Sea surface temperature super-resolution method and system based on global and local frequency domain perception

Abstract

The present application relates to the field of ocean remote sensing big data processing and computer vision technology, and discloses a sea surface temperature super-resolution method and system based on global and local frequency domain perception. The method comprises the following steps: low-resolution sea surface temperature data is mapped into shallow features, multi-layer frequency domain perception operation is performed, the shallow features are processed through global frequency domain aggregation operation and multi-scale gating network, and then intermediate features are output through convolution, the intermediate features are decoupled through frequency domain to obtain amplitude spectrum and phase spectrum, amplitude increment is generated through phase-guided amplitude modulation, and after high-frequency constraint, the amplitude increment is recombined with the phase spectrum, and after inverse transformation, the output result is fused with the shallow feature residual to obtain the output result. After convolution, the output result is connected with the shallow feature through skip connection and then up-sampled, the up-sampled features are fused with the original data residual, and super-resolution reconstruction data is output. The present application overcomes the over-smoothing tendency caused by the spatial domain method, and improves the reconstruction accuracy of high-frequency details of the sea surface temperature in the reconstruction process.

Description

Technical Field

[0001] This invention belongs to the field of marine remote sensing big data processing and computer vision technology, and specifically relates to a method and system for sea surface temperature super-resolution based on global and local frequency domain perception. Background Technology

[0002] Sea surface temperature is a crucial indicator for studying global climate change and a key reference for assessing the state of the marine environment. High-resolution sea surface temperature data not only reflects macroscopic temperature distribution but also reveals fine local texture features, thus playing a vital role in climate monitoring, environmental assessment, and real-time weather forecasting. However, in practical remote sensing observations, hardware performance limitations exist in the spatial coverage, resolution, and signal-to-noise ratio of imaging sensors, making it difficult for observation systems to simultaneously achieve wide-area coverage and high-resolution sampling. To meet the needs of large-scale coverage, existing systems often sacrifice sampling accuracy, making it difficult for the acquired sea surface temperature data to fully represent the subtle structure of local temperature changes, thus failing to meet the current urgent need for refined marine environmental monitoring.

[0003] To compensate for the limitations of hardware observations, researchers initially relied primarily on traditional spatial interpolation, statistical downscaling, and data assimilation reconstruction methods to improve the spatial resolution of sea surface temperature data. Initially, extrapolation techniques based on spatial geometry and topology, such as bicubic interpolation, nearest-neighbor interpolation, and Kriging interpolation from geostatistics, were widely used. However, these methods, relying solely on the numerical smoothing combination of adjacent pixels, often resulted in severe edge blurring and loss of dynamic details in the reconstruction results. To incorporate more physical priors, subsequent research gradually shifted towards statistical downscaling methods. This involved establishing multivariate regression models between low-resolution sea surface temperature and high-resolution auxiliary geophysical parameters such as sea surface height, water depth, offshore distance, or chlorophyll concentration, thereby uncovering deeper spatial details. Furthermore, methods such as optimal interpolation based on variational dynamic constraints and empirical orthogonal function decomposition have also played important roles in linear smoothing and multi-source remote sensing data fusion.

[0004] Although these traditional methods have laid the foundation for scale-up of ocean data, their generalization ability and high-frequency detail reconstruction accuracy are still greatly limited when facing complex ocean-atmosphere coupling scenarios with strong nonlinearity and multi-scale evolution characteristics, due to their heavy reliance on artificially designed physical features and linear simplification assumptions.

[0005] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] To address or at least alleviate one or more of the aforementioned problems, this invention constructs a global-aware, locally refined frequency-domain sensing architecture by mapping sea surface temperature data to the frequency domain. At the global level, frequency domain information is used as a guide to adaptively cluster and associate spatially separated but similarly frequency-domain feature regions. At the local level, an explicit frequency-domain decoupling mechanism is used to evaluate the frequency-domain complexity of local regions. Under the constraint of structural information, the intensity of feature enhancement is adaptively allocated based on the complexity of local high-frequency features. This global-local frequency-domain sensing design strategy effectively overcomes the oversmoothing tendency easily caused by spatial domain methods, improving the reconstruction accuracy of high-frequency details of sea surface temperature during the reconstruction process.

[0007] To achieve the above objectives, according to a first aspect of the present invention, a sea surface temperature super-resolution method based on global and local frequency domain sensing is provided, comprising: S1. Extraction of low-resolution sea surface temperature data: Low-resolution sea surface temperature data The data is mapped to shallow features and then subjected to multi-level frequency domain sensing operations. S2, Frequency Domain Guided Global Context Refinement: In each layer of frequency domain sensing operation, shallow features are normalized and then processed by a global frequency domain aggregation operation and a multi-scale gated feedforward network to obtain a gated fusion result. The gated fusion result is mapped to the output of the frequency domain-guided global context refinement part. Output results The first is obtained through convolution. Intermediate features of the layer ; S3, Frequency Domain Sensing Local Adaptive Enhancement: intermediate features The amplitude spectrum and phase spectrum are obtained through frequency domain decoupling operations. The amplitude increment is obtained from the phase spectrum through phase-guided amplitude modulation operations. ; for amplitude increment The final amplitude increment is obtained by performing high-frequency constraint processing. The final amplitude increment The phase spectrum is reconstructed in the frequency domain and transformed in the spatial domain, then convolved and fused with the shallow feature residuals to output the result. ; S4, Upsampling fusion: result The first layer is obtained by convolution and skip connection with shallow features. Features of the layer after frequency domain sensing local adaptive enhancement ,feature After upsampling, it is compared with low-resolution sea surface temperature data. Residual fusion is performed to obtain super-resolution reconstruction data.

[0008] Furthermore, after layer normalization of the shallow features, the gated fusion result is obtained through global frequency domain aggregation and multi-scale gated feedforward network processing, including: Shallow features are normalized and expanded into word sequences according to spatial location. After channel mean pooling, spatial features are extracted. The spatial features are then transformed into frequency domain features through frequency domain transformation. The frequency domain features are normalized by constructing frequency domain energy histograms for each frequency band to generate local frequency domain descriptors. The local frequency domain descriptors are clustered through joint similarity calculation of the spatial and frequency domains and a complexity-aware dual-weight routing mechanism to obtain an aggregated global feature sequence. After aggregating the global feature sequences and performing a linear transformation, the gated fusion result is obtained through linear processing via two independent convolutional branches.

[0009] Furthermore, the frequency domain features are normalized by constructing frequency domain energy histograms for each frequency band, generating local frequency domain descriptors, including: The frequency domain energy value at each frequency point is calculated using the real and imaginary parts of the frequency domain features. The frequency domain energy values ​​of all frequency points are arranged according to their frequency coordinates to form a frequency domain energy map. With the frequency domain origin as the center, the radial Euclidean distance from each frequency point to the frequency domain origin is calculated based on the longitudinal and transverse frequency coordinates of each frequency point. The radial Euclidean distance at the boundary of the frequency domain plane is used as a reference for normalization to obtain the normalized radial coordinates of each frequency point. The frequency domain plane containing the normalized radial coordinates is divided into multiple non-overlapping radial frequency bands. A binary radial mask is constructed, and all frequency points falling within the radial frequency bands are selected using the binary radial mask. The frequency energy values ​​of all frequency points are summed and divided by the number of frequency points within the radial frequency band to obtain the average energy of the radial frequency band. The average energy of all radial frequency bands is used to form a frequency domain energy histogram, which is then normalized to generate the local frequency domain descriptor for each term.

