Sea temperature completion method and system based on recursive dual-stream Mamba

Abstract

The present invention belongs to the field of image processing technology, and more particularly relates to a sea surface temperature completion method and system based on recursive dual-stream Mamba. The method comprises the following steps: splicing a damaged SST image and a weekly average SST image as input, recursively iterating N times through N identical recursive hierarchical Mamba blocks to output a predicted weekly average SST image and a predicted abnormal SST image, and adding these two output images to obtain a final completed SST image. The present invention provides a recursive hierarchical Mamba block for the sea surface temperature completion task. Each block integrates two parallel layers: a stability information representation module and an anomaly information representation module. These modules respectively extract features related to stability and features related to anomalies, thereby modeling long-range dependencies in the presence of large-area omissions and improving completion accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of image processing, and in particular relates to a sea temperature completion method and system based on recursive dual-stream Mamba. Background Art

[0002] Current deep learning-based ocean image restoration and completion methods generally adopt a "coarse-to-fine" image completion mechanism. First, the weekly mean of the missing area is estimated using the monthly mean. Then, the learned data pattern of the deviation between the daily data and the weekly mean is used to locally estimate the daily data of the missing part. Finally, the weekly mean is superimposed on the local estimate, achieving both global consistency and local fine-grained accuracy in the image completion process.

[0003] However, the above method has two shortcomings, which will be discussed one by one below:

[0004] (1) Insufficient modeling of long-range dependencies limits the robustness of completion under large-scale data loss. For example, the above methods use basic architectures such as convolutional neural networks (CNNs) and generative adversarial networks (GANs) for modeling. However, these architectures are difficult to fully model long-range dependencies in images, especially in the case of large-scale data loss, which greatly limits the robustness of completion, because long-range dependencies need to be effectively modeled when large-scale sea temperature data is missing. Therefore, in order to introduce an effective long-range dependency modeling method to solve the problem that current deep learning-based methods are difficult to effectively model long-range dependencies under large-scale data loss conditions, the present invention introduces Mamba, which is a selective state space model (SSM) derived from control systems. It can effectively model long-range dependencies by adaptively selecting features in space.

[0005] (2) Insufficient representation learning of stable information and abnormal information limits the accuracy of completion. The above methods use traditional saliency representation strategies such as convolution to complete sea surface temperature, ignoring that these representation strategies will smooth non-saliency information (such as local anomalies that do not meet the intra-period mean conditions), such as average pooling and maximum pooling used in convolution operations, and operations such as strengthening local features based on similarity correlation in traditional attention mechanisms, thereby limiting the accuracy of the final completion. Secondly, although this method models from the perspective of stability and abnormality, the modeling process mostly uses local or difficult-to-model long-range dependency representation strategies to directly represent abnormal and stable information. This modeling method makes it difficult to deeply mine stable and abnormal information. Summary of the Invention

[0006] In response to the shortcomings of the existing technology, the present invention provides a sea temperature completion method and system based on recursive dual-stream Mamba, using Mamba as the basic architecture to realize long-range dependency modeling under large-area missing conditions, fully modeling stable and abnormal information, and complete the completion task.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0008] The sea temperature completion method based on recursive dual-stream Mamba includes the following steps: , Weekly average SST image After splicing, it is used as input and outputs the predicted weekly average SST image through N recursive iterations of N identical recursive hierarchical Mamba blocks. and predicted abnormal SST images The two output images are added together to obtain the final completed SST image .

[0009] Furthermore, each of the recursive hierarchical Mamba blocks includes two parallel sub-modules: a stable information representation module and an abnormal information representation module, which respectively extract features related to stability and features related to abnormalities, and model stable information and abnormal information, wherein the output of the abnormal information representation module in each recursive hierarchical Mamba block serves as the input of the next recursive hierarchical Mamba block.

[0010] Furthermore, the final predicted weekly average SST image The final predicted abnormal SST image is obtained by summing the outputs of the stable information representation modules in the recursive hierarchical Mamba blocks from the 1st layer to the Nth layer. It is the output of the abnormal information representation module of the recursive hierarchical Mamba block at the Nth layer.

[0011] Furthermore, the stable information representation module and the abnormal information representation module have the same structure but independent parameters, and sequentially include a linear layer, depthwise convolution, SiLU activation, and Mamba long-range dependency modeling. The Mamba long-range dependency modeling adopts the basic architecture of the Mamba model for modeling long-range dependencies.

