Hyperspectral super-resolution reconstruction method and system fusing phase priori and degradation perception

Abstract

The application provides a hyperspectral super-resolution reconstruction method and system fusing phase priori and degradation perception, the method comprising: acquiring an observed image and a spectral response function matrix, and constructing an optimization objective function comprising a data fidelity term and a space-spectrum joint priori term; using a semi-quadratic splitting algorithm to decouple the objective function into three constraint terms of physical fidelity, spectral low rank and depth priori; using a Fourier phase-amplitude mixed processing model, a truncated singular value decomposition model and a double-branch proximal mapping network model to optimize and solve the three constraint terms respectively, to obtain and update a first auxiliary variable, a second auxiliary variable and a target hyperspectral image; through cyclic iteration until the iteration number reaches a number threshold, the target hyperspectral image output in the last iteration cycle is taken as a high-resolution hyperspectral reconstruction image. The application effectively improves the spatial texture recovery capability and spectral fidelity of the image.

Description

Technical Field

[0001] This application relates to the field of hyperspectral image processing technology, specifically to a hyperspectral super-resolution reconstruction method and system that integrates phase prior and degradation perception. Background Technology

[0002] Hyperspectral imaging technology can simultaneously capture the spatial geometry of a target and information from hundreds of continuous spectral bands, making it widely applicable in remote sensing, precision agriculture, and biomedicine. However, due to limitations in sensor physics, achieving both spatial and spectral resolution is difficult, and acquiring high-quality data is costly. Spectral super-resolution (SSR) technology aims to reconstruct high-fidelity hyperspectral imaging (HSI) from low-resolution input, becoming a key breakthrough in overcoming this bottleneck.

[0003] In related technologies, image reconstruction can be performed using deep learning networks. However, this method lacks frequency domain geometric constraints in physical degradation modeling, which leads to the easy loss of high-frequency edge structures in the Fourier phase. Furthermore, due to the bidirectional coherence of unidirectional modeling, it is difficult to balance long-range dependence and local continuity, causing spectral distortion. As a result, the reconstructed hyperspectral data cannot meet the needs of subsequent precise analysis, identification, and other application scenarios, seriously affecting the practicality and industrialization value of this type of method. Summary of the Invention

[0004] This application aims to at least partially address one of the technical problems in related technologies. To this end, embodiments of this application propose a hyperspectral super-resolution reconstruction method and system that integrates phase prior and degradation perception, effectively improving the spatial texture restoration capability and spectral fidelity of images.

[0005] According to the first aspect of this application, the hyperspectral super-resolution reconstruction method that integrates phase prior and degradation sensing provided by this application includes the following steps: S1, Based on the observed image, obtain the spectral response function matrix R corresponding to the observed image; S2, Based on the spectral response function matrix R, construct the optimization objective function; S3, according to the semi-quadratic splitting algorithm, the optimization objective function is decoupled to obtain the physical fidelity constraint term, the spectral low-rank constraint term, and the depth prior constraint term; S4, Based on the preset Fourier phase-first-first-second hybrid processing model, the physical fidelity constraint term is optimized and solved to obtain and update the first auxiliary variable Z. The first auxiliary variable Z is configured to process data fidelity and phase guidance. S5. Based on the preset truncated singular value decomposition model, the spectral low-rank constraint term is optimized and solved to obtain and update the second auxiliary variable S, which is used as the spectral low-rank prior. S6, based on the preset dual-branch proximal mapping network model, the depth prior constraint term is solved, and the target hyperspectral image X of the current cycle is updated by combining the first auxiliary variable Z and the second auxiliary variable S. The dual-branch proximal mapping network model includes a bidirectional spectral fusion unit and an orientation texture perception attention unit. Repeat steps S4 to S6 until the number of iterations reaches the threshold. Then, use the target hyperspectral image X output from the last iteration as the high-resolution hyperspectral reconstructed image.

