an intermediate state connecting the initial data and the target data ; the entire asynchronous diffusion process realizes the differential reconstruction of heterogeneous regions through pixel-level diffusion coefficients, wherein:

[0095] In the forward asynchronous diffusion sampling, the intermediate state is obtained by linearly superimposing noise on the initial data and the target data , and the noise intensity is controlled by the pixel-level forward diffusion coefficient: the offset of the low abnormal value region is small, close to the target data, the confidence is high during reconstruction, and the intermediate state after forward asynchronous diffusion sampling is closer to ; the offset of the high abnormal value region is large, close to the initial data, and the intermediate state after forward asynchronous diffusion sampling is closer to to protect the original information;

[0096] In the backward asynchronous diffusion sampling, the U-Net network predicts the score function and calculates the target data prediction value, i.e. the current predicted reconstructed SST image , the backward asynchronous diffusion sampling uses and the initial data , and gradually updates the intermediate state according to the pixel-level backward diffusion coefficient : for the low abnormal value region, the offset is small, the diffusion process is fast, and the denoising process relies more on the neural network predicted target data, achieving fast convergence; for the high abnormal value region, the offset is large, the diffusion process is slow, and the denoising process retains more information of the current intermediate state , achieving gradual detail repair.

[0097] As a preferred embodiment, step S2, the initial completed image is denoted as , as the initial data, and the real daily SST image is denoted as , as the target data, and the bidirectional optimization between the initial data and the target data is realized by using the diffusion Schrödinger bridge theory, and the specific steps are as follows:

[0098] Step S21, according to the abnormality degree weight , the diffusion time offset is calculated for each pixel , which is mapped to an effective range, and then a pixel-level offset time step is generated, and the calculation formula is as follows:

[0099] (4);

[0100] wherein, and are predefined time offset ranges, respectively minimum and maximum;

[0101] (5);

[0102] wherein, the function is used to limit the input value within the specified range, ensuring within the valid range 0 to , represents the current time step, represents the total number of steps;

[0103] Step S22, based on the pixel-level offset time step , calculate the corresponding independent diffusion coefficient for each pixel from the predefined noise schedule, and perform a non-uniform asynchronous diffusion process to generate an intermediate state connecting the initial data and the target data;

[0104] wherein, the forward diffusion sampling generates an intermediate state formula as follows:

[0105] (6);

[0106] wherein, is the standard normal noise, is the diffusion coefficient of all time steps of forward diffusion sampling, based on the predefined noise schedule calculation:

[0107] (7);

[0108] ;

[0109] ;

[0110] wherein, is the noise variance of time step , is the noise variance of time step , is the forward noise cumulative standard deviation when the time step is , is the backward noise cumulative standard deviation when the time step is ;

[0111] Precompute the diffusion coefficient of all time steps of forward diffusion sampling and are stored in three arrays respectively , , , the calculation formula is as follows:

[0112] ;

[0113] ;

[0114] wherein, stores the diffusion coefficient corresponding to the target data , stores the diffusion coefficient corresponding to the initial data , stores the diffusion coefficient corresponding to the noise , represents the current time step ;

[0115] Based on , an independent diffusion coefficient is generated for each pixel from the pre-defined noise schedule and the pre-computed diffusion coefficient, so as to realize forward asynchronous diffusion sampling, and the calculation formula is as follows:

[0116] (12);

[0117] (13);

[0118] The formula for updating the intermediate state in backward diffusion sampling is as follows:

[0119] (14);

[0120] wherein is the current predicted reconstructed SST image, represents the intermediate state at the current time step , represents the previous state, and the diffusion coefficient of all time steps in backward sampling , , is calculated as follows:

[0121] (15);

[0122] ;

[0123] ;

[0124] The backward diffusion sampling also passes through a pixel-level offset time step​​​ 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 backward sampling 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. .

[0125] Step S3, U-Net prediction score:

[0126] 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.

[0127] 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.