[0012] Furthermore, the loss function is as follows:

[0013] ;

[0014] Among them, L 总 Represents the total loss, including three parts: stable term, reconstruction term and abnormal term. represents the real SST image, Through and The difference is obtained, which represents the real abnormal SST image. represents element-wise multiplication, is the L2 norm, and the mask is The binary mask of:

[0015] ;

[0016] Where n represents the nth pixel in the mask.

[0017] The present invention also provides a sea temperature completion system based on recursive dual-stream Mamba, comprising an input module, N superimposed recursive hierarchical Mamba blocks, and an output module. The input module is used to obtain a damaged SST image. and weekly mean SST images , the two are concatenated as input;

[0018] Each of the recursive hierarchical Mamba blocks includes two parallel submodules: a stable information representation module and an abnormal information representation module, which respectively extract features related to stability and features related to abnormalities, and model stable information and abnormal information. The output of the abnormal information representation module in each recursive hierarchical Mamba block serves as the input of the next recursive hierarchical Mamba block; N recursive iterations are performed through N identical recursive hierarchical Mamba blocks to output the predicted weekly average SST image. and predicted abnormal SST images ;

[0019] The output module is used to output the predicted weekly average SST image of the recursive hierarchical Mamba block and predicted abnormal SST images Add together to get the final completed SST image , and output.

[0020] Compared with the prior art, the present invention has the following advantages:

[0021] First, it fully leverages long-range dependencies to complete data completion tasks for large areas with missing data, improving the robustness of the model. For example, previous methods used basic architectures such as convolutional neural networks (CNNs) and generative adversarial networks (GANs) for modeling. However, these architectures struggle to fully model long-range dependencies in images, particularly when large areas are missing, significantly limiting the robustness of the completion. This invention, however, incorporates stable information representation modules and anomaly information representation modules into the Mamba model and, based on this, proposes a sea surface temperature completion method for large areas with missing data. This method uses damaged SST images and weekly average SST images as input and uses Mamba to effectively capture long-range dependencies, improving the robustness of the model for completing sea surface temperature completion for large areas with missing data. This addresses the problem that existing methods fail to adequately model long-range dependencies, limiting the robustness of completion for large areas with missing data.

[0022] Second, by fully learning representations of stable and anomaly information, the accuracy of completion is improved. For example, existing methods rely on traditional saliency representation strategies such as convolution to complete sea surface temperature (SST). However, they ignore the fact that these representation strategies can smooth non-salient information (such as local anomalies that do not meet the intra-periodic mean). This includes operations such as average pooling and max pooling used in convolution, as well as the traditional attention mechanism that enhances local features based on similarity correlation, thus limiting the accuracy of the final completion. Secondly, while existing methods model from the perspective of stability and anomaly, most of them directly learn representations of anomaly and stable information using local or difficult-to-model long-range dependencies. This modeling approach is difficult to deeply mine stable and anomaly information. In contrast, this paper designs a recursive hierarchical Mamba block for the SST completion task. Each block integrates two parallel layers (a stable information representation module and an anomaly information representation module) to extract features related to stability and anomaly, respectively. By recursively stacking identical blocks, the model continuously propagates recursively to deeply mine and fully represent stable and anomaly information, improving the accuracy of model completion. This solves the problem that the existing technology is insufficient in characterizing stable information and abnormal information, which limits the accuracy of completion. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0024] Figure 1 Schematic diagram of the method flow of the present invention;

[0025] Figure 2 Schematic diagram of the system structure of the present invention;

[0026] Figure 3 3. Comparison of visualization results between the present invention and the existing method at a loss rate of 68% in the embodiment, where (a) is a real SST image; (b) is a damaged SST image; (c) is the AIN result; (d) is the DINEOF result; (e) is the Phy_INN result; (f) is the FMambaIR result; (g) is the DINFNN result; (h) is the SVIFNN result; and (i) is the result of the present invention. DETAILED DESCRIPTION

[0027] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0028] Example 1

[0029] like Figure 1 As shown, this embodiment provides a sea temperature completion method based on recursive dual-stream Mamba, including the following steps: , Weekly average SST image After splicing, it is used as input and outputs the predicted weekly average SST image through N recursive iterations of N identical recursive hierarchical Mamba blocks. (representing stable SST background information) and predicted abnormal SST images (representing local deviations and dynamic changes), then the two output images are added together to obtain the final completed SST image .