[0010] Furthermore, by clustering local frequency domain descriptors through joint similarity calculation in the spatial and frequency domains and a complexity-aware dual-weight routing mechanism, an aggregated global feature sequence is obtained, including: Initial cluster centers in the spatial domain and frequency domain are obtained by average pooling. Based on the current initial cluster centers in the spatial domain and frequency domain, the words are clustered and the mean of word features within each cluster is calculated. The initial cluster centers in the spatial domain and frequency domain are updated based on the mean using an exponential moving average method. In the spatial domain, the cosine similarity between the spatial features of a word and the current spatial domain cluster center is calculated to obtain the spatial domain similarity. In the frequency domain, the cosine similarity between the local frequency domain descriptor and the current frequency domain cluster center is calculated to obtain the frequency domain similarity. The spatial domain similarity and the frequency domain similarity are adaptively weighted and fused to obtain the joint similarity. Frequency energy is calculated based on the relative frequency energy of local frequency domain descriptors to obtain the high-frequency energy ratio and frequency domain information entropy; the 1st frequency domain descriptor in the word sequence is... The content features corresponding to each spatial location and the local frequency domain descriptor are concatenated along the feature dimension and input into the content gating branch. The input is then passed through the first fully connected layer, the ReLU activation function, the second fully connected layer, and the ReLU activation function to obtain the content gating features. At the same time, the high-frequency energy ratio and the frequency domain information entropy are concatenated along the feature dimension and input into the complexity gating branch. The input is then passed through the first fully connected layer, the ReLU activation function, and the second fully connected layer to obtain the complexity gating features. The content-gated features and complexity-gated features are added together and then subjected to a nonlinear mapping to obtain the joint gated features; The joint gating features are input into the spatial domain weight prediction head and the frequency domain weight prediction head, respectively. The spatial domain weight and frequency domain weight are obtained through the Sigmoid function, and then normalized to obtain the spatial domain routing weight and frequency domain routing weight. The final routing score is obtained by weighting and fusing spatial domain routing weights and frequency domain routing weights with spatial domain similarity and frequency domain similarity. The frequency domain cluster center to which the word belongs is selected based on the routing score. Internal self-attention is calculated for words belonging to the same cluster center, and cross-attention is calculated for words between different cluster centers. The calculated internal self-attention features and cross-attention features are added element-wise according to the corresponding word positions, and then rearranged according to the original spatial positions of each word to obtain the aggregated global feature sequence.

[0011] Furthermore, after aggregating the global feature sequences and performing a linear transformation, the gated fusion result is obtained through linear processing via two independent convolutional branches, including: The aggregated global feature sequence is fed into a multi-scale gated feedforward network, undergoes linear transformation, and is then processed through two convolutional branches: The result is obtained through spatially depth-separable convolution. Branches The result is obtained by performing a nonlinear mapping after spatially depth-separable convolutional layers. ,result With results The result of the fusion is a gated fusion.

[0012] Furthermore, intermediate features The amplitude spectrum and phase spectrum are obtained through frequency domain decoupling operations. The amplitude increment is obtained from the phase spectrum through phase-guided amplitude modulation operations. ; for amplitude increment The final amplitude increment is obtained by performing high-frequency constraint processing. ,include: intermediate features The signal is transformed to the frequency domain and decoupled into amplitude and phase spectra. The phase spectra are then concatenated along the channel axis. The concatenated phase spectra are fed into a lightweight complex frequency domain cross-bottom mapping layer for interaction, and then mapped by a sigmoid activation function to output a complex frequency domain attention mask. Complex frequency domain attention mask The amplitude increment is obtained by element-wise multiplication with the amplitude spectrum. ; The frequency domain complexity vector is composed of the high-frequency energy ratio and the frequency domain information entropy. It is input into the first fully connected layer and mapped as a hidden feature. The hidden feature is input into the second fully connected layer and mapped as the initial prediction weights of multiple high-frequency sub-bands and further mapped as the adjustment weights of each high-frequency sub-band. The adaptive cutoff radius is calculated based on the high-frequency energy ratio. A high-pass filter mask is constructed by the radial Euclidean distance and the adaptive cutoff radius. The region whose radial Euclidean distance is greater than the adaptive cutoff radius and is located within the boundary of the frequency domain plane is determined as the high-frequency region and is equally divided into multiple non-overlapping high-frequency sub-bands. Construct the corresponding sub-band binary mask based on the radial Euclidean distance of the current frequency domain unit, and assign the adjustment weight of each high-frequency sub-band to all frequency domain units within the sub-band to obtain the frequency band sensing weight map. Frequency band sensing weight map, high-pass filter mask, and amplitude increment By performing cascaded weighting, the final amplitude increment is obtained. .

[0013] Furthermore, the lightweight complex frequency domain cross-bottom mapping layer passes through a convolutional layer, a ReLU activation layer, and another convolutional layer in sequence.

[0014] Furthermore, the final amplitude increment The phase spectrum is reconstructed in the frequency domain and transformed in the spatial domain, then convolved and fused with the shallow feature residuals to output the result. ,include: Final amplitude increment The reconstructed spatial domain texture residual is obtained by recombination with the phase spectrum, projected onto space through a two-dimensional inverse discrete Fourier transform, and then convolved. A self-learning adjustable scaling factor is then used to combine the reconstructed spatial domain texture residual with intermediate features. The final output result is obtained by performing residual addition and fusion. .

[0015] To achieve the above objectives, according to a second aspect of the present invention, a sea surface temperature super-resolution system based on global and local frequency domain sensing is provided, the sea surface temperature super-resolution system comprising: The low-resolution sea surface temperature data extraction module is used for extracting low-resolution sea surface temperature data: [The module extracts low-resolution sea surface temperature data from the sea surface temperature data.] The data is mapped to shallow features and then subjected to multiple frequency domain sensing operations. The frequency-domain guided global context refinement module is used for frequency-domain guided global context refinement. In each layer of frequency-domain perception operation, shallow features are processed by layer normalization and then processed by a global frequency-domain aggregation operation and a multi-scale gated feedforward network to obtain a gated fusion result. The gated fusion result is mapped to the output of the frequency-domain guided global context refinement module. Output results The first is obtained through convolution. Intermediate features of the layer ; Frequency domain sensing local adaptive enhancement module, used for frequency domain sensing local adaptive enhancement: intermediate features The amplitude spectrum and phase spectrum are obtained through frequency domain decoupling operations. The amplitude increment is obtained from the phase spectrum through phase-guided amplitude modulation operations. ; for amplitude increment The final amplitude increment is obtained by performing high-frequency constraint processing. The final amplitude increment The phase spectrum is reconstructed in the frequency domain and transformed in the spatial domain, then convolved and fused with the shallow feature residuals to output the result. ; The upsampling fusion module is used for upsampling fusion: Results The first layer is obtained by convolution and skip connection with shallow features. Features of the layer after frequency domain sensing local adaptive enhancement ,feature After upsampling, it is compared with low-resolution sea surface temperature data. Residual fusion is performed to obtain super-resolution reconstruction data.

[0016] By adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art: This invention integrates frequency domain feature associations of distant spatial locations globally through global frequency domain aggregation operations and multi-scale gated feedforward network processing. This overcomes the limitation of the receptive field in spatial domain convolution, significantly improving the overall consistency and structural fidelity of macroscopic sea surface temperature (SST) distribution reconstruction. By obtaining amplitude and phase spectra through frequency domain decoupling, and using the phase spectrum to guide amplitude modulation followed by high-frequency constraint processing, it ensures that high-frequency details are accurately aligned with key structural locations such as fronts and vortices, avoiding artifacts caused by blind enhancement. After frequency domain recombination and spatial domain transformation, it is fused with shallow feature residuals, achieving sufficient enhancement of local high-frequency details while fully preserving the low-frequency background. By using skip connections and upsampling residual fusion, it effectively alleviates the attenuation of deep feature information, ensuring stable transmission of shallow spatial structure information to the reconstruction output. This invention achieves significant improvements in macroscopic temperature field consistency, local detail restoration accuracy, and noise immunity, providing high-quality data support for SST forecasting and marine environmental monitoring.

[0017] This invention proposes a Global and Local Frequency Domain Aware Super-Resolution Reconstruction Network (GLFA), mainly composed of two modules. The first module is a frequency domain-guided global context refinement module, which realizes cross-space global frequency domain feature association. First, the spatial features are divided into blocks, and the frequency domain coefficients of the local spatial neighborhood are captured using the two-dimensional discrete Fourier transform (DFT). Then, frequency bands are divided radially to construct normalized local frequency domain descriptors. Subsequently, a complexity-aware dual-weight routing mechanism is used to jointly measure the similarity between spatial features and frequency domain descriptors, adaptively routing feature blocks with similar frequency domain characteristics but spatial separation to different clusters for global interaction. During training, a frequency domain consistency loss constraint consisting of intra-class compactness and inter-class separation is explicitly introduced, which, together with a multi-scale gated feedforward network (MSG-FFN), reconstructs details and provides the model with consistent macro-global guidance. The second module is a frequency domain-aware local adaptive enhancement module (FLAE), which realizes spatial-frequency domain decoupling and adaptive enhancement of details. The module transforms the features to the frequency domain through DFT, explicitly splitting them into amplitude spectrum and phase spectrum. The phase spectrum is used as a priori to guide amplitude spectrum modulation. A frequency-domain attention mask is generated through lightweight bottleneck mapping to control amplitude increments, ensuring that high-frequency features match phase information. Simultaneously, the dynamic cutoff radius of the radial high-pass mask is adaptively calculated based on the high-frequency energy proportion and the complexity of the frequency-domain entropy quantization region, and high-frequency gain is finely allocated using multi-band sensing weights. While protecting the low-frequency background from noise disturbance, local detail enhancement is achieved. Finally, the image is reprojected back into the spatial domain via inverse IDFT for residual fusion.

