Sea Temperature Completion Method and System Based on Deep Learning Wavelet Multi-Scale Mining

Abstract

This application relates to the field of image processing, and discloses a sea temperature completion method and system based on deep learnable wavelet multi-scale mining. The method includes: S2, simulating the downsampling operation through learnable discrete wavelet transform, fusing the low-frequency information and high-frequency information and outputting until the Nth layer of the deep frequency-domain learnable wavelet downsampling module; S3, simulating the upsampling operation through inverse wavelet transform, fusing the obtained low-frequency information, high-frequency information and the low-frequency information of the Nth layer of the deep frequency-domain learnable wavelet downsampling module and outputting until the first layer of inverse wavelet upsampling module; S4, performing an upsampling operation by simulating the inverse wavelet transform on the fused features output to the first layer of inverse wavelet upsampling module and the features processed by global self-attention in S2, and outputting the finally completed complete sea temperature image. This application effectively solves the problems of rigid frequency-domain decomposition caused by fixed basis functions and the inability to adapt to the multi-scale characteristics of signals.

Description

Technical Field

[0001] This application relates to the field of image processing, and particularly to a sea surface temperature completion method and system based on deep learnable wavelet multi-scale mining. Background Art

[0002] Using deep learning for sea surface temperature image completion can improve the accuracy and spatio-temporal resolution of data completion, provide more reliable data for key fields such as meteorological prediction, climate research, and marine ecological monitoring, and thus enhance the comprehensive understanding and prediction ability of the ocean system. This is crucial for coping with climate change and protecting the marine ecological environment. Currently, the sea surface temperature image completion method based on deep learning adopts a feature modeling method of "frequency domain feature extraction + cascade fusion". This method uses the mechanism of "frequency domain feature extraction + cascade fusion", captures periodic steady-state features, adjacent time features, and current background information respectively through a three-stream neural network, and dynamically extracts key frequency domain information using high-pass and low-pass filters, so as to achieve high-quality reconstruction of sea temperature data.

[0003] However, this method has the following problems: First, the Fourier transform is used for frequency domain feature extraction, but the Fourier transform relies on fixed sine basis functions and cannot adapt to the multi-scale characteristics of signals. For example, when using the Fourier transform for frequency domain feature extraction, its fixed sine basis functions are difficult to adapt to high-frequency and low-frequency features of different scales, restricting the multi-scale modeling of sea surface temperature images. In sea surface temperature images, high-frequency information usually corresponds to temperature changes on short time scales, such as small-scale vortices, fronts, and short-period ocean current fluctuations, while low-frequency information reflects long-term trends, such as seasonal changes or large-scale ocean current systems. Although this method combines high-frequency and low-frequency information, the Fourier transform it uses cannot adapt to data structures of different scales and lacks an optimization strategy for high-low frequency features of different scales. For example, in the frontal area, small-scale high-frequency information is crucial for accurately depicting the boundary. If the high-frequency features of different scales are not adaptively optimized, the completion result may lead to blurred boundaries or lost details; while in the large-scale ocean current area, low-frequency information dominates the overall trend. If information of different scales cannot effectively interact, it may affect the global consistency of the completion result.

[0004] Second, the feature fusion method is relatively simple and lacks deep multi-scale feature interactions. For example, this method mainly patches the Fourier transform features and uses the cascaded fusion method for complementation. However, this direct patching method fails to fully establish the deep connections between features of different scales, making it difficult to effectively utilize the mutual information of each scale, which may lead to inconsistencies in the complementation results in local regions. For example, when complementing small-scale ocean vortices, fronts and other structures, the temperature changes often have complex spatio-temporal dependence relationships. Relying solely on simple patching of features may not be able to accurately capture the synergistic relationship between high-frequency local dynamics and low-frequency global background, resulting in problems such as blurred local details, unclear or discontinuous boundaries in the complemented temperature field, affecting the overall physical consistency and prediction accuracy. Summary of the Invention

[0005] The technical problem to be solved by this application is to overcome the deficiencies of the prior art and provide a sea surface temperature complementation method and system based on deep learnable wavelet multi-scale mining.

[0006] To achieve the above object, the first aspect of this application provides a sea surface temperature complementation method based on deep learnable wavelet multi-scale mining, including:

[0007] Obtain the weekly mean image and the missing image of the current day , subtract the two to obtain the daily fluctuation image , input the daily fluctuation image and the weekly mean image into the multi-scale adaptive wavelet encoder module, and after being processed by the multi-scale adaptive wavelet encoder module and then input into the inverse wavelet transform decoder module based on multi-scale fusion, output the finally complemented complete sea surface temperature image ; wherein, there are N layers of deep frequency-domain learnable wavelet downsampling modules connected in sequence in the multi-scale adaptive wavelet encoder module, and there are N layers of inverse wavelet upsampling modules connected in sequence in the inverse wavelet transform decoder module based on multi-scale fusion;

[0008] Specifically, it includes the following steps:

[0009] Step S1, after globally self-attention processing the daily fluctuation image and the weekly mean image , use them as the input of the N layers of deep frequency-domain learnable wavelet downsampling modules, obtain the low-frequency information and high-frequency information of the input image at different scales through learnable discrete wavelet transform, fuse the low-frequency information and high-frequency information of each scale and then output to the next layer of deep frequency-domain learnable wavelet downsampling module until the output reaches the Nth layer of deep frequency-domain learnable wavelet downsampling module;

[0010] Step S2: Use the fusion features output by the (N - 1)-th layer of the depth-frequency-domain learnable wavelet downsampling module as the input of the N-th layer of the inverse wavelet upsampling module, and use the low-frequency information of the N-th layer of the depth-frequency-domain learnable wavelet downsampling module as the input of the N-th layer of the inverse wavelet upsampling module. Obtain the low-frequency information and high-frequency information of different scales of the input fusion features through the learnable discrete wavelet transform. After fusing the obtained low-frequency information and high-frequency information of each scale with the low-frequency information of the N-th layer of the depth-frequency-domain learnable wavelet downsampling module input, output to the inverse wavelet upsampling module of the previous layer until the output reaches the first layer of the inverse wavelet upsampling module;

[0011] Step S3: Use the inverse wavelet transform to simulate the upsampling operation on the fusion features output to the first layer of the inverse wavelet upsampling module and the features processed by the global self-attention in Step S1, and output the finally completed full sea surface temperature image 。

[0012] Optionally, in Step S1, the daily fluctuation image and the weekly mean image are respectively processed by a linear layer and a global self-attention module to obtain weighted feature representations and . The acquisition operations and subsequent processing operations of the weighted feature representations and are the same. The specific steps for obtaining the weighted feature representation are as follows:

[0013] Process the daily fluctuation image through the linear layer to obtain input features with a dimension of . Process the input features through the global self-attention module to obtain the weighted feature representation .