[0128] 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 high-dimensional time embedding vector is converted through a sine-cosine position coding; then, the two-channel tensor input and the time embedding vector are jointly input into an encoder-decoder architecture of a U-Net network, spatial features are extracted through multi-level convolution operation, and time context information is fused; finally, a predicted score function pred is output, which is used to represent the direction of the denoising gradient.

[0129] In step S3, the score function formula is defined as follows:

[0130] ;

[0131] Wherein, represents the intermediate state of the current time step , represents the real daily SST image , represents the corresponding pixel-level forward noise cumulative standard deviation .

[0132] The score function is predicted by the U-Net network , and the output is denoted as pred. The predicted score function pred is used to replace to perform a denoising operation to calculate the target data prediction value, i.e., the current predicted reconstructed SST image , and the calculation formula is as follows:

[0133] ;

[0134] Wherein, is the score function predicted by the U-Net network.

[0135] In the training phase, the intermediate state sampled by forward asynchronous diffusion is predicted by the U-Net network to calculate the target data prediction value, i.e., the current predicted reconstructed SST image , which is used to calculate the loss function to optimize the model parameters, so as to realize the regional adaptive denoising learning; in the inference phase, the initial completed image is used as the initial data, the U-Net network score prediction and backward asynchronous diffusion sampling are iteratively performed, the gradually denoised reconstruction is performed, and the result of the last sampling prediction is used as the final reconstructed complete sea surface temperature image .

[0136] The loss function of the present application is as follows:

[0137] (20);

[0138] It is divided into two parts: wherein 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;

[0139] 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:

[0140] ;

[0141] Outlier constraint loss as follows:

[0142] (twenty two);

[0143] in, For the currently predicted reconstructed SST image, This is a real SST image from that day. Weekly mean image .

[0144] 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.

[0145] In the diffusion model, an asynchronous diffusion strategy is proposed to control the denoising strength by pixel-level offset time steps. This method uses the outlier weight to calculate the pixel-level offset time step, where the low outlier area has a smaller offset time step, and the diffusion parameter used is the parameter corresponding to the early time step, which quickly converges to provide spatial context constraints; the high outlier area has a larger offset time step, and the diffusion parameter used is the parameter corresponding to the middle and late time steps, which gradually repairs to improve accuracy. The original method applies uniform denoising strength to all pixels, which may cause some areas to be over-smoothed, destroying the details of the features (such as local temperature gradients), or some areas to be insufficiently repaired, affecting the image completion effect.

[0146] Embodiment 2

[0147] As shown in Figure 1 , this embodiment designs a sea surface temperature completion system based on an asynchronous diffusion Schrödinger bridge, which is used to implement the sea surface temperature completion method based on an asynchronous diffusion Schrödinger bridge as described in Embodiment 1.

[0148] The system includes a preprocessing module, an asynchronous diffusion Schrödinger module, and a U-Net prediction score function module.

[0149] The preprocessing module initializes the missing area with the weekly mean image to obtain an initial completion image ; then, according to the normalization formula, the abnormality weight is obtained from the daily missing image and the weekly mean image , which is used to guide the asynchronous diffusion process. The asynchronous diffusion Schrödinger bridge module performs forward asynchronous diffusion sampling and backward asynchronous diffusion sampling by inputting , the real daily SST image

[0150] , and the abnormality weight ; during the training process, the asynchronous diffusion Schrödinger module constructs a joint distribution path between and by forward asynchronous diffusion sampling, and outputs the intermediate state ; during the inference process, the intermediate state is iteratively updated by backward asynchronous diffusion sampling using and calculated by the U-Net prediction score function module. The U-Net prediction score function module calculates the score by inputting the time step

[0151] and the intermediate state at the current time step . and the weekly mean image as a physical constraint The prediction score function calculates the current predicted reconstructed SST image ; during the training process, the intermediate state generated by the forward diffusion sampling The prediction score function is predicted by the U-Net network and the target data of the current prediction, i.e. the current predicted reconstructed SST image, is calculated ; during the inference process, the input initial completion image The final reconstructed complete sea surface temperature image is obtained by iterative network score prediction and backward asynchronous diffusion sampling as initial data .