[0030] Thanks to its linear computational complexity, Mamba is particularly well-suited for complex tasks involving long sequences. Consequently, it has seen rapid adoption in computer vision applications such as image restoration and inpainting. While existing models have achieved promising results in various image restoration and completion tasks, applying Mamba to sea temperature (SST) completion remains a significant challenge. This is primarily because most existing Mamba-based applications assume fully observable inputs or unstructured noise, making them difficult to directly adapt to structured data completion scenarios such as SST reconstruction.

[0031] SST data are driven by physical processes and have inherent multi-scale characteristics, which lead to structural constraints at different spatial and temporal scales. Specifically, under conditions of large-scale missing data, accurate SST completion requires both global-scale physical consistency and local-scale anomaly preservation.

[0032] Therefore, to ensure that the completion results meet physical consistency across scales (a characteristic of SST data), this paper designs a recursive hierarchical Mamba block to gradually capture stable patterns and anomalous signals. While prior art has also proposed extracting stable and anomalous information separately, this paper further implements this concept through the design of the recursive hierarchical Mamba block. Furthermore, using Mamba further improves the quality of the learned representations of both types of information, ensuring more consistent and accurate reconstruction across large missing regions.

[0033] The following describes in detail the structure and data processing of the recursive hierarchical Mamba block.

[0034] Each recursive hierarchical Mamba block includes two parallel sub-modules: a stable information representation module and an abnormal information representation module, which respectively extract features related to stability and features related to abnormalities, and model stable information and abnormal information. The output of the abnormal information representation module in each recursive hierarchical Mamba block serves as the input of the next recursive hierarchical Mamba block.

[0035] Final predicted weekly average SST image The final predicted abnormal SST image is obtained by summing the outputs of the stable information representation modules in the recursive hierarchical Mamba blocks from the 1st layer to the Nth layer. is the output of the abnormal information representation module at the N+1th layer.

[0036] As a preferred embodiment, by recursively stacking N identical blocks [ , ,…, ](correspond Figure 1 The "Block 1, Block 2, ..., Block" in the lower left corner ”), the model continuously propagates recursively to form an N+1 layer structure (such as Figure 1 As shown in the diagram in the lower left corner), the stable information representation module of each Block (from the first layer to the layer) all get output [ , ,…, ]( represents the output of the first layer stable information representation module, represents the output of the second-layer stable information representation module, ..., Indicates the The output of the layer stable information representation module), while the output of the abnormal information representation module Then it serves as the input of the next Block. This process can be formalized as follows:

[0037] (1);

[0038] (2);

[0039]

[0040] (3):

[0041] Among them, the superscript represents the output of the first layer (e.g. Figure 1 As shown by the dotted line in the lower left corner, ,…, , Similar), subscript represents the stable information representation module, , ,......, represents the output of the abnormal information representation module of the second, third, ... N+1 layers (subscript represents the abnormal information representation module). Representative A recursive hierarchy of Mamba blocks.

[0042] Final predicted weekly average SST image Is to convert the first layer to the Specifically, the output of the stable information representation module in the recursive hierarchical Mamba block from the 1st layer to the Nth layer is summed up, and the final predicted abnormal SST image is Directly from the The output of the layer, specifically the output of the abnormal information representation module of the recursive hierarchical Mamba block of the Nth layer (this module serves as the N+1th layer):

[0043] (4);

[0044] (5).

[0045] As a preferred embodiment, the internal structure of the stable information representation module and the abnormal information representation module is the same, but the parameters are independent, which includes linear layer, depth convolution, SiLU activation, and Mamba long-range dependency modeling in sequence. The Mamba long-range dependency modeling adopts the basic architecture of the Mamba model for modeling long-range dependencies. For a given input , through the linear layer , depthwise convolution 、 Activate, last used Long-range modeling generation . The process can be formalized as:

[0046] (6).

[0047] The architecture of the stable information representation module and the abnormal information representation module adopts the basic architecture of the Mamba model. Mamba is a novel state space model (SSM). SSMs were originally developed in control theory and have recently been applied in deep learning because they are efficient in modeling long-range dependencies with linear time complexity. In its continuous form, SSMs describe a system whose equation of motion is as follows:

[0048] (7) ;

[0049] (8);

[0050] Among them, A is the state transfer matrix, B and C are mapping parameters, It is a potential state. is the time derivative of the state, is the input, is the output.