[0014] Optionally, in Step S1, the learnable discrete wavelet transform is used to obtain the low-frequency information and high-frequency information of different scales of the input image, including inputting the weighted feature representation into the depth-frequency-domain learnable wavelet downsampling module for processing. The learnable discrete wavelet transform module uses the learnable discrete wavelet transform to decompose the weighted feature representation into four sub-bands , , and . Among them, , , and respectively represent low-frequency, horizontal high-frequency, vertical high-frequency, and diagonal high-frequency convolution operators;

[0015] Obtain low-frequency information , horizontal high-frequency information , vertical high-frequency information and diagonal high-frequency information , expressed as:

[0016] ;

[0017] ;

[0018] ;

[0019] ;

[0020] wherein, represents a convolution operation, represents low-frequency information, represents horizontal high-frequency information, represents vertical high-frequency information, represents diagonal high-frequency information;

[0021] Fuse the horizontal high-frequency information , vertical high-frequency information and diagonal high-frequency information to obtain high-frequency information , expressed as:

[0022] ;

[0023] wherein, concat represents a concatenation operation.

[0024] Optionally, before fusing the low-frequency information and high-frequency information in step S1, first process the low-frequency information through a local self-attention module to obtain a weighted feature representation , including defining the size of the local region as , with a stride of 8, sliding to cover the entire input feature. For the input feature , use operation to extract local window features, expressed as:

[0025] ;

[0026] wherein, is the number of extracted windows, and the dimension of each window feature is ;

[0027] For each local window feature , calculate the weighted feature representation of each local window feature ​ ;

[0028] Use operation to recombine the obtained local attention features into a complete feature map:

[0029] ;

[0030] Among them, respectively represent the window features calculated by the attention mechanism;

[0031] The feature and the low-frequency information are calculated through residual connection to obtain a weighted feature representation , expressed as:

[0032] ;

[0033] Among them, represents the residual connection;

[0034] Fuse the low-frequency information and high-frequency information, including fusing the weighted feature representation and the high-frequency information together to obtain the feature , and the fusion process is expressed as:

[0035] ;

[0036] Among them, concat represents the concatenation operation.

[0037] Optionally, in step S2, N takes the integer three, and the low-frequency information of the third-layer depth-frequency domain learnable wavelet downsampling module is used as the input of the third-layer inverse wavelet upsampling module, including the daily fluctuation image and the weekly mean image weighted feature representations and are subjected to complex convolution operation to obtain the feature and then input into the third-layer inverse wavelet upsampling module, expressed as:

[0038] ;

[0039] Among them, represents the complex convolution operation;

[0040] Use the fused feature output by the second-layer depth-frequency domain learnable wavelet downsampling module as the input of the third-layer inverse wavelet upsampling module, including the fused feature output by the second-layer depth-frequency domain learnable wavelet downsampling module and Perform a complex convolution operation to obtain features and then input it into the third-layer inverse wavelet upsampling module, expressed as:

[0041] ;

[0042] The third-layer inverse wavelet upsampling module obtains high-frequency information of the input image at different scales through learnable discrete wavelet transform, including performing a learnable discrete wavelet transform operation on the features to respectively obtain low-frequency information and high-frequency information , and ;

[0043] The third-layer inverse wavelet upsampling module performs a complex convolution operation on the obtained features and the low-frequency information to obtain features , expressed as:

[0044] ;

[0045] Through the inverse learnable discrete wavelet transform module, use the inverse wavelet transform to simulate the upsampling operation, and fuse the obtained high-frequency information and the low-frequency information of the third-layer depth frequency domain learnable wavelet downsampling module and then output, including performing an inverse learnable discrete wavelet transform on the features , high-frequency information , and through the inverse learnable discrete wavelet transform module to fuse and output, obtaining features ;

[0046] The inverse wavelet upsampling module of the subsequent layer outputs the fused features to the inverse wavelet upsampling module of the previous layer until it is output to the first-layer inverse wavelet upsampling module, including the third-layer inverse wavelet upsampling module outputting the features to the second-layer inverse wavelet upsampling module, and the second-layer inverse wavelet upsampling module outputs the features to the first-layer inverse wavelet upsampling module, and the first-layer inverse wavelet upsampling module outputs the finally completed complete sea surface temperature image .

[0047] Optionally, after the features , high-frequency information , and are fused through the inverse learnable discrete wavelet transform module using the inverse learnable discrete wavelet transform, including the features , high-frequency information , and are concatenated and expressed as:

[0048] ;

[0049] where concat represents the concatenation operation;

[0050] Use the inverse wavelet kernel to perform grouped convolution on the feature map in the wavelet domain to obtain features , expressed as:

[0051] ;

[0052] The output fused features of the inverse wavelet upsampling module in the latter layer are given to the inverse wavelet upsampling module in the previous layer until it is output to the first-layer inverse wavelet upsampling module, including the features and features and the obtained features are input into the second-layer inverse wavelet upsampling module for processing to output features to the first-layer inverse wavelet upsampling module, and the first-layer inverse wavelet upsampling module will output the features and the daily fluctuation image and the weekly mean image The features output after being processed by the linear layer and the global self-attention module and perform inverse wavelet transform to simulate upsampling and output the final completed image .

[0053] Optionally, the loss function is expressed as:

[0054] ;

[0055] It is divided into two parts, where is the current training epoch, is the total number of training epochs, represents the absolute error between the generated image and the missing sea surface temperature image , represents the structural similarity error between the generated image and the missing sea surface temperature image ;

[0056] where is expressed as:

[0057] ;

[0058] Among them, represents the number of images;

[0059] is expressed as:

[0060] ;

[0061] Among them, and respectively represent the mean values of two images and , and represent the standard deviation, is the covariance of two images, and is a constant added to avoid a zero denominator.

[0062] To achieve the above object, the second aspect of the present application provides a sea surface temperature completion system based on deep learnable wavelet multi-scale mining, which applies the method as described above. The system includes:

[0063] A multi-scale adaptive wavelet encoder module and an inverse wavelet transform decoder module based on multi-scale fusion, which subtract the weekly mean image from the missing image of the current day to obtain the daily fluctuation image , and input the daily fluctuation image and the weekly mean image into the multi-scale adaptive wavelet encoder module. After being processed by the multi-scale adaptive wavelet encoder module and then input into the inverse wavelet transform decoder module based on multi-scale fusion, the finally completed complete sea surface temperature image is output;

[0064] The multi-scale adaptive wavelet encoder module includes a global self-attention module and an N-layer deep frequency domain learnable wavelet downsampling module connected in sequence. The inverse wavelet transform decoder module based on multi-scale fusion has an N-layer inverse wavelet upsampling module connected in sequence, where N is an integer greater than one; among them, the N-layer deep frequency domain learnable wavelet downsampling module processes the daily fluctuation image and the weekly mean image through a linear layer and a global self-attention module, and uses them as the input of the N-layer deep frequency domain learnable wavelet downsampling module. Through the learnable discrete wavelet transform, the low-frequency information and high-frequency information of different scales of the input image are obtained, and the low-frequency information and high-frequency information of each scale are fused and then output to the next layer of the deep frequency domain learnable wavelet downsampling module until the output reaches the Nth layer of the deep frequency domain learnable wavelet downsampling module;

