Sea temperature complementation method and system based on depth learnable wavelet multi-scale mining

Abstract

The invention relates to the field of image processing, and discloses a sea temperature completion method and system based on depth learnable wavelet multi-scale mining, and the method comprises the steps: S2, simulating down-sampling operation through learnable discrete wavelet transformation, fusing low-frequency information and high-frequency information, and outputting the fused information until an Nth layer depth frequency domain learnable wavelet down-sampling module; s3, simulating an up-sampling operation through inverse wavelet transform, fusing the obtained low-frequency information and high-frequency information with the low-frequency information of the Nth-layer depth frequency domain learnable wavelet down-sampling module, and outputting the fused information to a first-layer inverse wavelet up-sampling module; and S4, performing inverse wavelet transformation on the fusion features output to the first layer of inverse wavelet up-sampling module and the features subjected to global self-attention processing in the S2 to simulate up-sampling operation, and outputting a final complemented complete sea temperature image. According to the method, the problem of frequency domain decomposition stiffness caused by the fixed primary function and the problem that the multi-scale characteristic of the signal cannot be adapted are effectively solved.

Description

Technical Field

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

[0002] Using deep learning to complete sea surface temperature images can improve the accuracy and spatiotemporal resolution of data completion, provide more reliable data for key areas such as meteorological forecasting, climate research, and marine ecological monitoring, and thus enhance the comprehensive understanding and prediction capabilities of the marine system. This is crucial for addressing climate change and protecting the marine ecological environment. At present, the sea surface temperature image completion method based on deep learning adopts the feature modeling method of "frequency domain feature extraction + cascade fusion". This method uses the mechanism of "frequency domain feature extraction + cascade fusion" to capture periodic steady-state features, adjacent time features, and current background information through a three-stream neural network, and uses high-pass and low-pass filters to dynamically extract key frequency domain information, thereby achieving high-quality reconstruction of sea temperature data.

[0003] However, this method has the following problems: First, Fourier transform is used for frequency domain feature extraction, but Fourier transform relies on a fixed sinusoidal basis function and cannot adapt to the multi-scale characteristics of the signal. For example, when Fourier transform is used for frequency domain feature extraction, its fixed sinusoidal basis function is difficult to adapt to high-frequency and low-frequency features of different scales, which limits the multi-scale modeling of sea surface temperature images. In sea surface temperature images, high-frequency information usually corresponds to short-time scale temperature changes, such as small-scale eddies, 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 optimization strategies for high- and low-frequency features of different scales. For example, in the frontal area, small-scale high-frequency information is crucial to the accurate characterization of the boundaries. If the high-frequency features of different scales are not adaptively optimized, the completion results may lead to blurred boundaries or loss of details. In the large-scale ocean current area, low-frequency information dominates the overall trend. If information at different scales cannot interact effectively, it may affect the global consistency of the completion results.

[0004] Second, the feature fusion method is relatively simple and lacks deep multi-scale feature interaction. For example, this method mainly splices Fourier transform features and uses cascade fusion to complete them. However, this direct splicing method fails to fully establish the deep connection between features of different scales, and it is difficult to effectively utilize the mutual information of each scale, which may lead to inconsistency in the completion results in local areas. For example, when completing small-scale ocean eddies, fronts and other structures, temperature changes often have complex spatiotemporal dependencies. Simple splicing of features alone may not accurately capture the synergistic relationship between high-frequency local dynamics and low-frequency global background, resulting in blurred local details, unclear boundaries or discontinuities in the completed 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 shortcomings of the existing technology and provide a sea temperature completion method and system based on deep learnable wavelet multi-scale mining.

[0006] To achieve the above objectives, the first aspect of the present application provides a sea temperature completion method based on deep learnable wavelet multi-scale mining, comprising: 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 multi-scale fusion-based inverse wavelet transform decoder module to output the final completed sea temperature image. ; 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. .

[0007] Optionally, 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 .

[0008] Optionally, 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.

[0009] Optionally, before fusing the low-frequency information and the high-frequency information in step S1, 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.

[0010] Optionally, 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 .

[0011] Optionally, the feature , 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 .