[0018] The specific embodiments of the present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0019] The accompanying drawings, as part of this invention, are provided to further illustrate the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention, but do not constitute an undue limitation thereof. Clearly, the drawings described below are merely some embodiments; those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0020] In the attached diagram: Figure 1 This is a flowchart illustrating the sea surface temperature super-resolution method based on global and local frequency domain sensing in this specific embodiment. Figure 2 This is a schematic diagram of the frequency domain-guided global context refinement structure in this specific embodiment; Figure 3 This is a schematic diagram of frequency domain sensing local adaptive enhancement in this specific embodiment; Figure 4 This diagram illustrates a qualitative comparison of sea surface temperature fields and sea surface temperature gradient fields using different sea surface temperature products and super-resolution reconstruction methods in this specific embodiment. (a) is the OISST sea surface temperature field, (b) is the GLO12v4 sea surface temperature field, (c) is the HYCOM sea surface temperature field, (d) is the OSTIA reference sea surface temperature field, (e) is the sea surface temperature field reconstructed using the RRDB method, (f) is the sea surface temperature field reconstructed using the SwinIR method, (g) is the sea surface temperature field reconstructed using the ESC method, and (h) is the sea surface temperature field reconstructed using the GLFA method. The reconstructed sea surface temperature fields are as follows: (i) is the OISST sea surface temperature gradient field, (j) is the GLO12v4 sea surface temperature gradient field, (k) is the HYCOM sea surface temperature gradient field, (l) is the OSTIA reference sea surface temperature gradient field, (m) is the sea surface temperature gradient field corresponding to the reconstruction result of the RRDB method, (n) is the sea surface temperature gradient field corresponding to the reconstruction result of the SwinIR method, (o) is the sea surface temperature gradient field corresponding to the reconstruction result of the ESC method, and (p) is the sea surface temperature gradient field corresponding to the reconstruction result of the GLFA method. Figure 5 This is a schematic diagram comparing the power spectral density of different sea surface temperature products and super-resolution reconstruction methods in this specific embodiment; Figure 6 This is a schematic diagram comparing the annual daily evaluation indicators of different sea surface temperature reconstruction results in this specific embodiment. (a) is a comparison curve of the daily root mean square error of GLFA, GLO12v4 and HYCOM in 2024, and (b) is a comparison curve of the daily coefficient of determination of GLFA, GLO12v4 and HYCOM in 2024. Figure 7This diagram illustrates the comparison of sea surface temperature fields and point-by-point error fields for different sea surface temperature products and reconstruction methods in this specific embodiment. (a) is the OSTIA reference sea surface temperature field, (b) is the GLO12v4 sea surface temperature field, (c) is the HYCOM sea surface temperature field, (d) is the sea surface temperature field reconstructed by the GLFA method, (e) is the point-by-point error field of the GLO12v4 sea surface temperature field relative to the OSTIA reference sea surface temperature field, (f) is the point-by-point error field of the HYCOM sea surface temperature field relative to the OSTIA reference sea surface temperature field, and (g) is the point-by-point error field of the sea surface temperature field reconstructed by the GLFA method relative to the OSTIA reference sea surface temperature field. Figure 8 This is a schematic diagram of the architecture of the sea surface temperature super-resolution system based on global and local frequency domain sensing in this specific embodiment. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0022] It should be noted that the terms "first" and "second" in this embodiment are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the embodiments of the present invention, "multiple" means two or more, unless otherwise explicitly specified.

[0023] Example 1: Please see Figure 1 This invention provides a sea surface temperature super-resolution method based on global and local frequency domain sensing, comprising the following steps: S1. Extraction of low-resolution sea surface temperature data: Low-resolution sea surface temperature data The data is mapped to shallow features and then subjected to multi-level frequency domain sensing operations. S2, Frequency Domain Guided Global Context Refinement: In each layer of frequency domain sensing operation, shallow features are normalized and then processed by a global frequency domain aggregation operation and a multi-scale gated feedforward network to obtain a gated fusion result. The gated fusion result is mapped to the output of the frequency domain-guided global context refinement part. Output results The first is obtained through convolution. Intermediate features of the layer ; S3, Frequency Domain Sensing Local Adaptive Enhancement: intermediate features The amplitude spectrum and phase spectrum are obtained through frequency domain decoupling operations. The amplitude increment is obtained from the phase spectrum through phase-guided amplitude modulation operations. ; for amplitude increment The final amplitude increment is obtained by performing high-frequency constraint processing. The final amplitude increment The phase spectrum is reconstructed in the frequency domain and transformed in the spatial domain, then convolved and fused with the shallow feature residuals to output the result. ; S4, Upsampling fusion: result The first layer is obtained by convolution and skip connection with shallow features. Features of the layer after frequency domain sensing local adaptive enhancement ,feature After upsampling, it is compared with low-resolution sea surface temperature data. Residual fusion is performed to obtain super-resolution reconstruction data.

[0024] Specifically, input low-resolution sea surface temperature data. Through a Convolutional layers map image features to spatial features, thus obtaining shallow features. Shallow features Represented as: ; in, , Sea surface temperature data Height and width, Input the number of channels. Represents the convolutional layer mapping operation. This represents the number of feature channels.

[0025] Global-Local Frequency-Aware Network (GLFA) includes: See Figure 1 Shallow features Entering the deep feature mapping stage, the deep feature mapping stage is composed of... It consists of several cascaded frequency-aware blocks (FABs). Each FAB is designed with a collaborative architecture that combines global and local features. It uses a frequency-guided global context refinement module (FGCR) to capture long-distance dependencies and embeds a frequency-aware local adaptive enhancement module (FLAE) at the end to enhance high-frequency features.

[0026] See Figure 2 In some implementations, after shallow features are normalized, gated fusion results are obtained through global frequency domain aggregation and multi-scale gated feedforward network processing, including: Shallow features are normalized and expanded into token sequences according to spatial location. After channel mean pooling, local spatial windows are extracted. Spatial features are transformed into frequency domain features through frequency domain transformation. The frequency domain features are normalized by constructing frequency domain energy histograms for each frequency band to generate local frequency domain descriptors. The local frequency domain descriptors are clustered through joint similarity calculation of the spatial and frequency domains and a complexity-aware dual-weight routing mechanism to obtain an aggregated global feature sequence. After aggregating the global feature sequences and performing a linear transformation, the gated fusion result is obtained through linear processing via two independent convolutional branches.

[0027] Specifically, regarding the normalized shallow features The feature map is transformed from (B, L, C) dimensions to (B, C, H, W) dimensions, and then averaged along the channel dimension C to obtain a single-channel feature map; where, L represents the batch size, C represents the number of tokens, and C represents the channel dimension of each token. Centered on the spatial location corresponding to each word element, using a size of Local window extraction of spatial features, where Indicates the side length of the window; Perform a two-dimensional real-valued fast Fourier transform on the spatial features within each local spatial window to obtain the frequency domain features, i.e., the frequency domain complex coefficients. , This represents the vertical frequency coordinate of a frequency point in the frequency domain. This represents the horizontal frequency coordinate of a frequency point in the frequency domain.