[0065] The N - layer inverse wavelet upsampling module takes the fused feature output by the (N - 1)-layer depth - frequency - domain learnable wavelet downsampling module as the input of the N - layer inverse wavelet upsampling module, and takes the low - frequency information of the N - layer depth - frequency - domain learnable wavelet downsampling module as the input of the N - layer inverse wavelet upsampling module. It obtains the low - frequency information and high - frequency information of different scales of the input image through learnable discrete wavelet transform, fuses the obtained low - frequency information and high - frequency information of each scale with the low - frequency information of the N - layer depth - frequency - domain learnable wavelet downsampling module, and then outputs the result to the inverse wavelet upsampling module of the previous layer until it outputs to the first - layer inverse wavelet upsampling module;

[0066] The fused feature output until the first - layer inverse wavelet upsampling module and the feature processed by the global self - attention module in step S2 are used to simulate the upsampling operation through inverse wavelet transform, and the finally completed and complete sea surface temperature image is output. 。

[0067] Optionally, the depth - frequency - domain learnable wavelet downsampling module includes a learnable discrete wavelet transform module, a local self - attention module, and a fusion module;

[0068] The learnable discrete wavelet transform module obtains the low - frequency information and high - frequency information of different scales of the input image through learnable discrete wavelet transform. It includes that the learnable discrete wavelet transform module processes the weighted feature representation to obtain the low - frequency information and fuses to obtain the high - frequency information ;

[0069] The local self - attention module processes the low - frequency information through the attention mechanism to obtain the weighted feature representation ;

[0070] The fusion module fuses the low - frequency information and the high - frequency information, including fusing the weighted feature representation and the high - frequency information to fuse and output the fused feature ;

[0071] The learnable discrete wavelet transform module outputs the fused feature to the depth - frequency - domain learnable wavelet downsampling module of the next layer until it outputs to the N - layer depth - frequency - domain learnable wavelet downsampling module. The N - layer depth - frequency - domain learnable wavelet downsampling module outputs the obtained low - frequency information to the N - layer inverse wavelet upsampling module.

[0072] Optionally, the inverse wavelet upsampling module includes a first complex convolution module, a second complex convolution module, a learnable discrete wavelet transform module, and an inverse learnable discrete wavelet transform module;

[0073] The first complex convolution module performs complex convolution operations on the fused feature and to obtain a feature and then inputs it into the learnable discrete wavelet transform module;

[0074] The learnable discrete wavelet transform module performs learnable discrete wavelet transform operations on the feature to respectively obtain low-frequency information and high-frequency information 、 and ;

[0075] The second complex convolution module performs complex convolution operations on the low-frequency information and the feature to obtain a feature and inputs it into the inverse learnable discrete wavelet transform module;

[0076] The inverse learnable discrete wavelet transform module fuses the feature 、high-frequency information 、 and using the inverse learnable discrete wavelet transform and outputs the fused feature to the inverse wavelet upsampling module of the previous layer until it is output to the first-layer inverse wavelet upsampling module, including inputting the feature output by the first-layer depth frequency domain learnable wavelet downsampling module and the feature and the obtained feature into the second-layer inverse wavelet upsampling module for processing and outputting a feature to the first-layer inverse wavelet upsampling module. The first-layer inverse wavelet upsampling module processes the output feature and the daily fluctuation image and the weekly mean image through a linear layer and a global self-attention module and outputs the feature and to perform inverse wavelet transform to simulate upsampling and output the final completed image .

[0077] After adopting the above technical solutions, the present application has the following beneficial effects compared with the prior art:

[0078] In this application, by dynamically optimizing the wavelet basis function during the training process, frequency-domain adaptive feature extraction is achieved, significantly enhancing the modeling ability for the complex spatio-temporal dynamics of sea surface temperature data; through data-driven dynamic adjustment of the basis function, the modeling ability for the multi-scale spatio-temporal dynamics of sea surface temperature data is significantly enhanced; specifically, the decomposition weights of the low-frequency components (such as seasonal variations, large-scale ocean current trends) and high-frequency components (such as short-term vortices, frontal fluctuations) can be autonomously optimized according to the distribution characteristics of the input data, so as to accurately capture the global consistency features and local detail changes of the sea surface temperature field; effectively solving the problem of rigid frequency-domain decomposition caused by fixed basis functions in traditional methods, and significantly improving the physical rationality and detail restoration degree of the completion results.

[0079] In this application, the downsampling operation is simulated by learnable wavelet transform. By allowing the basis function to be adaptively optimized during training, the retention weight of the high-frequency components is dynamically adjusted, thereby reducing information loss and solving the problem that the traditional encoder downsampling process realizes feature dimensionality reduction by compressing the spatial dimension, resulting in irreversible loss of high-frequency detail information (such as edges, textures). At the same time, the local self-attention mechanism further processes the low-frequency information obtained by wavelet transform to more effectively capture the global background information and local context relationships. In addition, features of different scales can be extracted while minimizing feature loss, thereby improving the stability of completion. Solving the problem that the traditional method uses Fourier transform for frequency-domain feature extraction but relies on fixed sine basis functions and cannot adapt to the multi-scale characteristics of signals.

[0080] In this application, complex convolution is used to fuse the weekly mean and daily fluctuations of the current scale to enhance the interaction between local and global information. Subsequently, learnable wavelet transform is used to further extract high-frequency and low-frequency information, fuse the low-frequency features representing the global trend with the features of other scales, and then restore them to the spatial domain through inverse wavelet transform to achieve fine-grained completion; this method realizes more abundant frequency information modeling through inverse wavelet transform, improves the quality of the completion results, makes the local details of the sea surface temperature image clearer, and the learnable wavelet upsampling realizes high-precision reconstruction of multi-scale features in the decoding stage through inverse wavelet transform and dynamically optimized wavelet basis functions.

[0081] The following further describes the specific embodiments of this application in detail with reference to the accompanying drawings. Description of the Drawings

[0082] The accompanying drawings, as part of this application, are used to provide a further understanding of this application. The schematic embodiments and descriptions thereof of this application are used to explain this application, but do not constitute an improper limitation of this application. Obviously, the accompanying drawings in the following description are only some embodiments, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0083] In the accompanying drawings of the specification:

[0084] Figure 1 is the logical schematic diagram of the overall sea temperature completion based on deep learnable wavelet multi-scale mining in this specific embodiment;

[0085] Figure 2 is the logical schematic diagram of the global self-attention module in this specific embodiment;

[0086] Figure 3 is the logical schematic diagram of the local self-attention module in this specific embodiment. Specific Embodiment

[0087] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. The following embodiments are used to illustrate the present application but are not used to limit the scope of the present application.