[0152] Embodiment 3

[0153] As another embodiment of the present application, a computer readable storage medium is also provided, which stores a computer program, and the computer program is executed by a processor to implement the sea surface temperature completion method based on the asynchronous diffusion Schrödinger bridge as described in the foregoing embodiment 1.

[0154] The computer readable storage medium can be a non-volatile computer readable storage medium. For example, it can include but is not limited to: portable computer disk, hard disk, 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 device, magnetic storage device, or any suitable combination of the above. In the present application, the 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, device or apparatus.

[0155] Experimental results:

[0156] Data set and preprocessing: In order to verify the technical effect, the fourth level SST product of the national satellite ocean application service from January 2022 to April 2023 is selected in this embodiment. Subsequently, in order to simulate the real cloud coverage, the real cloud mask is selected from the WHU cloud data to preprocess the data, and the cloud coverage rate is set to 8%, 25%, 46% and 68% respectively. Secondly, a certain signal-to-noise ratio (0.1) is added to simulate the information loss during data acquisition. Finally, the image size is cropped to 64x64, and the data range is normalized to the interval (-1, 1) for experiment.

[0157] Evaluation index: the root mean square error (RMSE) ), and the coefficient of determination (R2) ) are used as evaluation indexes to evaluate the reconstruction results.

[0158] Baseline selection: To demonstrate the effectiveness and advancement of the proposed solution, the classical methods in the field and some frontier methods are selected for comparison: AIN, DINEOF, Phy_INN, I2SB, DINFNN, SVIFNN and the proposed method. Among them, DINEOF is a classical method in this field, which is based on statistical spatiotemporal interpolation to complete the missing data; AIN, Phy_INN, DINFNN, SVIFNN are all frontier methods in this field based on deep neural networks, while I²SB is a deep learning frontier method for image restoration task, which also applies the Schrödinger bridge theory framework. Details as follows:

[0159] AIN: A GAN-based SST completion method, which adopts the "coarse-to-fine" strategy in the image domain. First, the weekly average is predicted using the monthly average, and then the daily anomaly is predicted based on the predicted weekly average. Finally, the reconstructed SST image is obtained by directly adding the weekly average and daily anomaly.

[0160] DINEOF: A classical missing data completion method based on empirical orthogonal function (EOF), widely used in the field of geophysics. Combining EOF analysis with spatial interpolation, it helps to interpolate to fill in missing data by identifying the spatial patterns that best represent the main changes or structures of the data set.

[0161] Phy_INN: A GAN-based frontier SST completion method. This method uses the ASPP (Atrous Spatial Pyramid Pooling) module to learn the information of different scales of weekly mean and daily anomaly in the image domain, and then performs deep fusion on the feature embedding of different scales to achieve the image restoration task of SST.

[0162] I²SB: This method is a frontier image restoration method based on a nonlinear diffusion model. Its core idea is to build a nonlinear diffusion Schrödinger bridge between the distribution of clean images and degraded images, and directly learn the mapping relationship between them. Unlike traditional diffusion models that start from random noise, I²SB takes degraded images as initial conditions and gradually restores high-quality images through more efficient diffusion paths.

[0163] DINFNN: A GAN-based frontier SST completion method. It uses a three-flow structure to input weekly mean, historical data and daily broken data, respectively, to learn the periodic stable information, time series historical information and context information of the daily completion image. Then, the three are fused to complete the completion.

[0164] SVIFNN: A frontier SST completion method based on GAN. A double-flow structure is adopted, and an abnormal attention mechanism is designed to fully retain the abnormal pattern of negative correlation between daily SST data and weekly mean value, while stabilizing the attention to the stable pattern of positive correlation between daily SST data and weekly mean value.