[0012] Optionally, 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.

[0013] To achieve the above-mentioned purpose, the second aspect of the present application provides a sea temperature completion system based on deep learnable wavelet multi-scale mining, which is applied with the above-mentioned method, and 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. .

[0014] Optionally, 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 to the deep frequency domain learnable wavelet down-sampling module of the next layer until it is output 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.

[0015] 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; 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 .

[0016] After adopting the above technical solution, the present application has the following beneficial effects compared with the prior art: In this application, the wavelet basis functions are dynamically optimized during the training process to achieve frequency domain adaptive feature extraction, which significantly improves the modeling capability of complex spatiotemporal dynamics of SST data. The data-driven dynamic adjustment of the basis functions significantly enhances the modeling capability of multi-scale spatiotemporal dynamics of SST data. Specifically, the decomposition weights of low-frequency components (such as seasonal changes, large-scale ocean current trends) and high-frequency components (such as short-term eddies, frontal fluctuations) can be autonomously optimized according to the distribution characteristics of the input data, thereby accurately capturing the global consistency characteristics and local detail changes of the SST field. The problem of frequency domain decomposition rigidity caused by the fixed basis functions of traditional methods is effectively solved, which significantly improves the physical rationality and detail restoration of the completion results.

[0017] In this application, a learnable wavelet transform is used to simulate the downsampling operation, and the retention weights of high-frequency components are dynamically adjusted by allowing the basis function to be adaptively optimized during training, thereby reducing information loss. This solves the problem that the traditional encoder downsampling process achieves feature dimensionality reduction by compressing the spatial dimension, resulting in irreversible loss of high-frequency detail information (such as edges and textures). At the same time, the local self-attention mechanism further processes the low-frequency information obtained by the wavelet transform to more effectively capture global background information and local contextual relationships. In addition, features of different scales can be extracted while minimizing feature loss, thereby improving the stability of completion. This solves the problem that the traditional method uses Fourier transform for frequency domain feature extraction, but relies on a fixed sinusoidal basis function and cannot adapt to the multi-scale characteristics of the signal.

[0018] In this application, complex convolution is used to fuse the features of the weekly mean and daily fluctuation of the current scale to enhance the interaction between local and global information. Subsequently, high-frequency and low-frequency information is further extracted through learnable wavelet transform, and the low-frequency features representing the global trend are fused with the features of other scales, and then restored to the spatial domain through inverse wavelet transform to achieve fine-grained completion; this method achieves richer frequency information modeling through inverse wavelet transform, improves the quality of the completion result, and makes the local details of the sea surface temperature image clearer. Learnable wavelet upsampling achieves high-precision reconstruction of multi-scale features in the decoding stage through inverse wavelet transform and dynamically optimized wavelet basis function.

[0019] The specific implementation methods of the present application are further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The accompanying drawings are part of this application and are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application, but do not constitute an improper limitation on this application. Obviously, the drawings described below are only some embodiments. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0021] In the drawings of the specification: Figure 1 It is a logical schematic diagram of the overall sea temperature completion based on deep learnable wavelet multi-scale mining in this specific implementation method; Figure 2 is a logical schematic diagram of the global self-attention module in this specific implementation mode; Figure 3 It is a logical schematic diagram of the local self-attention module in this specific implementation. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments will be clearly and completely described below in conjunction with the 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.

[0023] See also Figure 1 , Figure 2 and Figure 3 This application provides a sea temperature completion method based on deep learnable wavelet multi-scale mining, including obtaining a 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. ; Among them, the multi-scale adaptive wavelet encoder module has N layers of deep frequency domain learnable wavelet down-sampling modules connected in sequence, and the multi-scale fusion-based inverse wavelet transform decoder module has N layers of inverse wavelet up-sampling modules connected in sequence; 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. .

[0024] It should be noted that the execution subject of the sea temperature completion method in this embodiment is a sea temperature completion device based on deep learnable wavelet multi-scale mining, which 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 PDA, a vehicle-mounted electronic device, a wearable device, etc., and the non-mobile electronic device can be a server and a personal computer, etc., which are not specifically limited in this application. The following takes the execution subject as an example of a server to describe the sea temperature completion method based on deep learnable wavelet multi-scale mining in this embodiment.