[0088] Please refer to Figure 1 、 Figure 2 and Figure 3 , the present application provides a sea temperature completion method based on deep learnable wavelet multi-scale mining, including obtaining a weekly mean image and the missing image of the current day , subtracting the two to obtain the daily fluctuation image , inputting the daily fluctuation image and the weekly mean image into the multi-scale adaptive wavelet encoder module, and after being processed by the multi-scale adaptive wavelet encoder module and then input into the inverse wavelet transform decoder module based on multi-scale fusion, the finally completed and complete sea temperature image is output ; wherein, there are N layers of deep frequency-domain learnable wavelet downsampling modules connected in sequence in the multi-scale adaptive wavelet encoder module, and there are N layers of inverse wavelet upsampling modules connected in sequence in the inverse wavelet transform decoder module based on multi-scale fusion;

[0089] Specifically, it includes the following steps:

[0090] Step S1, after the daily fluctuation image and the weekly mean image are processed by global self-attention, they are used as the input of the N layers of deep frequency-domain learnable wavelet downsampling modules. The low-frequency information and high-frequency information of different scales of the input image are obtained through learnable discrete wavelet transform. The low-frequency information and high-frequency information of each scale are fused and then output to the next layer of the deep frequency-domain learnable wavelet downsampling module until the output reaches the Nth layer of the deep frequency-domain learnable wavelet downsampling module;

[0091] Step S2: Use the fusion feature output by the (N - 1)-th layer of depth-frequency domain learnable wavelet downsampling module as the input of the N-th layer of inverse wavelet upsampling module, and use the low-frequency information of the N-th layer of depth-frequency domain learnable wavelet downsampling module as the input of the N-th layer of inverse wavelet upsampling module. Obtain the low-frequency and high-frequency information of different scales of the input fusion feature through learnable discrete wavelet transform. After fusing the obtained low-frequency and high-frequency information of each scale with the low-frequency information of the input N-th layer of depth-frequency domain learnable wavelet downsampling module, output it to the inverse wavelet upsampling module of the previous layer until it is output to the first layer of inverse wavelet upsampling module;

[0092] Step S3: Use inverse wavelet transform to simulate the upsampling operation on the fusion feature output to the first layer of inverse wavelet upsampling module and the feature processed by global self-attention in Step S1, and output the finally completed full sea surface temperature image 。

[0093] It should be noted that the execution subject of the sea surface temperature completion method in this embodiment is a sea surface temperature completion device based on depth-learnable wavelet multi-scale mining. This device can be an electronic device, a component in an electronic device, an integrated circuit, or a chip. The electronic device can be a mobile electronic device or a non-mobile electronic device. Exemplarily, the mobile electronic device can be a mobile phone, a tablet computer, a laptop computer, a handheld computer, a vehicle-mounted electronic device, a wearable device, etc., and the non-mobile electronic device can be a server and a personal computer, etc. This application does not make specific limitations. Hereinafter, taking the execution subject as a server as an example, the sea surface temperature completion method based on depth-learnable wavelet multi-scale mining in this embodiment will be described.

[0094] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the embodiments of this application, "a plurality" means two or more unless otherwise specifically defined.

[0095] Please refer to Figure 1 and Figure 2 , in a realizable embodiment, in Step S1, when the daily fluctuation image and the weekly average image are processed by the linear layer and the global self-attention module, the operations of obtaining the weighted feature representation and are the same as the subsequent processing operations, where obtaining the weighted feature representation specifically includes:

[0096] Process the daily fluctuation image through the linear layer to obtain a dimension of Input features The input features are processed through a global self-attention module to obtain a weighted feature representation ;

[0097] The steps for obtaining the weighted feature representation include:

[0098] Three vectors are generated through multiplication calculations and are expressed as:

[0099] ;

[0100] ;

[0101] ;

[0102] wherein , are three learnable parameter matrices representing the multiplication operation;

[0103] Calculations are performed through the attention formula and are expressed as:

[0104] ;

[0105] wherein is the dimension of the vector ;

[0106] The obtained output is subjected to a convolution operation and is expressed as:

[0107] ;

[0108] wherein represents the convolution operation.

[0109] Please refer to Figure 1 , in an implementable embodiment, in step S1, low-frequency information and high-frequency information at different scales of the input image are obtained through learnable discrete wavelet transform, including inputting the weighted feature representation into a depth frequency-domain learnable wavelet downsampling module for processing, and using the learnable discrete wavelet transform through the learnable discrete wavelet transform module to decompose the weighted feature representation into four subbands, and the decomposition formula is expressed as:

[0110] ;

[0111] ;

[0112] ;

[0113] ;

[0114] Among them, respectively represent low-frequency, horizontal high-frequency, vertical high-frequency, and diagonal high-frequency convolution operators, and represent analysis vectors, which are used for low-frequency waves and high-frequency waves respectively, and are expressed as:

[0115] ;

[0116] ;

[0117] Among them, and are the scaling function and the wavelet function respectively, k is the translation parameter, which controls the moving position of the wavelet function and the scaling function on the signal, and t represents the spatial variable;

[0118] Obtain low-frequency information , horizontal high-frequency information , vertical high-frequency information and diagonal high-frequency information , which are expressed as:

[0119] ;

[0120] ;

[0121] ;

[0122] ;

[0123] Among them, represents the convolution operation, represents the low-frequency information, represents the horizontal high-frequency information, represents the vertical high-frequency information, represents the diagonal high-frequency information;

[0124] Fuse the horizontal high-frequency information , vertical high-frequency information and diagonal high-frequency information to obtain the high-frequency information , which is expressed as:

[0125] ;

[0126] Among them, concat represents the concatenation operation.

[0127] In this embodiment, by introducing a learnable discrete wavelet transform module, the wavelet basis function is dynamically optimized during the training process in a data-driven manner. According to the frequency distribution characteristics of the sea surface temperature data, the high-frequency and low-frequency decomposition methods are flexibly adjusted to more accurately model multi-scale signals such as short-period (high-frequency) and seasonal ocean current trends (low-frequency), and have the ability of frequency-domain adaptive modeling. This dynamic adjustment characteristic is the key breakthrough for this embodiment to solve the problem that the fixed wavelet method cannot take into account multi-scale modeling.

[0128] In this embodiment, by using the learnable wavelet transform to replace the convolutional downsampling operation, not only the scale compression is performed, but more importantly, the learnable wavelet transform can dynamically control the ratio of low-frequency / high-frequency information, enabling the model to achieve a balance between retaining local boundary sensitivity and overall trend consistency. Therefore, the feature extraction mechanism of this embodiment is essentially an "adaptive frequency-domain dimensionality reduction strategy", which is more preservative and directional than the traditional spatial convolutional downsampling, and the information loss is significantly reduced.

[0129] Please refer to Figure 1 and Figure 3 , in a feasible implementation manner, before fusing the low-frequency information and the high-frequency information in step S1, the low-frequency information is first processed through a local self-attention module to obtain a weighted feature representation , including defining the size of the local area as , the stride is 8, and the whole input feature is slid over. For the input feature , use operation to extract the local window feature, expressed as:

[0130] ;

[0131] Among them, is the number of extracted windows, and the dimension of each window feature is ;

[0132] For each local window feature , calculate the weighted feature representation of each local window feature : Three vectors are generated through multiplication calculation, expressed as:

[0133] ;

[0134] ;

[0135] ;

[0136] Among them, 、 are three learnable parameter matrices, representing a multiplication operation;

[0137] Calculated through the attention formula, expressed as:

[0138] ;

[0139] where, is the dimension of the vector ;

[0140] Perform a convolution operation on the obtained output, expressed as:

[0141] ;

[0142] Use operation to recombine the obtained local attention features into a complete feature map:

[0143] ;

[0144] where, respectively represent the window features calculated through the attention mechanism;

[0145] The feature and the low-frequency information are calculated through a residual connection to obtain a weighted feature representation , expressed as:

[0146] ;

[0147] where, represents a residual connection;

[0148] Fuse the low-frequency information and the high-frequency information, including fusing the weighted feature representation and the high-frequency information together to obtain the feature , and the fusion process is expressed as:

[0149] ;

[0150] where concat represents a concatenation operation.