[0165] The results are shown in Tables 1-2 as follows:

[0166] Table 1. Comparison of RMSE indicators of the present application and existing methods

[0167] Cover Ratio AIN DINEOF Phy_INN 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

[0168] Table 2. Comparison of R2 indicators of the present application and existing methods

[0169] Cover Ratio AIN DINEOF Phy_INN 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

[0170] Secondly, part of the experimental results under 68% missing rate are visualized and displayed, and the results are shown in Figure 2 , Figure 2 The visualization results of the present application and existing methods under 68% missing rate are shown in (a) damaged SST image; (b) real SST image; (c) AIN result; (d) DINEOF result; (e) Phy_INN result; (f) I 2 SB result; (g) DINFNN result; (h) SVIFNN result; (i) result of the method of the present application.

[0171] The results show that, as shown in Tables 1-2, in the task of sea surface temperature image completion under four missing rates, the method of the present application always shows better results, which proves the effectiveness of the present application in improving the completion effect, and the completion result significantly exceeds other methods under large area missing (46% and 68% missing rate, especially under 68% missing). In addition, the comparison of the visualization results (such as Figure 2 ) further proves the robustness of the completion effect of the present application under large area missing. In summary, the experimental results prove the advancement of the present method compared with other frontier methods, and the robustness of the model under large area data missing.

[0172] In summary, the innovation of the present application is: 1) The U-Net prediction module combines bidirectional sampling to explicitly model the joint probability distribution from missing data to target data, which solves the problem of insufficient use of initial data information and weak spatial correlation caused by implicit fitting of the original method, and avoids detail loss or excessive smoothing. 2) In the asynchronous diffusion Schrodinger bridge module, introduce the pixel-level offset time step, dynamically adjust the denoising strength according to the weight of abnormal value, solve the problem that the synchronous denoising strategy of the original method ignores the heterogeneity of sea surface temperature area, the low abnormal value area converges quickly to provide spatial context constraints, and the high abnormal value area gradually repairs to ensure integrity and avoid excessive smoothing.

[0173] Of course, the above description is not a limitation on the present application, and the present application is not limited to the above examples. Within the scope of the present application, changes, modifications, additions or substitutions made by those skilled in the art should be within the scope of the present application.

Claims

1. A method for sea surface temperature completion based on asynchronous diffusion Schrodinger bridge, characterized in that, Comprising the following steps: Step S1, preprocessing: The input data includes a daily missing image , a weekly mean image , and a mask, which is used to fill the missing areas in the daily missing image with the weekly mean image to generate an initial completed image , and then by calculating the normalized difference between the initial completed image and the weekly mean image , the abnormality weight reflecting the abnormality degree of each pixel is obtained , which provides guidance for the subsequent asynchronous diffusion process; Step S2, asynchronous diffusion: Based on the diffusion Schrodinger bridge theory, in the initial completed image A bidirectional diffusion path is established between the real day SST image, including a forward asynchronous diffusion sampling and a backward asynchronous diffusion sampling two dual processes; According to the abnormal degree weight of pixel level Generate diffusion time offset , and then generate pixel level offset time step , based on Perform forward asynchronous diffusion sampling or backward asynchronous diffusion sampling, dynamically adjust the diffusion coefficient of the noise adding and denoising process, and finally generate the intermediate state of the current time step in the diffusion process; Step S3, U-Net prediction score: the current time step , the intermediate state and the weekly mean image providing spatial and physical constraints input into the U-Net network, using the encoder-decoder structure of the U-Net network to extract and spatial features and fuse temporal embeddings, realize region adaptive denoising prediction, output the predicted score function pred; based on the score function pred, the current predicted reconstruction SST image backward asynchronous diffusion sampling uses to update the intermediate state; In the training phase, for computing a loss function to optimize the model parameters; in the inference phase, the initial state is iteratively processed through the U-Net network to score predictions and backward asynchronous diffusion sampling, progressively denoising reconstruction, and the final iteration's prediction is outputted as the final reconstructed complete sea surface temperature image as the final reconstructed complete sea surface temperature image output.

2. The asynchronous diffusion Schrodinger bridge-based sea surface temperature completion method 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）； wherein is a binary mask: （2）； Subsequently, by comparing the difference between the normalized abnormality degree weight for reflecting the abnormality degree of each pixel in the non-missing region with respect to the average value of the neighborhood, the following formula is used: （3）； wherein, represents operates, is a scaling factor defining a significance threshold for the temperature difference.