[0025] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of the present application, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0026] See also Figure 1 and Figure 2 In one achievable implementation, in step S1, the daily fluctuation image and weekly mean images Through the linear layer and the global self-attention module, the weighted feature representation and The acquisition operation and subsequent processing operation are the same, where the weighted feature representation is obtained Specifically include: The current day's volatility graph After processing through the linear layer, the dimension is Input features , the input feature Processed by the global self-attention module to obtain weighted feature representation ; Obtaining weighted feature representation The steps include: The three vectors are generated by multiplication , expressed as: ; ; ; in, , are three learnable parameter matrices, Represents the multiplication operation; Calculated by the attention formula, expressed as: ; in, It refers to the vector Dimensions; The obtained output is convolved and expressed as: ; in, Represents a convolution operation.

[0027] See also Figure 1 In one achievable implementation, 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 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, the decomposition formula is expressed as: ; ; ; ; in, Respectively represent low frequency, horizontal high frequency, vertical high frequency and diagonal high frequency convolution operators, and denotes the analysis vectors, used for low-frequency waves and high-frequency waves respectively, and It is expressed as: ; ; in, and are the scale function and wavelet function respectively, k is the translation parameter, which controls the moving position of the wavelet function and the scale function on the signal, and t represents the spatial variable; 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.

[0028] In this embodiment, a learnable discrete wavelet transform module is introduced to dynamically optimize the wavelet basis function during the training process in a data-driven manner. The high- and low-frequency deconstruction methods are flexibly adjusted according to the frequency distribution characteristics of the sea temperature data, and multi-scale signals such as short-cycle (high frequency) and seasonal ocean current trends (low frequency) are more accurately modeled, with frequency domain adaptive modeling capabilities. This dynamic adjustment feature is the key breakthrough in this embodiment to solve the problem that the fixed wavelet method cannot take into account multi-scale modeling.

[0029] This embodiment uses a learnable wavelet transform to replace the convolution downsampling operation, which not only performs scale compression, but more importantly, the learnable wavelet transform can dynamically control the ratio of low-frequency / high-frequency information, so that the model can 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 conservative and directional than traditional spatial convolution downsampling, and significantly reduces information loss.

[0030] See also Figure 1 and Figure 3 In one achievable implementation, before fusing the low-frequency information and the high-frequency information in step S1, 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 : Generate three vectors through multiplication , expressed as: ; ; ; in, , are three learnable parameter matrices, Represents the multiplication operation; Calculated by the attention formula, expressed as: ; in, It refers to the vector Dimensions; The obtained output is convolved and expressed as: ; 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; Fusion of low-frequency information and high-frequency information, 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.

[0031] See also Figure 1 , Figure 2 and Figure 3 In practical applications, the multi-scale adaptive wavelet encoder module is used to decode the daily fluctuation image. and weekly mean images The processing operation is the same as that of step S1. In step S2, N is an integer of three. Weighted feature representation obtained by processing the linear layer and the global self-attention module And the weekly mean image Features processed by linear layer and global self-attention module Input the first layer of deep frequency domain to learn the wavelet downsampling module, the first layer of deep frequency domain to learn the wavelet downsampling module output fusion features and fusion features The second-layer deep frequency domain can learn the wavelet downsampling module, and the second-layer deep frequency domain can learn the wavelet downsampling module output fusion features and fusion features The third layer of deep frequency domain can learn the wavelet downsampling module, and the third layer of deep frequency domain can learn the wavelet downsampling module output weighted feature representation and .