[0028] In some implementations, frequency domain features are normalized by constructing a frequency domain energy histogram for each frequency band to generate local frequency domain descriptors, including: The frequency domain energy value at each frequency point is calculated using the real and imaginary parts of the frequency domain features. The frequency domain energy values ​​of all frequency points are arranged according to their frequency coordinates to form a frequency domain energy map. With the frequency domain origin as the center, the radial Euclidean distance from each frequency point to the frequency domain origin is calculated based on the longitudinal and transverse frequency coordinates of each frequency point. The radial Euclidean distance at the boundary of the frequency domain plane is used as the reference for normalization to obtain the normalized radial coordinates of each frequency point. The frequency domain plane containing the normalized radial coordinates is divided into multiple non-overlapping radial frequency bands. A binary radial mask is constructed. Using the binary radial mask, all frequency points falling into the radial frequency bands are selected from the frequency domain energy map. The frequency energy values ​​of all frequency points are summed and divided by the number of frequency points in the radial frequency band to obtain the average energy of the radial frequency band. The average energies of all radial frequency bands are used to form a frequency domain energy histogram, which is then normalized to generate a local frequency domain descriptor for each term.

[0029] Specifically, the frequency point is calculated using the frequency characteristics, i.e., the real and imaginary parts of the complex coefficients in the frequency domain. The frequency domain energy value at that point is expressed as: ; in, Indicates the first The local space window corresponding to each word in the frequency coordinate Frequency domain energy value at that point Indicates the first The local spatial window corresponding to each word in the frequency coordinate The frequency domain complex coefficients at that point, Represents the real part of the frequency domain complex coefficients. Represents the imaginary part of the complex coefficients in the frequency domain. Indicates the ordinal number of the lexical unit. Represents the vertical frequency coordinate. Represents the horizontal frequency coordinate.

[0030] Specifically, the frequency domain energy values ​​of all frequency points are arranged according to their frequency coordinates to form a frequency domain energy map, which is represented as follows: ; in, Indicates the first Each lexical element corresponds to a frequency domain energy map of a local spatial window. Represents frequency coordinates Frequency domain energy value, sign This means that the frequency domain energy values ​​corresponding to all vertical and horizontal frequency coordinates are arranged according to the two-dimensional frequency position.

[0031] Specifically, with the origin of the frequency domain as the center, the radial Euclidean distance is calculated based on the horizontal and vertical frequency coordinates of the frequency point, expressed as: ; in, Representing frequency point The radial Euclidean distance to the origin of the frequency domain, where the origin of the frequency domain corresponds to a position where both the longitudinal and transverse frequency coordinates are zero.

[0032] Specifically, using the radial Euclidean distance at the boundary of the frequency domain plane as a reference, the radial Euclidean distance is normalized to the interval [0,1] to obtain the normalized radial coordinates, expressed as: ; in, The frequency coordinates are represented as The normalized radial coordinates corresponding to the frequency points. This represents the radial Euclidean distance corresponding to the frequency domain plane boundary of the current local window. This represents a very small positive number used to avoid a denominator of zero.

[0033] Specifically, the frequency domain plane containing the normalized radial coordinates is divided into... Construct a binary radial mask using non-overlapping radial frequency bands, and then use the 1st... Binary radial mask corresponding to each radial frequency band Select the element falling into the frequency domain energy diagram. All frequency points of the radial band, specifically: for the first... Construct a binary radial mask using one radial frequency band. When the frequency point satisfies At that time, let the binary radial mask This indicates that the frequency point belongs to the th A radial frequency band, when the frequency point Not satisfied At that time, let the binary radial mask , indicating frequency point Not belonging to the first One radial frequency band; among which... Indicates the left boundary. Indicates the right boundary, and the last radial frequency band uses To include the right boundary; Sum the frequency energy values ​​of all frequency points and divide by the first frequency. The number of frequency points within the radial frequency band is obtained to determine the number of the first... The average energy of each radial frequency band is expressed as: ; in, Indicates the first Average energy of each radial frequency band This indicates that only the first [item] is retained. Frequency energy values ​​at frequency points within a radial frequency band Indicates the first The number of frequency points contained within a radial frequency band This represents a very small positive number used to avoid a denominator of zero; The average energy of all radial frequency bands is used to construct a frequency domain energy histogram, which is then normalized to obtain the local frequency domain descriptor corresponding to the current term. This descriptor is used to capture the relative distribution of frequency domain energy across different radial frequency bands, and is represented as follows: ; in, Represents the frequency domain energy histogram. This represents the normalized local frequency domain descriptor, used to characterize the relative energy distribution of low-frequency, mid-frequency, and high-frequency components within the local neighborhood of the current word.

[0034] In other implementations, local frequency domain descriptors are clustered using a joint similarity calculation in the spatial and frequency domains and a complexity-aware dual-weight routing mechanism to obtain an aggregated global feature sequence, including: Initial cluster centers in the spatial domain and frequency domain are obtained by average pooling. Based on the current initial cluster centers in the spatial domain and frequency domain, the words are clustered and the mean of word features within each cluster is calculated. The initial cluster centers in the spatial domain and frequency domain are updated based on the mean using an exponential moving average method. In the spatial domain, the cosine similarity between the spatial features of a word and the current spatial domain cluster center is calculated to obtain the spatial domain similarity. In the frequency domain, the cosine similarity between the local frequency domain descriptor and the current frequency domain cluster center is calculated to obtain the frequency domain similarity. The spatial domain similarity and the frequency domain similarity are adaptively weighted and fused to obtain the joint similarity. Frequency energy is calculated based on the relative frequency energy of local frequency domain descriptors to obtain the high-frequency energy ratio and frequency domain information entropy; the 1st frequency domain descriptor in the word sequence is... The content features corresponding to each spatial location and the local frequency domain descriptor are concatenated along the feature dimension and input into the content gating branch. The input is then passed through the first fully connected layer, the ReLU activation function, the second fully connected layer, and the ReLU activation function to obtain the content gating features. At the same time, the high-frequency energy ratio and the frequency domain information entropy are concatenated along the feature dimension and input into the complexity gating branch. The input is then passed through the first fully connected layer, the ReLU activation function, and the second fully connected layer to obtain the complexity gating features. The content-gated features and complexity-gated features are added together and then subjected to a nonlinear mapping to obtain the joint gated features; The joint gating features are input into the spatial domain weight prediction head and the frequency domain weight prediction head, respectively. The spatial domain weight and frequency domain weight are obtained through the Sigmoid function, and then normalized to obtain the spatial domain routing weight and frequency domain routing weight. The final routing score is obtained by weighting and fusing spatial domain routing weights and frequency domain routing weights with spatial domain similarity and frequency domain similarity. The frequency domain cluster center to which the word belongs is selected based on the routing score. Internal self-attention is calculated for words belonging to the same cluster center, and cross-attention is calculated for words between different cluster centers. The calculated internal self-attention features and cross-attention features are added element-wise according to the corresponding word positions, and then rearranged according to the original spatial positions of each word to obtain the aggregated global feature sequence.

[0035] Specifically, spatial domain similarity reflects lexical consistency, while frequency domain similarity measures the consistency of local frequency domain distributions.

[0036] Specifically, spatial domain similarity and frequency domain similarity are adaptively weighted and fused to obtain a joint similarity, expressed as: ; in, and Let represent the spatial domain routing weight and frequency domain routing weight corresponding to the lexical unit, respectively, and satisfy . + =1, Represents spatial domain similarity. Represents frequency domain similarity. This indicates the joint similarity.

[0037] Specifically, based on the local frequency domain descriptor... The relative frequency energy of each word in the b-th frequency band The high-frequency energy proportion and frequency domain information entropy are obtained by performing frequency energy calculations, and are expressed as follows: ; ; in, Indicates the proportion of high-frequency energy. Represents frequency domain information entropy, This represents 16 non-overlapping radial frequency bands.

[0038] Specifically, the content-gated features and complexity-gated features are added together and then subjected to a tanh nonlinear mapping to obtain the joint gated features, which are expressed as follows: ; in, Indicates content gating features, Represents complexity-gated features. Indicates joint gating features, This represents the tanh nonlinear mapping operation.

[0039] Specifically, the joint gating features are input into the spatial domain weight prediction head and the frequency domain weight prediction head, respectively. After passing through the Sigmoid function, the spatial domain weights and frequency domain weights are obtained, as follows: ; ; Where l represents the lexical number, Indicates the first Joint gating features corresponding to each word element This represents the weight matrix of the spatial domain weighted prediction head. The bias parameters represent the spatial domain weighted prediction head. This represents the weight matrix of the frequency domain weighted prediction head. This represents the bias parameters of the frequency domain weighted prediction head. This represents the Sigmoid activation function. Indicates the first The spatial domain weights corresponding to each word element Indicates the first Frequency domain weights corresponding to each word.