[0151] Please refer to Figure 1 , Figure 2 and Figure 3 , in practical applications, the multi-scale adaptive wavelet encoder module has the same processing operation for the daily fluctuation image and the weekly average image . In step S1, N takes the integer three, and for the daily fluctuation image Weighted feature representation obtained by processing through a linear layer and a global self-attention module and the weekly mean image Features obtained by processing through a linear layer and a global self-attention module Input the first-layer depth-frequency domain learnable wavelet downsampling module, and the first-layer depth-frequency domain learnable wavelet downsampling module outputs the fused features and the fused features To the second-layer depth-frequency domain learnable wavelet downsampling module, and the second-layer depth-frequency domain learnable wavelet downsampling module outputs the fused features and the fused features To the third-layer depth-frequency domain learnable wavelet downsampling module, and the third-layer depth-frequency domain learnable wavelet downsampling module outputs the weighted feature representation and 。

[0152] Among them, the first-layer depth-frequency domain learnable wavelet downsampling module and the second-layer depth-frequency domain learnable wavelet downsampling module both simulate the downsampling operation and output the fused representation containing low-frequency and high-frequency features, which is used to capture the multi-level coupling mode between short-term perturbations (high frequencies) and large-scale background trends (low frequencies); while in the third-layer depth-frequency domain learnable wavelet downsampling module, the downsampling is simulated, and only low-frequency features are extracted, and the high-frequency information is no longer retained. The reasons include: after multiple downsamplings, the image size continuously shrinks, and the features gradually enter the abstract expression stage. At this time, the information contained in the high-frequency subband is mainly the residual of edge details, which often has a weak correlation with the macrostructure of sea surface temperature. Retaining the high-frequency components may instead introduce redundant noise or mislead the feature fusion judgment. Sea surface temperature data has obvious smooth evolution characteristics on a global scale, and the core structure information such as seasonal trends and ocean circulation is mainly contained in the low-frequency subband. At the deepest layer of the network, only retaining the low-frequency information is beneficial to strengthening the global steady-state modeling ability and providing strong consistent background information support for the subsequent reconstruction stage.

[0153] It should be noted that in the multi-scale adaptive wavelet encoder module based on daily fluctuations, for the problem that the Fourier transform is used for frequency-domain feature extraction, but the Fourier transform relies on fixed sine basis functions and cannot adapt to the multi-scale characteristics of signals, this embodiment proposes a depth-frequency domain learnable wavelet downsampling module. By simulating the downsampling operation with learnable wavelets, the low-frequency and high-frequency information of different scales of the image is obtained, solving the problem that traditional methods cannot adapt to the multi-scale characteristics of signals. At the same time, the learnable wavelet transform adopted enables the wavelet basis to be adaptively adjusted according to the data distribution during the training process, so as to more accurately extract features of different scales.

[0154] Please refer to Figure 1, in practical applications, in step S2, N is taken as the integer three, and the low-frequency information of the third-layer depth-frequency-domain learnable wavelet downsampling module is used as the input of the third-layer inverse wavelet upsampling module, including the daily fluctuation image in the third-layer depth-frequency-domain learnable wavelet downsampling module and the weekly mean image of the weighted feature representation and are subjected to a complex convolution operation to obtain a feature and then input into the third-layer inverse wavelet upsampling module, which is expressed as:

[0155] ;

[0156] Among them, represents the complex convolution operation;

[0157] The fused feature output by the second-layer depth-frequency-domain learnable wavelet downsampling module is used as the input of the third-layer inverse wavelet upsampling module, including the fused feature output in the second-layer depth-frequency-domain learnable wavelet downsampling module and are subjected to a complex convolution operation to obtain a feature and then input into the third-layer inverse wavelet upsampling module, which is expressed as:

[0158] ;

[0159] The third-layer inverse wavelet upsampling module obtains the high-frequency information of different scales of the input image through the learnable discrete wavelet transform, including performing the learnable discrete wavelet transform operation on the feature to respectively obtain the low-frequency information and the high-frequency information , and ;

[0160] The third-layer inverse wavelet upsampling module performs a complex convolution operation on the obtained feature and the low-frequency information to obtain a feature , which is expressed as:

[0161] ;

[0162] Through the inverse learnable discrete wavelet transform module, the inverse wavelet transform is used to simulate the upsampling operation, and the obtained high-frequency information and the low-frequency information of the third-layer depth-frequency-domain learnable wavelet downsampling module are fused and output, including the feature , the high-frequency information , and The output after fusion is obtained by performing inverse learnable discrete wavelet transform through the inverse learnable discrete wavelet transform module, and features are obtained. ;

[0163] The output of the inverse wavelet upsampling module in the subsequent layer outputs the fused features to the inverse wavelet upsampling module in the previous layer until it is output to the first-layer inverse wavelet upsampling module, including the third-layer inverse wavelet upsampling module outputting the features to the second-layer inverse wavelet upsampling module, and the second-layer inverse wavelet upsampling module outputs the features to the first-layer inverse wavelet upsampling module, and the first-layer inverse wavelet upsampling module outputs the finally completed full sea surface temperature image .

[0164] In this embodiment, the inverse learnable wavelet transform module is used to simulate upsampling, and a data-driven wavelet kernel is used to gradually reconstruct multi-scale frequency information. This mechanism retains the wavelet information in the encoding stage, supports fine control of the reduction ratio of each scale information in the decoding stage, realizes end-to-end high-frequency precision control and full-frequency domain reconstruction closed-loop, and is significantly better than the blurring problem in the existing methods using fixed interpolation for reconstruction.

[0165] Please refer to Figure 1 , in a realizable embodiment, the features , high-frequency information , and after being fused through the inverse learnable discrete wavelet transform by the inverse learnable discrete wavelet transform module, including concatenating the features , high-frequency information , and , which is expressed as:

[0166] ;

[0167] where concat represents the concatenation operation;

[0168] Using the inverse wavelet kernel to perform grouped convolution on the feature map in the wavelet domain , and obtaining the features , which is expressed as:

[0169] ;

[0170] The inverse wavelet kernel is composed of the following four convolution kernels concatenated together:

[0171] ;

[0172] ;

[0173] ;

[0174] ;

[0175] Among them, and are the inverse analysis vectors for low-frequency and high-frequency analysis respectively, expressed as:

[0176] ;

[0177] ;

[0178] The output of the inverse wavelet upsampling module of the latter layer outputs the fused features to the inverse wavelet upsampling module of the previous layer until it outputs to the first-layer inverse wavelet upsampling module, including the features and the features and the obtained features input into the second-layer inverse wavelet upsampling module for processing and outputting features to the first-layer inverse wavelet upsampling module. The first-layer inverse wavelet upsampling module will output the features and the daily fluctuation image and the weekly mean image after being processed by the linear layer and the global self-attention module and output and perform inverse wavelet transform to simulate upsampling and output the final completed image .

[0179] In this embodiment, by introducing the global self-attention module and the local self-attention module, residual connection and inverse wavelet transform reconstruction, not only the context understanding between features is enhanced, but also the information of different scale sub-bands is connected through the deep frequency domain feature interaction fusion structure, enabling the model to establish a stronger coupling relationship between spatial details and frequency components. Especially in non-stationary scenes such as sea surface temperature anomaly regions (such as fronts), the boundary consistency and structural coherence are improved.