[0032] Among them, the first layer of deep frequency domain learnable wavelet downsampling module and the second layer of deep frequency domain learnable wavelet downsampling module simulate downsampling operations and both output fusion representations containing low-frequency and high-frequency features, which are used to capture the multi-level coupling mode between short-term disturbances (high frequency) and large-scale background trends (low frequency); while the third layer of deep frequency domain learnable wavelet downsampling module simulates downsampling, only extracts low-frequency features, and no longer retains high-frequency information. The reasons include: after multiple downsampling, the image size continues to shrink, and the features gradually enter the abstract expression stage. At this time, the information contained in the high-frequency sub-band is mainly the residual of edge details, which is often weakly correlated with the macroscopic structure of sea temperature. Retaining high-frequency components may introduce redundant noise or mislead feature fusion judgment. Sea temperature data has obvious smooth evolution characteristics on a global scale, and core structural information such as seasonal trends and ocean circulation is mainly contained in low-frequency sub-bands. At the deepest layer of the network, only low-frequency information is retained, which is conducive to strengthening the global steady-state modeling capability and providing strong consistency background information support for the subsequent reconstruction stage.

[0033] It should be noted that in the multi-scale adaptive wavelet encoder module based on daily fluctuations, Fourier transform is used for frequency domain feature extraction, but Fourier transform relies on a fixed sinusoidal basis function and cannot adapt to the multi-scale characteristics of the signal. In this embodiment, a deep frequency domain learnable wavelet downsampling module is proposed. Through the learnable wavelet simulation downsampling operation, low-frequency and high-frequency information of different scales of the image is obtained, which solves the problem that the traditional method cannot adapt to the multi-scale characteristics of the signal. At the same time, the learnable wavelet transform adopted allows the wavelet basis to be adaptively adjusted during the training process according to the data distribution, thereby more accurately extracting features of different scales.

[0034] See also Figure 1 In practical applications, 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 daily fluctuation image in the third-layer deep frequency domain learnable wavelet downsampling module. and weekly mean images The weighted feature representation of and After performing the complex convolution operation, the features are obtained Then input the third layer of 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 of inverse wavelet upsampling module, expressed as: ; The third layer of inverse wavelet upsampling module obtains high-frequency information of different scales of the input image through the learnable discrete wavelet transform, including the feature Perform learnable discrete wavelet transform operations to obtain low-frequency information and high frequency information , and ; The third layer of 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 uses the inverse wavelet transform to simulate the upsampling operation, and the high-frequency information obtained is fused with the low-frequency information of the third-layer deep frequency domain learnable wavelet downsampling module and then 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 inverse wavelet upsampling module, the second layer 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 .

[0035] This embodiment uses an inverse learnable wavelet transform module to simulate upsampling, and uses a data-driven wavelet kernel to achieve gradual reconstruction of multi-scale frequency information. This mechanism retains the wavelet information in the encoding stage, supports fine control of the restoration ratio of each scale information in the decoding stage, and achieves end-to-end high-frequency precision control and full-frequency domain reconstruction closed loop, which is significantly better than the fuzzy problem of fixed interpolation reconstruction in existing methods.

[0036] See also Figure 1 In one possible implementation, the feature , 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: ; Inverse wavelet kernel It is composed of the following four convolution kernels: ; ; ; ; in, and are the inverse analysis vectors for low-frequency and high-frequency analysis, respectively, 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 daily volatility graph and weekly mean images The output after processing by the linear layer and the global self-attention module and Perform inverse wavelet transform to simulate upsampling and output the final completed image .

[0037] This embodiment not only enhances the contextual understanding between features by introducing global self-attention modules and local self-attention modules, residual connections and inverse wavelet transform reconstruction, but also connects sub-band information of different scales through deep frequency domain feature interactive fusion structure, so that the model can establish a stronger coupling relationship between spatial details and frequency components. In particular, in non-stationary scenes such as sea temperature anomalies (such as fronts), boundary consistency and structural coherence are improved.

[0038] 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 to extract frequency domain features, but the Fourier transform relies on a fixed sine basis function, which cannot adapt to the multi-scale characteristics of the signal and the feature fusion method is relatively simple, lacking the problem of deep multi-scale feature interaction. This embodiment proposes to simulate the upsampling operation with the help of inverse wavelet transform, and uses an optimizable wavelet basis during the training process, so that the wavelet basis can be adaptively adjusted during the training process, so that the completion result is more in line with the actual feature distribution of the sea surface temperature image. The problem that the traditional method uses Fourier transform to extract frequency domain features, but the Fourier transform relies on a fixed sine basis function and cannot adapt to the multi-scale characteristics of the signal. At the same time, each inverse wavelet upsampling module receives features of different scales and the weekly mean and outliers of the current scale as input, realizes multi-scale feature interaction, and solves the problem that the feature fusion method is relatively simple and lacks deep multi-scale feature interaction.