3. The asynchronous diffusion Schrodinger bridge-based sea surface temperature completion method according to claim 1, characterized in that, In step S2, first, the abnormality degree weight is determined according to the abnormality degree of each pixel The diffusion time offset is calculated for each pixel , which is used to adjust the time step to generate a pixel-level offset time step ; then based on the pixel-level offset time step , the corresponding independent forward and backward diffusion coefficients are extracted for each pixel based on the pre-defined noise scheduling, and a non-uniform asynchronous diffusion process is performed to generate an intermediate state connecting the initial data and the target data ; the entire asynchronous diffusion process realizes the differential reconstruction of the heterogeneous regions through the pixel-level diffusion coefficients, wherein: In forward asynchronous diffusion sampling, the intermediate state From the initial data With the target data Based on the linear superposition noise of the diffusion coefficient, the noise intensity is controlled by the pixel-level forward diffusion coefficient: the low abnormal value area has small offset, close to the target data, high confidence during reconstruction, and the intermediate state after forward asynchronous diffusion sampling is closer ; High abnormal value area has large offset, close to initial data, and the intermediate state after forward asynchronous diffusion sampling is closer To protect the original information; In the backward asynchronous diffusion sampling, the U-Net network predicts a score function and calculates the predicted value of the target data, i.e. the current predicted reconstructed SST image , the backward asynchronous diffusion sampling uses and the initial data , and gradually updates the intermediate state according to the pixel-level backward diffusion coefficient : for the low abnormal value area, the offset is small, the diffusion process is fast, and the target data predicted by the neural network is more dependent in the denoising process, realizing fast convergence; for the high abnormal value area, the offset is large, the diffusion process is slow, and the information of the current intermediate state is more retained in the denoising process , realizing gradual detail repair.

4. The asynchronous diffusion Schrodinger bridge-based sea surface temperature completion method according to claim 1, characterized in that, Step S2, the initial complete image is complemented denoted as , as initial data, the real daily SST image is denoted as , as target data, the bidirectional optimization between the initial data and the target data is realized by using the diffusion Schrodinger bridge theory, and the specific steps are as follows: Step S21, calculating the abnormality degree weight calculating the diffusion time offset for each pixel mapping it to the valid range, and generating a pixel-level offset time step The calculation formula is as follows: （4）； wherein and are predefined time offset ranges, respectively minimum and maximum values; （5）； wherein, The function is used to limit the input value within the specified range, ensuring In the valid range 0 to Within, Represents the current time step, Represents the total number of steps; Step S22, based on the pixel-level offset time step From the pre-defined noise schedule, the corresponding independent diffusion coefficient is calculated for each pixel, and the non-uniform asynchronous diffusion process is performed to generate the intermediate state connecting the initial data and the target data; Wherein, the forward diffusion sampling generates the intermediate state formula as follows: （6）； wherein, is a standard normal noise, is the diffusion coefficient for all time steps of the forward diffusion sampling, based on a predefined noise schedule Compute: （7）； ； ； wherein, is the noise variance at time step is the noise variance at time step is the noise variance at time step is the noise variance at time step is the forward noise cumulative standard deviation at time step is the forward noise cumulative standard deviation at time step is the backward noise cumulative standard deviation at time step is the backward noise cumulative standard deviation at time step Pre-compute diffusion coefficients for all time steps of forward diffusion samples and stored in three arrays respectively , , The calculation formula is as follows: ； ； wherein, a diffusion coefficient of the corresponding target data is stored, , a diffusion coefficient of the corresponding initial data is stored, , a diffusion coefficient of the corresponding noise is stored, , representing the current time step is ; Based on An independent diffusion coefficient is generated for each pixel from a predefined noise schedule and a pre-computed diffusion coefficient Thus enabling forward asynchronous diffusion sampling, with the following formula: （12）； （13）； The backward diffusion sampling updates the intermediate state formula as follows: （14）； where is the current predicted reconstructed SST image, represents the intermediate state at the current time step , represents the previous state, the diffusion coefficient of all time steps backwardly sampled , , is computed as follows: （15）； ； ； Backward diffusion sampling also through pixel-level offset time step Generate independent diffusion coefficient for each pixel 、 、 , realize backward asynchronous diffusion sampling, keep dual with forward asynchronous diffusion sampling, realize region adaptive diffusion process: because of low abnormal value area Small, the weight is large in backward sampling Small, the weight is large in backward sampling , realize fast convergence to ; because of high abnormal value area Large, the weight is small in backward sampling Large, the weight is small in backward sampling , realize slow repair to .