[0040] Specifically, the spatial domain routing weights and frequency domain routing weights are obtained after normalization, and are expressed as follows: ; ; in, This represents the smallest positive number used to avoid the normalized denominator being zero and to improve the stability of numerical computation. Indicates the spatial domain routing weight. This represents the frequency domain routing weight.

[0041] Specifically, the routing weights in the spatial domain and frequency domain are weighted and fused with spatial domain similarity and frequency domain similarity to obtain the first... The final routing assignment score between each term and the q-th cluster center is represented as: .

[0042] See Figure 2 In some embodiments, the aggregated global feature sequence undergoes a linear transformation and is then linearly processed through two independent convolutional branches to obtain the gated fusion result, including: The aggregated global feature sequence is fed into a multi-scale gated feedforward network, undergoes linear transformation, and is then processed through two convolutional branches: The result is obtained through spatially depth-separable convolution. Branches The result is obtained by performing a nonlinear mapping after spatial depth separable convolution. ,result With results The result of the fusion is a gated fusion.

[0043] Specifically, to reconstruct the local small-scale geometry of the flow field, the aggregated global feature sequence is fed into a multi-scale gated feed-forward network (MSG-FFN). In MSG-FFN, the flow field is reconstructed through a... After the convolution performs a high-dimensional mapping of the aggregated global feature sequence on the channel axis, it is processed by two convolutional branches: in order to capture the multi-scale geometric spatial context, the branches... Through a The result is obtained by spatial depth separable convolution. Branches Through another The spatial depth can be obtained by nonlinear mapping after separable convolution. The outputs of the two branches are fused to obtain the gated fusion result, which specifically amplifies and supplements the fine high-frequency dynamic local details weakened in the global nonlocal aggregation process, achieving complementary advantages with the global frequency domain context, as expressed as: ; in, and They represent as well as Spatial depth separable convolution, For the dot product operator at the spatial element level, Represents the GELU activation function. This indicates the result of gating fusion.

[0044] See Figure 3 In some embodiments, intermediate features The amplitude spectrum and phase spectrum are obtained through frequency domain decoupling operations. The amplitude increment is obtained from the phase spectrum through phase-guided amplitude modulation operations. ; for amplitude increment The final amplitude increment is obtained by performing high-frequency constraint processing. ,include: intermediate features The signal is transformed to the frequency domain and decoupled into amplitude and phase spectra. The phase spectra are then concatenated along the channel axis. The concatenated phase spectra are fed into a lightweight complex frequency domain cross-bottom mapping layer for interaction, and then mapped by a sigmoid activation function to output a complex frequency domain attention mask. See Figure 3 Attention mask, complex frequency domain attention mask The amplitude increment is obtained by element-wise multiplication with the amplitude spectrum. ; The frequency domain complexity vector is composed of the high-frequency energy ratio and the frequency domain information entropy. It is input into the first fully connected layer and mapped as a hidden feature. The hidden feature is input into the second fully connected layer and mapped as the initial prediction weights of multiple high-frequency sub-bands and further mapped as the adjustment weights of each high-frequency sub-band. The adaptive cutoff radius is calculated based on the high-frequency energy ratio. A high-pass filter mask is constructed by the radial Euclidean distance and the adaptive cutoff radius. The region whose radial Euclidean distance is greater than the adaptive cutoff radius and is located within the boundary of the frequency domain plane is determined as the high-frequency region and is equally divided into multiple non-overlapping high-frequency sub-bands. Construct the corresponding sub-band binary mask based on the radial Euclidean distance of the current frequency domain unit, and assign the adjustment weight of each high-frequency sub-band to all frequency domain units within the sub-band to obtain the frequency band sensing weight map. Frequency band sensing weight map, high-pass filter mask, and amplitude increment By performing cascaded weighting, the final amplitude increment is obtained. .

[0045] Specifically, intermediate features The frequency response is transformed to the frequency domain and then decoupled into independent, orthogonal response components: the amplitude spectrum. ) and phase response (Phase Response) Phase spectrum It implicitly encodes information such as the structural characteristics of sea surface temperature, while the amplitude spectrum... This reflects the energy distribution of each corresponding frequency component.

[0046] Specifically, phase spectrum As a structural physics prior to guide amplitude spectrum The modulation, through this geometric guidance mechanism, ensures that the details generated by the network when amplifying and supplementing high-frequency components can match the boundary contours of the underlying layer, thereby avoiding the introduction of false artifacts.

[0047] Specifically, phase spectrum The phase spectrum is spliced ​​along the channel axis and then fed into a lightweight complex frequency domain cross-bottom mapping layer for interaction. Finally, it is mapped by a Sigmoid activation function to output a complex frequency domain attention mask. Complex frequency domain attention mask With amplitude spectrum Element-wise multiplication yields the amplitude increment. This allows for a better reconstruction of specific high-frequency components related to sea surface temperature details, represented as: ; ; in, This represents the spatial convolution within the lightweight bottleneck layer. and These represent the corresponding activation functions. This is the element-wise dot product of the corresponding frequency domain matrix.

[0048] Specifically, to ensure that the enhancement of high-frequency features does not disturb the already extremely smooth wide-area low-frequency macroscopic background or introduce unnecessary noise, this embodiment adds a set of complexity-aware high-pass filtering constraints. Specifically, frequency domain complexity is calculated using two complementary indicators: high-frequency energy proportion and frequency domain information entropy. The high-frequency energy proportion quantifies the density of high-frequency fluctuations in the total radiated energy, while the frequency domain information entropy measures the degree of dispersion and chaos of frequency domain energy in different radial frequency sub-bands.

[0049] Specifically, the frequency domain complexity vector is composed of the high-frequency energy proportion and the frequency domain information entropy. The input to the first fully connected layer is mapped to hidden features, represented as: ; in, This represents the hidden feature corresponding to the b-th frequency domain complexity vector. and These represent the weight matrix and bias of the first fully connected layer, respectively.

[0050] Specifically, the hidden features are input to the second fully connected layer and mapped to initial prediction weights for multiple high-frequency sub-bands. These weights are further mapped to a range of 0.5 to 1 to obtain the adjustment weights for each high-frequency sub-band, as follows: ; ; in: These represent the initial prediction weights for the first, second, and third high-frequency sub-bands, respectively, with values ​​ranging from 0 to 1; and These represent the weight matrix and bias of the second fully connected layer, respectively. This represents the Sigmoid activation function. Indicates the first Initial prediction weights for each high-frequency sub-band. This represents the adjustment weight of the k-th high-frequency subband.

[0051] Specifically, the adaptive cutoff radius is calculated based on the proportion of high-frequency energy, and is expressed as: ; in, This represents the adaptive cutoff radius corresponding to the b-th sample. Indicates the base cutoff radius. This indicates the adjustment range of the cutoff radius. This indicates the preset reference threshold for the proportion of high-frequency data. This represents the proportion of the high-frequency spectrum amplitude of the b-th sample. This means restricting the variable z to the interval [a, b]. and These represent the lower and upper limits of the allowable values ​​for the adaptive cutoff radius, respectively. In this embodiment, , , , , .

[0052] Specifically, a high-pass filter mask is constructed using radial Euclidean distance and an adaptive cutoff radius, as follows: ; in, Let r(u,v) represent the high-pass filter mask value of the b-th sample at frequency coordinates (u,v), and let r(u,v) represent the radial distance from this frequency element to the zero frequency point. This represents the adaptive cutoff radius of the b-th sample; a mask value of 0 indicates that the corresponding low-frequency amplitude increment is blocked, and a mask value of 1 indicates that the corresponding high-frequency amplitude increment is retained. Specifically, the region with a radial Euclidean distance greater than the adaptive cutoff radius and located within the boundary of the frequency domain plane is defined as the high-frequency region, and is equally divided into three non-overlapping high-frequency sub-bands. A corresponding sub-band binary mask is constructed based on the radial Euclidean distance of the current frequency domain unit, and the adjustment weights of each high-frequency sub-band are assigned to all frequency domain units within the sub-band, resulting in a frequency band-aware weight map, which is used for adaptive redistribution of gain in the high-frequency band; expressed as: ; ; ; in, Indicates the adaptive cutoff radius. This represents the maximum radial Euclidean distance from all frequency domain cells in the current frequency domain plane to the zero frequency point, i.e., the maximum radial distance in the frequency domain plane. Let represent the starting radius of the m-th high-frequency subband in the b-th sample. Let represent the termination radius of the m-th high-frequency subband in the b-th sample. This represents the binary mask for the m-th high-frequency subband in the b-th sample. This represents the frequency band sensing weight map.