[0006] In some embodiments, step S3, which involves decoupling the optimization objective function according to a semi-quadratic splitting algorithm to obtain physical fidelity constraints, spectral low-rank constraints, and depth prior constraints, includes: According to the semi-quadratic splitting algorithm, the optimization objective function is transformed to obtain a multivariate unconstrained penalty function, which includes: a physical fidelity constraint term, a first penalty term, a second penalty term, a depth prior constraint term, and a regularization term.

[0007] Wherein, the physical fidelity constraint term is used to constrain the physical degradation relationship between the observed image and the first auxiliary variable Z; the first penalty term is used to constrain the difference between the target hyperspectral image X and the first auxiliary variable Z; the second penalty term is used to constrain the difference between the target hyperspectral image X and the second auxiliary variable S; the regularization term is used to characterize the spectral low-rank characteristics of the second auxiliary variable S, and the regularization term and the second penalty term together constitute the spectral low-rank constraint term; the depth prior constraint term is used to characterize the joint depth space-spectral prior.

[0008] In some embodiments, step S4, which optimizes the physical fidelity constraint term based on a preset Fourier phase-first-secondary-value hybrid processing model to obtain and update the first auxiliary variable Z, includes: The observed image or the target hyperspectral image X from the previous iteration is processed and transformed to obtain a reference signal; According to a preset frequency domain transformation algorithm, the reference signal is transformed in the frequency domain to obtain structural components; The frequency domain transformation algorithm is used to perform a frequency domain transformation on the target hyperspectral image or observation image of the previous iteration to obtain the amplitude component. Based on the structural components and the amplitude components, the guiding features are calculated; Based on the guiding features and the physical fidelity constraints, the first auxiliary variable Z for the current stage is updated through an iterative optimization algorithm.

[0009] In some embodiments, the step of processing and transforming the observed image or the target hyperspectral image X from the previous iteration to obtain a reference signal includes: Based on the preset inverse projection matrix algorithm, the observed image or the target hyperspectral image X from the previous iteration is projected into the hyperspectral space to obtain the reference signal; And / or, the step of calculating the guiding features based on the structural components and the amplitude components includes: The structural components and amplitude components are combined in the frequency domain to construct a complex spectrum; Based on the inverse Fourier transform algorithm, the complex spectrum is transformed and guided features are generated; And / or, the step of updating the first auxiliary variable Z for the current stage through an iterative optimization algorithm based on the guiding features and the physical fidelity constraint term includes: Using the guiding feature as the initial value, and combining it with the physical fidelity constraint term, the gradient descent method is used to perform a single-step iterative update to obtain the first auxiliary variable Z.

[0010] In some embodiments, step S5, which optimizes the low-rank constraint term of the spectrum based on a preset truncated singular value decomposition model to obtain and update the second auxiliary variable S, includes: The target hyperspectral image X or the observed image corresponding to the previous iteration is used as the input tensor and flattened in the spatial dimension to obtain a two-dimensional matrix; The two-dimensional matrix is ​​standardized to obtain the mean vector, standard deviation vector, and standardized signal matrix. The standardized signal matrix is ​​used as a high-dimensional signal. It is extracted and a low-rank orthogonal basis is constructed by truncating singular value decomposition. The high-dimensional signal is then projected onto the low-rank orthogonal basis for reconstruction, resulting in a reconstructed spectral low-rank matrix. The reconstructed spectral low-rank matrix is ​​denormalized based on the mean vector, the standard deviation vector, and the outer product operation algorithm, and then reshaped back to the original tensor dimension to obtain the updated second auxiliary variable.

[0011] In some embodiments, the step of using the standardized signal matrix as a high-dimensional signal, extracting and constructing a low-rank orthogonal basis through truncated singular value decomposition, and projecting the high-dimensional signal onto the low-rank orthogonal basis for reconstruction to obtain a reconstructed spectral low-rank matrix includes: The standardized signal matrix is ​​processed according to the economic singular value decomposition algorithm to obtain the left singular vector matrix, the singular value matrix, and the right singular vector matrix. Based on the preset low-rank constraint parameters, the first t largest singular values ​​and their corresponding left and right singular vectors are extracted to form a low-rank orthogonal basis. The inner product of the normalized signal matrix and the low-rank orthogonal basis is calculated, and redundant noise in the spectral dimension is eliminated by reconstruction to obtain a pure low-rank spectral matrix.