[0051] The process of modeling long-range dependencies through the Mamba model is as follows:

[0052] Discretization: Introducing a learnable step size parameter , convert the continuous parameters A and B of the continuous equation into discrete form and Typically, the discretization is performed using the zero-order hold technique (ZOH) (e.g., Mamba), which can be expressed as:

[0053] (9);

[0054] (10);

[0055] After discretization, the SSM-based model can be expressed in a recursive form as follows:

[0056] (11);

[0057] (12);

[0058] in, express The hidden state of the moment, express The hidden state of the moment, express Input at the moment, express The output at the moment. At the same time, it can also be expressed as an equivalent convolution form:

[0059] (13);

[0060] (14);

[0061] in, Indicates input, Indicates output, express indivual Multiply ( represents the number of convolutions). represents the convolution operation, Represents a structured convolution kernel.

[0062] Two-dimensional expansion (SS2D):

[0063] Mamba in order to 、 and Depending on the input, they are all set to dynamic. To extend Mamba to two-dimensional image data, such as SST fields, the 2D Selective Scanning Module (SS2D) proposed by VMamba is used. SS2D scans in four different directions (from top left to bottom right, from bottom right to top left, from top right to bottom left, and from bottom left to top right). This approach captures the long-range dependencies of each sequence based on discrete state-space equations. Finally, all sequences are combined by summing to restore the two-dimensional structure.

[0064] In summary, ① the introduction of the Mamba model in the stable information representation module and the abnormal information representation module solves the problem that existing methods insufficiently model long-range dependencies, which limits the robustness of completion under large-scale data loss; ② the design of recursively hierarchical Mamba blocks to model stable information and abnormal information solves the problem that the representation learning of stable information and abnormal information is insufficient, which limits the accuracy of completion.

[0065] The loss function of this method is as follows:

[0066] (15);

[0067] Among them, L 总 Represents the total loss, including three parts: stable term, reconstruction term and abnormal term. represents the real SST image, Through and The difference is obtained, which represents the real abnormal SST image. represents element-wise multiplication, is the L2 norm, and the mask is The binary mask of:

[0068] (16);

[0069] Where n represents the nth pixel in the mask.

[0070] Example 2

[0071] This embodiment provides a sea temperature completion system based on recursive dual-stream Mamba, such as Figure 2 As shown, it includes an input module, N superimposed recursive hierarchical Mamba blocks, an output module and a loss calculation module (not shown in the figure), wherein the input module is used to obtain a damaged SST image and weekly mean SST images , and the two are concatenated as input.

[0072] Each of the recursive hierarchical Mamba blocks includes two parallel submodules: a stable information representation module and an abnormal information representation module, which respectively extract features related to stability and features related to abnormalities, and model stable information and abnormal information. The output of the abnormal information representation module in each recursive hierarchical Mamba block serves as the input of the next recursive hierarchical Mamba block; N recursive iterations are performed through N identical recursive hierarchical Mamba blocks to output the predicted weekly average SST image. and predicted abnormal SST images .

[0073] The output module is used to output the predicted weekly average SST image of the recursive hierarchical Mamba block and predicted abnormal SST images Add together to get the final completed SST image , and output.

[0074] The loss calculation module is used to calculate the loss.

[0075] The functions and implementation processes of each module can be found in the description of Example 1 and will not be repeated here.

[0076] Example 3

[0077] As another embodiment of the present invention, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, it is used to implement the sea temperature completion method based on recursive dual-stream Mamba as described in the above embodiment 1.

[0078] A computer-readable storage medium may be a non-volatile computer-readable storage medium. Examples include, but are not limited to, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0079] Experimental results:

[0080] Dataset and Preprocessing: To validate the effectiveness of this technique, we selected Level 4 SST products from the National Satellite Ocean Application Service (NSATUS) from January 2022 to April 2023. To simulate realistic cloud cover, we preprocessed the data using realistic cloud masks from the WHU cloud data, setting cloud coverage to 8%, 25%, 46%, and 68%, respectively. Furthermore, we added a signal-to-noise ratio (SNR) of 0.1 to simulate information loss during data acquisition. Finally, we cropped the image to 64×64 pixels and normalized the data range to the (-1, 1) interval for the experiment.

[0081] Evaluation index: Root mean square error ( ), coefficient of determination ( ), structural similarity index (SSIM), and peak signal-to-noise ratio (PSNR) are used as evaluation indicators to evaluate the reconstruction results.