[0053] Specifically, this involves the frequency band sensing weight map, high-pass filter mask, and amplitude increment. By performing cascaded weighting, the final amplitude increment is obtained. , is represented as: ; in, This represents element-wise multiplication between corresponding frequency domain units. Used to shield low-frequency regions, retaining only the amplitude increment in high-frequency regions. This is used to apply different adjustment weights to the amplitude increments within different high-frequency subbands. This represents the result obtained after high-pass constraint and adaptive frequency band weighting. A refined amplitude increment.

[0054] In some embodiments, the lightweight complex frequency domain cross bottleneck mapping layer sequentially passes through Convolutional layers, ReLU activation layers and Convolutional layer.

[0055] In some embodiments, the final amplitude increment Phase spectrum Frequency domain reconstruction and spatial domain transformation are performed, followed by convolution processing and integration with shallow features. Residual fusion output results ,include: Final amplitude increment Phase spectrum The reconstructed spatial domain texture residual is obtained by recombining the components, projecting them onto the spatial domain through a two-dimensional inverse discrete Fourier transform, and then performing convolution. This residual is represented as: ; express convolution, This represents the two-dimensional inverse discrete Fourier transform. This represents the reconstructed spatial domain texture residual; Using a self-learning adjustable scaling factor initialized to zero, the reconstructed spatial domain texture residuals and intermediate features are compared. The final output result is obtained by performing residual addition and fusion. , is represented as: ; in, This represents the self-learning adjustable scaling factor initialized to zero.

[0056] In some embodiments, to ensure the stability of deep network training, layer normalization and residual connections are integrated into the FAB block to effectively alleviate the gradient vanishing problem, as shown below: ; ; in, Representation layer normalization, These represent the features used for feature channel integration. Convolution and convolution, This indicates a frequency domain-guided global context refinement module, which internally includes a global frequency domain aggregation and a multi-scale gated feedforward network (MSG-FFN). This represents a frequency domain sensing local adaptive enhancement module; Indicates the first FAB blocks ( ) input, This represents the intermediate features after passing through the frequency domain-guided global context refinement module and convolution. This represents the features of the frequency domain sensing local adaptive enhancement part.

[0057] Example 2: This invention uses OISST as the low-resolution sea surface temperature data input and OSTIA as the high-resolution reference data; the low-resolution image is cropped to 64×64, and the corresponding high-resolution image is cropped to 320×320, resulting in 80,355 valid samples. 60,225 samples from 2021 to 2023 were used for training, and 20,130 samples from 2024 were used for testing; min-max normalization was applied before input.

[0058] The model was implemented in PyTorch and trained on an NVIDIA L40 GPU; the super-resolution magnification was 5, and random rotations and horizontal flips were used for data augmentation during training. The optimizer was Adam, and the initial learning rate was 2×10⁻⁶. −4 The batch size for each GPU is 16, and a total of 400,000 iterations are trained.

[0059] Loss function: During the end-to-end parallel optimization process, the network constructs a loss function to dynamically optimize the model parameters, expressed as: ; in, Represents spatial pixel level Reconstruction loss is used to ensure the absolute accuracy of the sea surface temperature value based on the baseline fit. Represents frequency domain loss, and These represent the intra-class frequency domain compaction loss and the inter-class frequency domain separation loss, respectively. , and These are the corresponding hyperparameter loss weight coefficients, where, =0.1, = =5×10 −4 .

[0060] Example 3: In the experimental section of this invention, the global and local frequency domain sensing super-resolution reconstruction network GLFA of this invention is compared with ocean analysis products GLO12v4, HYCOM, and typical learning-based super-resolution methods RRDB, SwinIR, HAT, and ESC. The evaluation metrics include RMSE, R², PSNR, SSIM, and Bias, as shown in Table 1: Table 1: Super-resolution results of sea surface temperature in four major ocean basins and global sea areas using different products and methods

[0061] As shown in Table 1, the baseline comparisons include ocean analysis products GLO12v4 and HYCOM, as well as deep learning-based super-resolution methods RRDB, SwinIR, HAT, and ESC. Evaluation metrics include root mean square error, coefficient of determination, peak signal-to-noise ratio, structural similarity, and bias. Bold values ​​indicate the best results, and underlined values ​​indicate the second-best results. The results show that in global ocean testing, GLFA achieves RMSE=0.2692, R²=0.9564, PSNR=38.4537, and SSIM=0.9868, which are generally superior to the RRDB, SwinIR, HAT, and ESC methods. Compared to the better-performing ESC method, GLFA's RMSE decreased from 0.2823 to 0.2692, and its PSNR increased from 38.1894 to 38.4537, indicating that this invention can more accurately reconstruct the high-resolution sea surface temperature field. Furthermore, in the reconstruction of the sea surface temperature gradient ΔSST, GLFA achieved the best or near-best results with RMSE=0.0432, PSNR=22.1455, SSIM=0.7058, and Bias=0.0150, indicating that it has a stronger ability to recover local high-frequency details, temperature fronts, and fine-scale structures.

[0062] (1) Quantitative experiment Compared to GLO12v4 and HYCOM, learning-based methods typically achieve lower RMSE and higher PSNR, demonstrating a stronger ability to recover the SST structure. Among them, GLFA achieved competitive quantitative results, producing the lowest RMSE and highest PSNR on a global dataset. This improvement primarily stems from the proposed FGCR, which mitigates the attenuation of high-frequency features common in Transformer-based architectures when modeling long-range spatial dependencies. Results for four ocean basins were further examined.

[0063] The Atlantic Ocean presented the most challenging reconstruction task due to its sharp heat fronts and strong boundary currents, yet GLFA maintained consistent performance compared to other baselines. This demonstrates the robustness of global-local frequency sensing mechanisms in complex ocean environments.

[0064] Gradient reconstruction was further evaluated using the ΔSST metric, where ΔSST represents the gradient of the SST. Methods relying on spatial domain optimization often produce oversmoothing results, leading to the loss of high-frequency gradient information. In contrast, GLFA enhances high-frequency reconstruction through FLAE. Quantitative results show that GLFA achieves lower ΔSST RMSE and PSNR in the global ocean and four basins, indicating that the model not only improves pixel-level accuracy but also enhances the structural fidelity of the SST gradient.

[0065] (2) Qualitative experiment Figure 4 The image shows a visual comparison of reconstructed sea surface temperature (SST) fields in the 100°W–85°W and 54°S–44°S regions. Due to its coarse spatial resolution, the OISST input exhibits a significant attenuation of fine-scale structure. Although analysis products such as GLO12v4 and HYCOM show more realistic fine-scale variability, they exhibit structural distortion compared to the OSTIA reference. Among learning-based methods, RRDB, SwinIR, and ESC improve the structural representation of mesoscopic features. Of these, GLFA generates the SST field visually closest to the reference, preserving large-scale structure while enhancing the reconstruction of fine-scale details and reducing artifacts.

[0066] To further analyze high-frequency recovery, Figure 4 (i)-(p) in the figure show the corresponding ΔSST plot, where SST represents sea surface temperature and ΔSST represents the gradient of SST, which is used to reflect the intensity of sea surface temperature change between adjacent spatial locations. The larger the ΔSST value, the more drastic the spatial change of sea surface temperature at the corresponding location, and the more obvious the high-frequency boundary and other structures. Figure 4In the figure, deg represents the magnitude of ΔSST (in °C), indicating the range of temperature variation, and the gradient map directly reflects high-frequency spatial variations. In the OISST input, high-frequency details are largely smoothed. Although GLO12v4 and HYCOM exhibit strong gradient responses, their edge morphology deviates significantly from OSTIA. Among learning-based methods, RRDB produces slightly blurred gradient boundaries, while SwinIR and ESC exhibit minor structural artifacts. In contrast, GLFA generates a gradient distribution closest to the OSTIA reference, reducing artifacts and improving the reconstruction of high-frequency gradient boundaries. These observations demonstrate that by combining frequency-aware global refinement with local enhancement, GLFA not only improves pixel-level reconstruction accuracy but also enhances the structural fidelity of high-frequency details.