[0180] It should be noted that in the inverse wavelet transform decoder module based on multi-scale fusion, in the sea surface temperature completion task, the traditional method uses Fourier transform for frequency domain feature extraction. However, the Fourier transform relies on fixed sine basis functions, which cannot adapt to the multi-scale characteristics of signals and has a relatively simple feature fusion method, lacking deep multi-scale feature interaction. In this embodiment, an inverse wavelet transform is proposed to simulate the upsampling operation, and an optimizable wavelet basis is used during the training process, enabling the wavelet basis to be adaptively adjusted during training, so that the completion result is more in line with the actual feature distribution of the sea surface temperature image. This solves the problem that the traditional method uses Fourier transform for frequency domain feature extraction, but the Fourier transform relies on fixed sine basis functions and cannot adapt to the multi-scale characteristics of signals. At the same time, each inverse wavelet upsampling module receives features of different scales as well as the weekly mean and outliers of the current scale as inputs, realizing multi-scale feature interaction and solving the problem of relatively simple feature fusion methods and lack of deep multi-scale feature interaction.

[0181] In this embodiment, a processing mechanism with time modeling ability is designed for the strong time evolution characteristics shown by sea temperature data in actual observations. Specifically, in the data preprocessing stage of this embodiment, the difference operation of "missing image on the current day - weekly mean image" is introduced to generate a so-called "fluctuation map" for explicitly representing the short-term temperature perturbation of the current observation and the historical average. This difference processing strategy is essentially equivalent to constructing a temporal residual information expression method, which can guide the model to focus on the time dynamic change area from the input end. At the same time, in this embodiment, the "weekly mean image" and the "fluctuation image" are used as inputs, representing the long-term steady-state background and the short-term change trend respectively, and are processed in parallel by a multi-scale learnable wavelet encoder, and a cross-scale and cross-time dynamic feature fusion path is established in cooperation with the global and local attention mechanisms. Although this mechanism does not directly use time series models such as RNN and Transformer, it indirectly realizes the deep modeling of dynamic information in the time dimension at the structural design level, significantly enhancing the model's response ability to spatio-temporal non-stationary characteristics.

[0182] In an implementable embodiment, the loss function is expressed as:

[0183] ;

[0184] It is divided into two parts, where is the current training epoch, is the total number of training epochs, represents the absolute error between the generated image and the missing sea temperature image ; represents the generated image The structural similarity error between the missing sea surface temperature image ;

[0185] Among them, is expressed as:

[0186] ;

[0187] Among them, represents the number of images;

[0188] is expressed as:

[0189] ;

[0190] Among them, and respectively represent the means of the two images and , and represent the standard deviations, represents the covariance of the two images, and represent the constants added to avoid a zero denominator.

[0191] To verify the technical effects achievable by this embodiment, this embodiment selects the complete dataset of SST level 4 products of the National Satellite Ocean Application Service from January 2022 to April 2023. To simulate real cloud cover, this embodiment integrates real cloud masks from the WHU cloud dataset, and the cloud coverages are set to 8%, 25%, 46%, 68% respectively, the signal-to-noise ratios are 0.1, 0.2, 0.3, and the image size is set to 64×64.

[0192] This embodiment uses the root mean square error ( ) and the coefficient of determination ( ) as evaluation indicators to evaluate the reconstruction results. To prove the effectiveness of this embodiment, this embodiment selects the AIN, DINEOF, DINCAE, and Phy_INN methods for comparative experiments. N / S in Tables 1 and 2 represents the signal-to-noise ratio, Cover Ration represents the cloud coverage, Ours represents the method using this embodiment, and the detailed information of the experimental effects is shown in Tables 1 and 2 below:

[0193] Table 1 is the comparison of RMSE between this embodiment and existing methods:

[0194] ;

[0195] Table 2 is the comparison of R 2 between this embodiment and existing methods:

[0196] ;

[0197] As can be seen from Table 1 and Table 2, in all sea surface temperature image completion tasks, the method of this embodiment always shows the lowest value and the highest value, which proves the reliability of this embodiment in improving the completion effect and proves the potential and advantages of this embodiment in practical applications.

[0198] Based on the same inventive concept, the present application also provides a sea temperature completion system based on deep learnable wavelet multi-scale mining, which applies the method described above. The system includes:

[0199] A multi-scale adaptive wavelet encoder module and an inverse wavelet transform decoder module based on multi-scale fusion, which subtract the weekly mean image from the missing image of the current day to obtain the daily fluctuation image . The daily fluctuation image and the weekly mean image are input into the multi-scale adaptive wavelet encoder module. After being processed by the multi-scale adaptive wavelet encoder module and then input into the inverse wavelet transform decoder module based on multi-scale fusion, the finally completed full sea temperature image is output;

[0200] The multi-scale adaptive wavelet encoder module includes a global self-attention module and an N-layer deep frequency domain learnable wavelet downsampling module connected in sequence. The inverse wavelet transform decoder module based on multi-scale fusion has an N-layer inverse wavelet upsampling module connected in sequence, where N is an integer greater than one. Among them, the N-layer deep frequency domain learnable wavelet downsampling module subtracts the weekly mean image from the daily fluctuation image After being processed by the linear layer and the global self-attention module, it serves as the input to the N-layer deep frequency-domain learnable wavelet downsampling module. Through the learnable discrete wavelet transform, the low-frequency information and high-frequency information of different scales of the input image are obtained. The low-frequency information and high-frequency information of each scale are fused and then output to the next layer of the deep frequency-domain learnable wavelet downsampling module until the output reaches the N-layer deep frequency-domain learnable wavelet downsampling module; the N-layer inverse wavelet upsampling module takes the fused features output by the N-1 layer deep frequency-domain learnable wavelet downsampling module as the input of the N-layer inverse wavelet upsampling module, and takes the low-frequency information of the N-layer deep frequency-domain learnable wavelet downsampling module as the input of the N-layer inverse wavelet upsampling module. Through the learnable discrete wavelet transform, the low-frequency information and high-frequency information of different scales of the input image are obtained. The obtained low-frequency information and high-frequency information of each scale and the low-frequency information of the N-layer deep frequency-domain learnable wavelet downsampling module are fused and then output to the previous layer of the inverse wavelet upsampling module until the output reaches the first layer inverse wavelet upsampling module;

[0201] The fused features output until the first layer inverse wavelet upsampling module and the features processed by the global self-attention module in step S2 are used to simulate the upsampling operation through the inverse wavelet transform, and the final complete sea surface temperature image is output 。

[0202] In an implementable embodiment, the deep frequency-domain learnable wavelet downsampling module includes a learnable discrete wavelet transform module, a local self-attention module, and a fusion module;

[0203] The learnable discrete wavelet transform module obtains the low-frequency information and high-frequency information of different scales of the input image through the learnable discrete wavelet transform, including the learnable discrete wavelet transform module processing the weighted feature representation to obtain the low-frequency information and fusing to obtain the high-frequency information ;

[0204] The local self-attention module processes the low-frequency information through the attention mechanism to obtain the weighted feature representation ;