[0082] Baseline Selection: To demonstrate the technical effectiveness of this invention, we selected classic methods in this field as well as some cutting-edge methods: AIN, DINEOF, Phy_INN, FMambaIR, DINFNN, and SVIFNN for comparative experiments with this invention. DINEOF is a classic method in this field, which uses statistics to complete missing data through spatiotemporal interpolation. AIN, Phy_INN, DINFNN, and SVIFNN are all cutting-edge methods in this field based on deep neural networks. FMambaIR is a cutting-edge deep learning method for general image restoration tasks, which also uses the Mamba architecture. The details are as follows:

[0083] AIN: A GAN-based SST completion method that employs a coarse-to-fine strategy in the image domain. It first predicts the weekly mean using the monthly mean, then predicts the daily anomalies based on the predicted weekly mean. Finally, the reconstructed SST image is obtained by directly adding the weekly mean and daily anomalies.

[0084] DINEOF: A classic missing data imputation method based on empirical orthogonal functions (EOFs), widely used in geophysics. Combining EOF analysis with spatial interpolation helps fill missing data by identifying spatial patterns that best represent the primary variation or structure of a dataset.

[0085] Phy_INN: A cutting-edge GAN-based SST completion method. This method uses the ASPP (Atrous Spatial Pyramid Pooling) module to learn information at different scales of weekly means and daily anomalies in the image domain. It then deeply fuses the feature embeddings at different scales to achieve SST image restoration.

[0086] FMambaIR: A cutting-edge method in image restoration that combines frequency domain and Mamba in a deep learning architecture to denoise a single plain image.

[0087] DINFNN: A cutting-edge GAN-based SST completion method. It employs a three-stream architecture, simultaneously inputting weekly averages, historical data, and daily damage data. It learns cyclic stability information, temporal history information, and contextual information for the daily completion image, respectively. These three inputs are then fused to complete the completion.

[0088] SVIFNN: A cutting-edge GAN-based SST completion method. It uses a dual-stream architecture and a designed anomaly attention mechanism to fully preserve the abnormal patterns of negative correlation between the daily SST data and the weekly mean, while simultaneously focusing on the stable patterns of positive correlation between the daily SST data and the weekly mean.

[0089] The results are shown in Tables 1 to 4 below:

[0090] Table 1. Comparison of RMSE between the present invention and existing methods

[0091] Cover Ratio AIN DINEOF Phy_INN FMambaIR DINFNN SVIFNN Ours 8% 0.1005 0.1287 0.0802 0.0988 0.0678 0.0625 0.0593 25% 0.1161 0.1427 0.1015 0.1133 0.0616 0.0697 0.0643 46% 0.1220 0.1513 0.1030 0.1341 0.0987 0.1045 0.0654 68% 0.1292 0.1911 0.1223 0.1536 0.0951 0.1299 0.0694

[0092] Table 2. Comparison of R2 index between the present invention and existing methods

[0093] Cover Ratio AIN DINEOF Phy_INN FMambaIR DINFNN SVIFNN Ours 8% 0.7759 0.9441 0.9901 0.9873 0.9936 0.9949 0.9937 25% 0.7498 0.8570 0.9227 0.9471 0.9825 0.9801 0.9791 46% 0.7341 0.7834 0.8620 0.8946 0.9254 0.9038 0.9595 68% 0.6455 0.0829 0.7598 0.6459 0.8896 0.7761 0.9251

[0094] Table 3. Comparison of SSIM index between the present invention and existing methods

[0095] Cover Ratio AIN DINEOF Phy_INN FMambaIR DINFNN SVIFNN Ours 8% 0.4360 0.3086 0.5477 0.4843 0.7283 0.7421 0.7510 25% 0.4270 0.2653 0.4874 0.3697 0.6975 0.6602 0.6830 46% 0.4144 0.2572 0.4633 0.3716 0.5941 0.5812 0.6817 68% 0.4189 0.2045 0.4700 0.3310 0.5499 0.4962 0.6661

[0096] Table 4. PSNR comparison between the present invention and existing methods

[0097] Cover Ratio AIN DINEOF Phy_INN FMambaIR DINFNN SVIFNN Ours 8% 67.4913 64.5002 70.2087 68.8444 72.9162 72.3638 72.9091 25% 67.0389 63.6185 68.1396 67.6879 72.6370 71.5118 72.2467 46% 66.0663 63.1268 68.1937 66.1778 68.4372 67.9200 72.1118 68% 66.0875 62.8313 66.8839 65.4043 68.9262 66.2110 71.6073

[0098] Secondly, this example selects some experimental results under a 68% missing rate for visualization, and the results are as follows: Figure 3 As shown in the figure, (a) represents a true SST image, (b) represents a damaged SST image, (c)-(h) represent the results of AIN, DINEOF, Phy_INN, FMambaIR, DINFNN, and SVIFNN, respectively, and (i) represents the result of our method. As can be seen from the example, when a large area of ​​data is missing (68%) (as shown in (b)), the completion result of our method (as shown in (i)) is closer to the actual situation (as shown in (a)). This verifies the effectiveness and robustness of our method's SST completion under large-area data gaps.