[0067] (3) PSD Experiment In order to quantitatively evaluate the SST reconstruction capability from the frequency domain perspective, Figure 5 The power spectral density (PSD) of different products was compared. For example... Figure 5 As shown, the OISST input exhibits significant attenuation in the high-frequency range, indicating that coarse resolution leads to the loss of fine-scale information and excessive smoothing of local structures. Although GLO12v4 and HYCOM recover some spectral energy in the mid-frequency band, both still exhibit deficiencies in the ultra-high-frequency region and remain below the OSTIA reference value.

[0068] In contrast, the PSD curve of GLFA is closer to OSTIA over a wide wavelength range, especially in the high-frequency region associated with fine structure. This result indicates that GLFA alleviates the suppression of spectral energy in LR input and conventional reconstruction methods, improving the recovery of fine-scale sea surface temperature characteristics. Therefore, frequency domain analysis shows that GLFA can recover the sea surface temperature field by better preserving high-frequency components.

[0069] (4) Daily indicator analysis To evaluate the temporal robustness of the SST super-resolution model, this invention analyzes the daily RMSE and R2 metrics for the entire year of 2024, such as... Figure 6As shown in (a) and (b) above, GLFA consistently exhibits the lowest RMSE value throughout the year with a confidence interval of 95%, indicating stable performance. In contrast, GLO12v4 and HYCOM show higher daily RMSEs, reflecting their limited ability to capture fine-scale changes. Furthermore, GLFA maintains an R² value above 0.96 for most of the year. Conversely, GLO12v4 consistently shows a lower R² than GLFA, fluctuating between 0.93 and 0.96, while HYCOM shows greater temporal variability, with occasional decreases in R². These results demonstrate that GLFA achieves excellent temporal consistency and generalization across ocean conditions, maintaining accuracy and structural fidelity in daily sea surface temperature reconstruction. Overall, the analysis confirms that GLFA reliably adapts to seasonal variations, demonstrating its temporally stable sea surface temperature reconstruction capability.

[0070] (5) Error Analysis To further analyze the reconstruction accuracy of each model for local fine structures more intuitively, Figure 7 The reconstruction results of different methods and their corresponding error distribution plots are shown. The color bar at the top, "Sea Surface Temperature (°C)," is used to indicate... Figure 7 The sea surface temperature values ​​are shown in (a) through (d). The colors gradually transition from dark purple and red to light yellow, representing sea surface temperatures from low to high, and the unit is degrees Celsius. The color bar below, "Error (°C)," is used to indicate... Figure 7 Point-by-point errors of the reconstruction results of each method relative to the OSTIA reference sea surface temperature field are shown in (e)-(g). Blue indicates negative error, i.e., the reconstructed temperature is lower than the OSTIA reference value; white indicates error close to 0; and red indicates positive error, i.e., the reconstructed temperature is higher than the OSTIA reference value. The darker the color, the larger the absolute value of the error, in degrees Celsius. The main error regions of GLO12v4 and HYCOM are spatially aligned with high gradient regions in OSTIA. When reconstructing regions characterized by severe gradient changes, the analysis product suffers from local detail loss, resulting in edge artifacts. In contrast, GLFA exhibits relatively low error in most spatial locations. Furthermore, the error map of GLFA shows smaller and more uniform error amplitudes. By utilizing frequency-aware local adaptive enhancement, GLFA not only reduces local reconstruction errors but also better preserves high-frequency SST features.

[0071] Example 4: See Figure 8 Based on the same inventive concept, this invention also provides a sea surface temperature super-resolution system based on global and local frequency domain sensing, comprising: The low-resolution sea surface temperature data extraction module is used for extracting low-resolution sea surface temperature data: [The module extracts low-resolution sea surface temperature data from the sea surface temperature data.] The data is mapped to shallow features and then subjected to multiple frequency domain sensing operations. The frequency-domain guided global context refinement module is used for frequency-domain guided global context refinement. In each layer of frequency-domain perception operation, shallow features are processed by layer normalization and then processed by a global frequency-domain aggregation operation and a multi-scale gated feedforward network to obtain a gated fusion result. The gated fusion result is mapped to the output of the frequency-domain guided global context refinement module. Output results The first is obtained through convolution. Intermediate features of the layer ; Frequency domain sensing local adaptive enhancement module, used for frequency domain sensing local adaptive enhancement: intermediate features The amplitude spectrum and phase spectrum are obtained through frequency domain decoupling operations. The amplitude increment is obtained from the phase spectrum through phase-guided amplitude modulation operations. ; for amplitude increment The final amplitude increment is obtained by performing high-frequency constraint processing. The final amplitude increment The phase spectrum is reconstructed in the frequency domain and transformed in the spatial domain, then convolved and fused with the shallow feature residuals to output the result. ; The upsampling fusion module is used for upsampling fusion: Results The first layer is obtained by convolution and skip connection with shallow features. Features of the layer after frequency domain sensing local adaptive enhancement ,feature After upsampling, it is compared with low-resolution sea surface temperature data. Residual fusion is performed to obtain super-resolution reconstruction data.

[0072] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-described technical content to create equivalent embodiments without departing from the scope of the present invention. The implementation schemes in the above embodiments can also be further combined or replaced. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A sea surface temperature super-resolution method based on global and local frequency domain sensing, characterized in that, Includes the following steps: S1. Extraction of low-resolution sea surface temperature data: Low-resolution sea surface temperature data The data is mapped to shallow features and then subjected to multi-level frequency domain sensing operations. S2, Frequency Domain Guided Global Context Refinement: In each layer of frequency domain sensing operation, shallow features are normalized and then processed by a global frequency domain aggregation operation and a multi-scale gated feedforward network to obtain a gated fusion result. The gated fusion result is mapped to the output of the frequency domain-guided global context refinement part. Output results The first is obtained through convolution. Intermediate features of the layer ; After shallow features are normalized, gated fusion results are obtained through global frequency domain aggregation and multi-scale gated feedforward network processing, including: Shallow features are normalized and expanded into word sequences according to spatial location. After channel mean pooling, spatial features are extracted. The spatial features are then transformed into frequency domain features through frequency domain transformation. The frequency domain features are normalized by constructing frequency domain energy histograms for each frequency band to generate local frequency domain descriptors. The local frequency domain descriptors are clustered through joint similarity calculation of the spatial and frequency domains and a complexity-aware dual-weight routing mechanism to obtain an aggregated global feature sequence. After aggregating the global feature sequence and performing a linear transformation, the gated fusion result is obtained through linear processing via two independent convolutional branches. S3, Frequency Domain Sensing Local Adaptive Enhancement: intermediate features The amplitude spectrum and phase spectrum are obtained through frequency domain decoupling operations. The amplitude increment is obtained from the phase spectrum through phase-guided amplitude modulation operations. ; for amplitude increment The final amplitude increment is obtained by performing high-frequency constraint processing. The final amplitude increment The phase spectrum is reconstructed in the frequency domain and transformed in the spatial domain, then convolved and fused with the shallow feature residuals to output the result. ; S4, Upsampling fusion: result The first layer is obtained by convolution and skip connection with shallow features. Features of the layer after frequency domain sensing local adaptive enhancement ,feature After upsampling, it is compared with low-resolution sea surface temperature data. Residual fusion is performed to obtain super-resolution reconstruction data.

2. The method according to claim 1, characterized in that, Frequency domain features are normalized by constructing frequency-band-specific frequency domain energy histograms to generate local frequency domain descriptors, including: The frequency domain energy value at each frequency point is calculated using the real and imaginary parts of the frequency domain features. The frequency domain energy values ​​of all frequency points are arranged according to their frequency coordinates to form a frequency domain energy map. With the frequency domain origin as the center, the radial Euclidean distance from each frequency point to the frequency domain origin is calculated based on the longitudinal and transverse frequency coordinates of each frequency point. The radial Euclidean distance at the boundary of the frequency domain plane is used as the reference for normalization to obtain the normalized radial coordinates of each frequency point. The frequency domain plane containing the normalized radial coordinates is divided into multiple non-overlapping radial frequency bands. A binary radial mask is constructed, and all frequency points falling within the radial frequency bands are selected using the binary radial mask. The frequency energy values ​​of all frequency points are summed and divided by the number of frequency points within the radial frequency band to obtain the average energy of the radial frequency band. The average energies of all radial frequency bands are used to form a frequency domain energy histogram, which is then normalized to generate a local frequency domain descriptor for each term.