[0205] The fusion module fuses the low-frequency information and the high-frequency information, including fusing the weighted feature representation and the high-frequency information to fuse and output the fused features 。

[0206] In an implementable embodiment, the inverse wavelet upsampling module includes a first complex convolution module, a second complex convolution module, a learnable discrete wavelet transform module, and an inverse learnable discrete wavelet transform module;

[0207] The first complex convolution module performs complex convolution operations on the fused features and to obtain features and then inputs them into the learnable discrete wavelet transform module;

[0208] The learnable discrete wavelet transform module performs learnable discrete wavelet transform operations on the features to respectively obtain low-frequency information and high-frequency information 、 and ;

[0209] The second complex convolution module performs complex convolution operations on the low-frequency information and the features to obtain features and inputs them into the inverse learnable discrete wavelet transform module;

[0210] The inverse learnable discrete wavelet transform module fuses the features , high-frequency information , and using the inverse learnable discrete wavelet transform and outputs the fused features to the inverse wavelet upsampling module of the previous layer until the output reaches the first-layer inverse wavelet upsampling module, including inputting the features output by the first-layer depth-frequency domain learnable wavelet downsampling module, the features and the obtained features into the second-layer inverse wavelet upsampling module for processing and outputting features to the first-layer inverse wavelet upsampling module. The first-layer inverse wavelet upsampling module processes the output features and the daily fluctuation image and the weekly mean image through the linear layer and the global self-attention module and outputs the features and to perform inverse wavelet transform to simulate upsampling and output the final completed image .

[0211] The above are only the preferred embodiments of the present application, and there is no restriction on the present application in any form. Although the present application has been disclosed above with the preferred embodiments, it is not intended to limit the present application. Any person skilled in the art can make some changes or modifications to the above-mentioned technical content as equivalent embodiments with equivalent changes within the scope of the technical solution of the present application. The implementation schemes in the above embodiments can also be further combined or replaced. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present application without departing from the technical solution of the present application still belong to the scope of the present application.

Claims

1. The sea temperature completion method based on deep learnable wavelet multi-scale mining is characterized by: include: Get weekly mean image and missing images of the day , and the difference between the two is used to obtain the fluctuation image of the day , the daily fluctuation image and weekly mean images The multi-scale adaptive wavelet encoder module is input, and after being processed by the multi-scale adaptive wavelet encoder module, it is input into the inverse wavelet transform decoder module based on multi-scale fusion, and the final completed sea temperature image is output. ; In the multi-scale adaptive wavelet encoder module, N layers of deep frequency domain learnable wavelet down-sampling modules are sequentially connected, and in the multi-scale fusion-based inverse wavelet transform decoder module, N layers of inverse wavelet up-sampling modules are sequentially connected; The specific steps include: Step S1: The fluctuation image of the day and weekly mean images After global self-attention processing, it is used as the input of the N-layer deep frequency domain learnable wavelet downsampling module. The low-frequency information and high-frequency information of the input image at different scales are obtained through the learnable discrete wavelet transform. The low-frequency information and high-frequency information of each scale are fused and output to the deep frequency domain learnable wavelet downsampling module of the next layer until it is output to the N-th layer deep frequency domain learnable wavelet downsampling module. Step S2, using the fusion features output by the N-1th layer of deep frequency domain learnable wavelet down-sampling module as the input of the Nth layer of inverse wavelet up-sampling module, using the low-frequency information of the Nth layer of deep frequency domain learnable wavelet down-sampling module as the input of the Nth layer of inverse wavelet up-sampling module, obtaining low-frequency information and high-frequency information of different scales of the input fusion features through learnable discrete wavelet transform, fusing the obtained low-frequency information and high-frequency information of each scale with the input low-frequency information of the Nth layer of deep frequency domain learnable wavelet down-sampling module, and outputting them to the previous layer of inverse wavelet up-sampling module until they are output to the first layer of inverse wavelet up-sampling module; Step S3: The fusion features output to the first layer of the inverse wavelet upsampling module and the features after the global self-attention processing in step S1 are simulated by the inverse wavelet transform to simulate the upsampling operation, and the final completed sea temperature image is output. .

2. The method according to claim 1, characterized in that The daily fluctuation image in step S1 and the weekly mean image The weighted feature representation is obtained by processing the linear layer and the global self-attention module respectively. and , the weighted feature representation and The acquisition operation and subsequent processing operation are the same, wherein the weighted feature representation is obtained Specifically include: The current day's volatility graph After processing through the linear layer, the dimension is obtained Input features , the input feature The weighted feature representation is obtained by processing through the global self-attention module .

3. The method according to claim 2, characterized in that In step S1, low-frequency information and high-frequency information of different scales of the input image are obtained by using a learnable discrete wavelet transform, including converting the weighted feature representation The input deep frequency domain learnable wavelet downsampling module is processed, and the weighted feature representation is transformed into the learnable discrete wavelet transform module using the learnable discrete wavelet transform. Decomposed into four sub-bands , , and ,in, , , and Respectively represent low frequency, horizontal high frequency, vertical high frequency and diagonal high frequency convolution operators; Get low frequency information , horizontal high frequency information , vertical high frequency information and diagonal high frequency information , expressed as: ； ； ； ； in, represents the convolution operation, Represents low-frequency information, Represents horizontal high-frequency information, Represents vertical high-frequency information, Represents diagonal high-frequency information; The horizontal high frequency information , vertical high frequency information and diagonal high frequency information Fusion to obtain high-frequency information , expressed as: ； Among them, concat represents a concatenation operation.

4. The method according to claim 3, characterized in that In step S1, before fusing the low-frequency information and the high-frequency information, the low-frequency information is first Processed by local self-attention module to obtain weighted feature representation , including defining the size of the local region as , the step size is 8, sliding covers the entire input feature, for the input feature ,use The operation extracts local window features, which can be expressed as: ； in, is the number of windows extracted, and each window feature The dimension is ; For each local window feature , calculate each local window feature The weighted feature representation of ; use The operation reassembles the obtained local attention features into a complete feature map: ； in, Represents the window Features calculated by the attention mechanism; The characteristics and low frequency information Obtain weighted feature representation through residual connection calculation , expressed as: ； in, represents residual connection; The low-frequency information and the high-frequency information are fused, including weighted feature representation and high frequency information Fusion together to obtain features , the fusion process is expressed as: ； Among them, concat represents a concatenation operation.