[0099] The results show that, as shown in Tables 1 to 4, the method of the present invention consistently performs better in the sea surface temperature image completion task under four missing rates, which proves the effectiveness of the present invention in improving the completion effect. At the same time, the completion results under large area missing conditions (missing rates of 46% and 68%, especially under 68%) significantly exceed those of other methods. In addition, the visualization results (such as Figure 3 ) comparison further demonstrates the robustness of the present invention's completion effect in the presence of large-scale missing data. In summary, the experimental results demonstrate that the present invention's method has superior completion effect and model robustness under large-scale data loss compared to other cutting-edge methods.

[0100] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Any changes, modifications, additions or substitutions made by ordinary technicians in this technical field within the essential scope of the present invention should fall within the scope of protection of the present invention.

Claims

1. The sea temperature completion method based on recursive dual-stream Mamba is characterized by: The following steps are involved: Convert the damaged SST image to SST cor , Weekly Average SST Image SST ave After splicing, it is used as input and outputs the predicted weekly average SST image through N recursive iterations of N identical recursive hierarchical Mamba blocks. and predicted abnormal SST images The two output images are added together to obtain the final completed SST image SST rec ; Each of the recursive hierarchical Mamba blocks includes two parallel submodules: a stable information representation module and an abnormal information representation module, which respectively extract features related to stability and features related to abnormalities, and model stable information and abnormal information, wherein the output of the abnormal information representation module in each recursive hierarchical Mamba block serves as the input of the next recursive hierarchical Mamba block; Final predicted weekly average SST image The final predicted abnormal SST image is obtained by summing the outputs of the stable information representation modules in the recursive hierarchical Mamba blocks from the 1st layer to the Nth layer. It is the output of the abnormal information representation module of the recursive hierarchical Mamba block at the Nth layer.

2. The sea temperature completion method based on recursive dual-stream Mamba according to claim 1 is characterized in that: The stable information representation module and the abnormal information representation module have the same structure but independent parameters, and include linear layer, depth convolution, SiLU activation, and Mamba long-range dependency modeling in sequence. The Mamba long-range dependency modeling adopts the basic architecture of the Mamba model for modeling long-range dependencies.

3. The sea temperature completion method based on recursive dual-stream Mamba according to claim 1 is characterized in that: The loss function is as follows: Among them, L 总 Represents the total loss, including three parts: stability term, reconstruction term and abnormal term. SST gro Represents the real SST image, SST ano Through SST ave and SST cor The difference is obtained, which represents the real abnormal SST image, ⊙ represents element-by-element multiplication, ||·||2 is the L2 norm, and mask is SST cor The binary mask of: Where n represents the nth pixel in the mask.

4. The sea temperature completion system based on recursive dual-stream Mamba is characterized by: It includes an input module, N superimposed recursive hierarchical Mamba blocks, and an output module. The input module is used to obtain a damaged SST image SST. cor and weekly average SST image SST ave , the two are concatenated as input; Each of the recursive hierarchical Mamba blocks includes two parallel submodules: a stable information representation module and an abnormal information representation module, which respectively extract features related to stability and features related to abnormalities, and model stable information and abnormal information. The output of the abnormal information representation module in each recursive hierarchical Mamba block serves as the input of the next recursive hierarchical Mamba block; N recursive iterations are performed through N identical recursive hierarchical Mamba blocks to output the predicted weekly average SST image. and predicted abnormal SST images Final predicted weekly average SST image The final predicted abnormal SST image is obtained by summing the outputs of the stable information representation modules in the recursive hierarchical Mamba blocks from the 1st layer to the Nth layer. The output of the abnormal information representation module of the recursive hierarchical Mamba block at the Nth layer; The output module is used to output the predicted weekly average SST image of the recursive hierarchical Mamba block and predicted abnormal SST images Add together to get the final completed SST image SST rec , and output.

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