5. The asynchronous diffusion Schrodinger bridge-based sea surface temperature completion method according to claim 1, characterized in that, In step S3, first, the current time step The intermediate state And the weekly mean image as a physical constraint Channel dimension splicing is performed to form a two-channel tensor input; at the same time, the time step The diffusion process is converted into a high-dimensional time embedding vector through sine-cosine position encoding; then, the two-channel tensor input and the time embedding vector are jointly input into the encoder-decoder architecture of the U-Net network, spatial features are extracted through multi-level convolution operation, and time context information is fused; finally, the predicted score function pred is output, which is used to represent the direction of the denoising gradient.

6. The asynchronous diffusion Schrodinger bridge-based sea surface temperature completion method according to claim 5, characterized in that, In step S3, the score function is defined as follows: ； wherein, represents the intermediate state at the current time step , represents the real-time-of-day SST image, represents the corresponding pixel-wise forward noise accumulated standard deviation; The score function is predicted by a U-Net network , whose output is denoted by pred, which is used in the inference phase instead of The denoising operation is performed to calculate the target data prediction, i.e. the currently predicted reconstructed SST image , which is calculated as follows: ； where, is the score function predicted by the U-Net network.

7. The asynchronous diffusion Schrodinger bridge-based sea surface temperature completion method according to claim 1, characterized in that, In the training phase, the intermediate state obtained by forward asynchronous diffusion sampling The score function predicted by the U-Net network The target data prediction value, i.e. the current predicted reconstructed SST image , for calculating the loss function to optimize the model parameters, realizing regional adaptive denoising learning; In the inference phase, the initial completed image As initial data, the U-Net network score prediction and backward asynchronous diffusion sampling are iteratively performed, the step-by-step denoising reconstruction is performed, and the result of the last sampling prediction is taken as the final reconstructed complete sea surface temperature image As the final reconstructed complete sea surface temperature image .

8. The asynchronous diffusion Schrodinger bridge-based sea surface temperature completion method according to claim 1, wherein, The loss function is as follows: （20）； is split into two parts: where denotes the reconstruction loss between the true label, is the weight of denotes the difference between the current predicted reconstructed SST image and the weekly mean image and the true difference, and is the weight of reconstruction loss score function for the U-Net network prediction mean squared error between the predicted and true labels The loss function is as follows:​ ； Outlier-constrained loss As follows: （22）； wherein, is the current predicted reconstructed SST image, is the true current day SST image, is the weekly mean image .

9. A sea surface temperature completion system based on an asynchronous diffusion Schrodinger bridge, characterized in that, A system for implementing the sea surface temperature completion method based on the asynchronous diffusion Schrodinger bridge according to any one of claims 1-7, comprising a preprocessing module, an asynchronous diffusion Schrodinger 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 according to the normalization formula. This is used to guide asynchronous diffusion processes; The asynchronous diffusion Schrodinger bridge module performs forward asynchronous diffusion sampling and backward asynchronous diffusion sampling by inputting , real day SST images and abnormal degree weights ; during the training process, the asynchronous diffusion Schrodinger bridge module constructs a joint distribution path between and by forward asynchronous diffusion sampling, and outputs an intermediate state ; In the inference process, the intermediate state is iteratively updated by backward asynchronous diffusion sampling using and the U-Net prediction score function module calculated ; 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. ; In the inference process, the input initial completion image The final reconstructed complete sea surface temperature image is obtained by iterative network score prediction and backward asynchronous diffusion sampling as initial data .

Images