[0039] This embodiment designs a processing mechanism with time modeling capabilities in view of the strong temporal evolution characteristics of sea temperature data in actual observations. Specifically, this embodiment introduces the difference operation of "missing image of the day-weekly average image" in the data preprocessing stage to generate the so-called "fluctuation map" to explicitly represent the short-term temperature disturbance between the current observation and the historical average. This difference processing strategy is essentially equivalent to constructing a time series residual information expression method, which can guide the model to pay attention to the time dynamic change area from the input end. At the same time, in this embodiment, both "weekly average image" and "fluctuation image" are used as inputs, representing the long-term steady-state background and short-term change trend respectively, and are processed in parallel through multi-scale learnable wavelet encoders, and global and local attention mechanisms are used to establish a cross-scale and cross-time dynamic feature fusion path. 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, and significantly enhances the model's response ability to spatiotemporal non-stationary characteristics.

[0040] In one feasible implementation, 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, represents the covariance of the two images, and Represents a constant added to avoid the denominator being zero.

[0041] In order to verify the technical effect that can be achieved by this embodiment, this embodiment selects the complete data set of SST4-level products of the National Satellite Ocean Application Service from January 2022 to April 2023. In order to simulate real cloud coverage, this embodiment integrates real cloud masks from the WHU cloud data set. The cloud coverage rates are set to 8%, 25%, 46%, and 68%, respectively, the signal-to-noise ratios are 0.1, 0.2, and 0.3, and the image size is set to 64×64.

[0042] This embodiment uses the root mean square error ( ) and the coefficient of determination ( ) is used as an evaluation index to evaluate the reconstruction results. To prove the effectiveness of the proposed embodiment, this embodiment selects 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 rate, and Ours represents the method of this embodiment. The detailed information of the experimental results is shown in Tables 1 and 2 below: Table 1 is a comparison of RMSE between this embodiment and the existing method: ; Table 2 shows the relationship between R in this embodiment and the existing method. 2 Comparison: ; According to Table 1 and Table 2, in all sea surface temperature image completion tasks, the method of this embodiment always shows the lowest Value and highest This proves the reliability of this embodiment in improving the completion effect and proves the potential and advantages of this embodiment in practical applications.

[0043] 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 is applied with the method described above, and the system includes: 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. 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. Among them, the N-layer deep frequency domain learnable wavelet downsampling module converts the daily fluctuation image and weekly mean images 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 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; the N-layer inverse wavelet upsampling module uses the fused features output by the N-1-th layer deep frequency domain learnable wavelet downsampling module as the input of the N-th layer inverse wavelet upsampling module, and uses the low-frequency information of the N-th layer deep frequency domain learnable wavelet downsampling module as the input of the N-th layer inverse wavelet upsampling module. The low-frequency information of the N-th layer deep frequency domain learnable wavelet downsampling module is obtained through the learnable discrete wavelet transform. The low-frequency information and high-frequency information of each scale obtained are fused with the low-frequency information of the N-th layer deep frequency domain learnable wavelet downsampling module and output to the previous layer inverse wavelet upsampling module until it is output to the first layer 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. .

[0044] In one achievable implementation, 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 to represent the weighted features 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 low-frequency information with high-frequency information, including weighted feature representation and high frequency information Fusion output fusion features .

[0045] In an achievable implementation, 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 will fuse the features and Perform complex convolution operation to obtain features The latter input can learn the 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 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 daily volatility graph and weekly mean images 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 .

[0046] The above are only preferred embodiments of the present application, and are not intended to limit the present application in any form. Although the present application has been disclosed as above with preferred embodiments, it is not intended to limit the present application. Any technician familiar with the present application can make some changes or modifications to equivalent embodiments of equivalent changes using the above-mentioned technical contents without departing from 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 modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present application without departing from the content of the technical solution of the present application are still within the scope of the solution 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 .

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