5. The method according to claim 4, characterized in that In step S2, N is an integer of three, and the low-frequency information of the third-layer deep frequency domain learnable wavelet downsampling module is used as the input of the third-layer inverse wavelet upsampling module, including the intraday fluctuation image in the third-layer deep frequency domain learnable wavelet downsampling module. and the weekly mean image The weighted feature representation of and After performing the complex convolution operation, the features are obtained Then input the third layer inverse wavelet upsampling module, expressed as: ； in, Represents a complex convolution operation; The fused features output by the second-layer deep frequency domain learnable wavelet downsampling module are used as the input of the third-layer inverse wavelet upsampling module, including the fused features output by the second-layer deep frequency domain learnable wavelet downsampling module. and Perform complex convolution operation to obtain features Then input the third layer inverse wavelet upsampling module, expressed as: ； The third layer inverse wavelet upsampling module obtains high-frequency information of different scales of the input image through a learnable discrete wavelet transform, including converting the feature Perform learnable discrete wavelet transform operations to obtain low-frequency information and high frequency information , and ; The third layer inverse wavelet upsampling module will obtain the features With low frequency information Perform complex convolution operation to obtain features , expressed as: ； The inverse learnable discrete wavelet transform module is used to simulate the upsampling operation by using the inverse wavelet transform, and the obtained high-frequency information and the low-frequency information of the third-layer deep frequency domain learnable wavelet downsampling module are fused and output, including the feature , high frequency information , and The inverse learnable discrete wavelet transform module is used to fuse and output the features. ; The inverse wavelet upsampling module of the next layer outputs the fused features to the inverse wavelet upsampling module of the previous layer until it is output to the inverse wavelet upsampling module of the first layer, including the inverse wavelet upsampling module of the third layer. Output to the second layer of inverse wavelet upsampling module, the second layer of inverse wavelet upsampling module outputs the feature To the first layer of inverse wavelet upsampling module, the first layer of inverse wavelet upsampling module outputs the final completed sea temperature image .

6. The method according to claim 5, characterized in that The features , high frequency information , and After fusion using the inverse learnable discrete wavelet transform module, the features , high frequency information , and The concatenation is expressed as: ； Among them, concat represents the concatenation operation; Using the inverse wavelet kernel Feature map in wavelet domain Perform group convolution to obtain features , expressed as: ； The inverse wavelet upsampling module of the next layer outputs the fused features to the inverse wavelet upsampling module of the previous layer until it is output to the inverse wavelet upsampling module of the first layer, including the features output by the deep frequency domain learnable wavelet downsampling module of the first layer. and Features and the features obtained Input the second layer of inverse wavelet upsampling module to process the output features To the first layer of inverse wavelet upsampling module, the first layer of inverse wavelet upsampling module will output the features And the same day fluctuation image and the weekly mean image The features output after being processed by the linear layer and the global self-attention module and Perform inverse wavelet transform to simulate upsampling and output the final completed image .

7. The method according to claim 5, characterized in that The loss function is expressed as: ； It is divided into two parts, is the current training epoch, is the total number of training rounds, Represents the generated image With missing SST images The absolute error between Represents the generated image With missing SST images The structural similarity error between in, It is expressed as: ； in, Indicates the number of images; It is expressed as: ； in, and Represents two images respectively and The mean of and represents the standard deviation, is the covariance of the two images, and is a constant added to avoid the denominator being zero.

8. The sea temperature completion system based on deep learnable wavelet multi-scale mining is characterized by: The method according to any one of claims 1 to 7 is applied, wherein the system comprises: The multi-scale adaptive wavelet encoder module and the inverse wavelet transform decoder module based on multi-scale fusion transform the weekly mean image and missing images of the day Subtract and get the volatility image of the day , the daily fluctuation image and weekly mean images The multi-scale adaptive wavelet encoder module is input, and after being processed by the multi-scale adaptive wavelet encoder module, it is input into the inverse wavelet transform decoder module based on multi-scale fusion, and the final completed sea temperature image is output. ; The multi-scale adaptive wavelet encoder module includes a global self-attention module and an N-layer deep frequency domain learnable wavelet downsampling module connected in sequence, and the multi-scale fusion-based inverse wavelet transform decoder module includes N-layer inverse wavelet upsampling modules connected in sequence, where N is an integer greater than one; wherein the N-layer deep frequency domain learnable wavelet downsampling module converts the intraday fluctuation image and the weekly mean image After being processed by the linear layer and the global self-attention module, it is used as the input of the N-layer deep frequency domain learnable wavelet downsampling module, and the low-frequency information and high-frequency information of different scales of the input image are obtained through the learnable discrete wavelet transform, and the low-frequency information and high-frequency information of each scale are fused and output to the deep frequency domain learnable wavelet downsampling module of the next layer until it is output to the N-th layer deep frequency domain learnable wavelet downsampling module; N-layer inverse wavelet upsampling module, taking the fusion features output by the N-1th layer deep frequency domain learnable wavelet downsampling module as the input of the N-layer inverse wavelet upsampling module, taking the low-frequency information of the N-layer deep frequency domain learnable wavelet downsampling module as the input of the N-layer inverse wavelet upsampling module, obtaining low-frequency information and high-frequency information of different scales of the input image through learnable discrete wavelet transform, fusing the obtained low-frequency information and high-frequency information of each scale with the low-frequency information of the N-layer deep frequency domain learnable wavelet downsampling module, and outputting them to the previous layer of inverse wavelet upsampling module until they are output to the first layer of inverse wavelet upsampling module; The fusion features output to the first layer of the inverse wavelet upsampling module and the features processed by the global self-attention module in step S2 are transformed through inverse wavelet to simulate the upsampling operation and output the final completed sea temperature image. .

9. The system according to claim 8, characterized in that The deep frequency domain learnable wavelet downsampling module includes a learnable discrete wavelet transform module, a local self-attention module and a fusion module; The learnable discrete wavelet transform module obtains low-frequency information and high-frequency information of different scales of the input image through the learnable discrete wavelet transform, including the learnable discrete wavelet transform module converting the weighted feature representation Processing to obtain low-frequency information And fusion to get high frequency information ; The local self-attention module converts low-frequency information Processed through the attention mechanism to obtain weighted feature representation ; The fusion module fuses the low-frequency information and the high-frequency information, including weighting the feature representation and high frequency information Fusion output fusion features ; The learnable discrete wavelet transform module outputs the fusion feature The output is sent to the deep frequency domain learnable wavelet down-sampling module of the next layer until it is sent to the deep frequency domain learnable wavelet down-sampling module of the Nth layer. The deep frequency domain learnable wavelet down-sampling module of the Nth layer outputs the acquired low-frequency information to the inverse wavelet up-sampling module of the Nth layer.

10. The system according to claim 9, characterized in that The inverse wavelet upsampling module includes a first complex convolution module, a second complex convolution module, a learnable discrete wavelet transform module and an inverse learnable discrete wavelet transform module; The first complex convolution module fuses the features and Perform complex convolution operation to obtain features Then input the learnable discrete wavelet transform module; The learnable discrete wavelet transform module transforms the features Perform learnable discrete wavelet transform operations to obtain low-frequency information and high frequency information , and ; The second complex convolution module converts low-frequency information and Features After performing the complex convolution operation, the features are obtained Input the inverse learnable discrete wavelet transform module; The inverse learnable discrete wavelet transform module transforms the features , high frequency information , and After fusion using inverse learnable discrete wavelet transform, the fusion features are output to the inverse wavelet upsampling module of the previous layer until they are output to the first layer of inverse wavelet upsampling module, including the features output by the first layer of deep frequency domain learnable wavelet downsampling module. and Features and the features obtained Input the second layer of inverse wavelet upsampling module to process the output features To the first layer of inverse wavelet upsampling module, the first layer of inverse wavelet upsampling module will output the features And the same day fluctuation image and the weekly mean image The features output after being processed by the linear layer and the global self-attention module and Perform inverse wavelet transform to simulate upsampling and output the final completed image .

Images