3. The method according to claim 1, characterized in that, Local frequency domain descriptors are clustered using a joint similarity calculation in the spatial and frequency domains and a complexity-aware dual-weight routing mechanism to obtain an aggregated global feature sequence, including: Initial cluster centers in the spatial domain and frequency domain are obtained by average pooling. Based on the current initial cluster centers in the spatial domain and frequency domain, the words are clustered and the mean of word features within each cluster is calculated. The initial cluster centers in the spatial domain and frequency domain are updated based on the mean using an exponential moving average method. In the spatial domain, the cosine similarity between the spatial features of a word and the current spatial domain cluster center is calculated to obtain the spatial domain similarity. In the frequency domain, the cosine similarity between the local frequency domain descriptor and the current frequency domain cluster center is calculated to obtain the frequency domain similarity. The spatial domain similarity and the frequency domain similarity are adaptively weighted and fused to obtain the joint similarity. Frequency energy is calculated based on the relative frequency energy of local frequency domain descriptors to obtain the high-frequency energy ratio and frequency domain information entropy; the 1st frequency domain descriptor in the word sequence is... The content features corresponding to each spatial location and the local frequency domain descriptor are concatenated along the feature dimension and input into the content gating branch. The input is then passed through the first fully connected layer, the ReLU activation function, the second fully connected layer, and the ReLU activation function to obtain the content gating features. At the same time, the high-frequency energy ratio and the frequency domain information entropy are concatenated along the feature dimension and input into the complexity gating branch. The input is then passed through the first fully connected layer, the ReLU activation function, and the second fully connected layer to obtain the complexity gating features. The content-gated features and complexity-gated features are added together and then subjected to a nonlinear mapping to obtain the joint gated features; The joint gating features are input into the spatial domain weight prediction head and the frequency domain weight prediction head, respectively. The spatial domain weight and frequency domain weight are obtained through the Sigmoid function, and then normalized to obtain the spatial domain routing weight and frequency domain routing weight. The final routing score is obtained by weighting and fusing spatial domain routing weights and frequency domain routing weights with spatial domain similarity and frequency domain similarity. The frequency domain cluster center to which the word belongs is selected based on the routing score. Internal self-attention is calculated for words belonging to the same cluster center, and cross-attention is calculated for words belonging to different cluster centers. The calculated internal self-attention features and cross-attention features are added element-wise according to the corresponding word positions, and then rearranged according to the original spatial positions of each word to obtain the aggregated global feature sequence.

4. The method according to claim 1, characterized in that, After aggregating the global feature sequences and performing a linear transformation, the gated fusion result is obtained through linear processing via two independent convolutional branches, including: The aggregated global feature sequence is fed into a multi-scale gated feedforward network, undergoes linear transformation, and is then processed through two convolutional branches: The result is obtained through spatially depth-separable convolution. Branches The result is obtained by performing a nonlinear mapping after spatial depth separable convolution. ,result With results The result of the fusion is a gated fusion.

5. The method according to claim 1, characterized in that, intermediate features The amplitude spectrum and phase spectrum are obtained through frequency domain decoupling operations. The amplitude increment is obtained from the phase spectrum through phase-guided amplitude modulation operations. ; for amplitude increment The final amplitude increment is obtained by performing high-frequency constraint processing. ,include: intermediate features The signal is transformed to the frequency domain and decoupled into amplitude and phase spectra. The phase spectra are then concatenated along the channel axis. The concatenated phase spectra are fed into a lightweight complex frequency domain cross-bottom mapping layer for interaction, and then mapped by a sigmoid activation function to output a complex frequency domain attention mask. Complex frequency domain attention mask The amplitude increment is obtained by element-wise multiplication with the amplitude spectrum. ; The frequency domain complexity vector is composed of the high-frequency energy ratio and the frequency domain information entropy. It is input into the first fully connected layer and mapped as a hidden feature. The hidden feature is input into the second fully connected layer and mapped as the initial prediction weights of multiple high-frequency sub-bands and further mapped as the adjustment weights of each high-frequency sub-band. The adaptive cutoff radius is calculated based on the high-frequency energy ratio. A high-pass filter mask is constructed by the radial Euclidean distance and the adaptive cutoff radius. The region whose radial Euclidean distance is greater than the adaptive cutoff radius and is located within the boundary of the frequency domain plane is determined as the high-frequency region and is equally divided into multiple non-overlapping high-frequency sub-bands. Construct the corresponding sub-band binary mask based on the radial Euclidean distance of the current frequency domain unit, and assign the adjustment weight of each high-frequency sub-band to all frequency domain units within the sub-band to obtain the frequency band sensing weight map. Frequency band sensing weight map, high-pass filter mask, and amplitude increment By performing cascaded weighting, the final amplitude increment is obtained. .

6. The method according to claim 5, characterized in that, The lightweight complex frequency domain cross-bottom mapping layer passes through a convolutional layer, a ReLU activation layer, and another convolutional layer in sequence.

7. The method according to claim 1, characterized in that, Final amplitude increment The phase spectrum is reconstructed in the frequency domain and transformed in the spatial domain, then convolved and fused with the shallow feature residuals to output the result. ,include: Final amplitude increment The reconstructed spatial domain texture residual is obtained by recombination with the phase spectrum, projected onto space through a two-dimensional inverse discrete Fourier transform, and then convolved. A self-learning adjustable scaling factor is then used to combine the reconstructed spatial domain texture residual with intermediate features. The final output result is obtained by performing residual addition and fusion. .

8. A sea surface temperature super-resolution system based on global and local frequency domain sensing, characterized in that, include: The low-resolution sea surface temperature data extraction module is used for extracting low-resolution sea surface temperature data: [The module extracts low-resolution sea surface temperature data from the sea surface temperature data.] The data is mapped to shallow features and then subjected to multiple frequency domain sensing operations. The frequency-domain guided global context refinement module is used for frequency-domain guided global context refinement. In each layer of frequency-domain perception operation, shallow features are processed by layer normalization and then processed by a global frequency-domain aggregation operation and a multi-scale gated feedforward network to obtain a gated fusion result. The gated fusion result is mapped to the output of the frequency-domain guided global context refinement module. Output results The first is obtained through convolution. Intermediate features of the layer The process involves several steps: First, shallow features undergo layer normalization. Then, a global frequency domain aggregation operation and a multi-scale gated feedforward network are used to obtain the gated fusion result. This includes: normalizing shallow features and expanding them into a sequence of terms based on their spatial location; extracting spatial features through channel mean pooling; transforming the spatial features to frequency domain features using frequency domain transformation; normalizing the frequency domain features by constructing a frequency-band frequency domain energy histogram to generate local frequency domain descriptors; clustering the local frequency domain descriptors using joint similarity calculation between the spatial and frequency domains and a complexity-aware dual-weight routing mechanism to obtain an aggregated global feature sequence; and finally, linearly transforming the aggregated global feature sequence and then processing it through two independent convolutional branches to obtain the gated fusion result. Frequency domain sensing local adaptive enhancement module, used for frequency domain sensing local adaptive enhancement: intermediate features The amplitude spectrum and phase spectrum are obtained through frequency domain decoupling operations. The amplitude increment is obtained from the phase spectrum through phase-guided amplitude modulation operations. ; for amplitude increment The final amplitude increment is obtained by performing high-frequency constraint processing. The final amplitude increment The phase spectrum is reconstructed in the frequency domain and transformed in the spatial domain, then convolved and fused with the shallow feature residuals to output the result. ; The upsampling fusion module is used for upsampling fusion: Results The first layer is obtained by convolution and skip connection with shallow features. Features of the layer after frequency domain sensing local adaptive enhancement ,feature After upsampling, it is compared with low-resolution sea surface temperature data. Residual fusion is performed to obtain super-resolution reconstruction data.

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