[0012] In some embodiments, step S6, which involves solving the depth prior constraint term based on a preset dual-branch proximal mapping network model and updating the target hyperspectral image X of the current cycle by combining the first auxiliary variable Z and the second auxiliary variable S, includes: The first auxiliary variable Z and the second auxiliary variable S are input into the bidirectional spectral fusion unit. The forward branch is used to model the global long-range dependence of the spectral sequence, and the reverse branch is used to extract multi-scale band-specific absorption features. The spectral enhancement features are obtained through fusion. The spectral enhancement features are input into the orientation texture perception attention unit, and the directional perception attention weights are generated through the spatial coordinate attention branch. The high-frequency directional texture is adaptively enhanced through the learnable Gabor filter branch, and the texture perception features are obtained through residual fusion. The target hyperspectral image X for the current cycle is obtained by updating the texture-aware features.

[0013] In some embodiments, the steps of inputting the first auxiliary variable Z and the second auxiliary variable S into the bidirectional spectral fusion unit, modeling the global long-range dependence of the spectral sequence using the forward branch, extracting multi-scale band-specific absorption features using the reverse branch, and obtaining spectral enhancement features through fusion include: Use the observed image or the target hyperspectral image obtained from the previous iteration as the input feature map. In the forward branch of the bidirectional spectral fusion unit, the input feature map is flattened into a sequence vector according to the band dimension; according to the preset spectral multi-head self-attention mechanism, feature mapping is performed on different bands, modeling and obtaining the global long-range dependency features of the spectral sequence. In the reverse branch of the bidirectional spectral fusion unit, the input feature map is mirrored and flipped in reverse order according to the spectral dimension. The spatial dimension is compressed by global average pooling, and multi-scale band-specific absorption features are extracted by using one-dimensional convolution kernels of various sizes. Attention weights are generated to reweight the reversed features by channel and then flipped back to the forward order to obtain channel-reweighted features. The global long-range dependency feature and the channel reweighted feature are fused element-wise to obtain the fused spectral enhancement feature.

[0014] In some embodiments, the steps of inputting the spectral enhancement features into the orientation texture-aware attention unit, generating directional attention weights through a spatial coordinate attention branch, adaptively enhancing high-frequency directional textures through a learnable Gabor filter branch, and obtaining texture-aware features through residual fusion include: A one-dimensional adaptive average pooling kernel is used to encode global context information along the horizontal and vertical spatial coordinate axes of the input feature map, generating two independent channel description vectors. The channel description vectors are then merged through a concatenation operation and processed by a convolutional layer and activation function to generate a spatial attention weight matrix with directional awareness. The input feature map is convolved using a pre-defined complex Gabor filter bank to adaptively enhance high-frequency directional texture features and suppress low-frequency noise components under joint constraints in the frequency and spatial domains. The spatial frequency, orientation rotation angle, and axial standard deviation of the Gaussian envelope within the complex Gabor filter bank are all set as trainable network parameters. The input feature map is multiplied element-wise with the spatial attention weight matrix, and the result is concatenated channel-wise with the texture feature map output by the learnable Gabor filter branch. The target hyperspectral image X of the current loop is then output through the residual connection structure.

[0015] In a second aspect of this application, the hyperspectral super-resolution reconstruction system that integrates phase prior and degradation sensing provided by this application includes: The acquisition module is configured to acquire the observed image and the corresponding spectral response function matrix R; A construction module is configured to construct an optimization objective function based on the spectral response function matrix R, wherein the optimization objective function includes at least a data fidelity term and a spatial-spectral joint prior term; A decoupling module is provided, which includes a semi-quadratic splitting algorithm. The decoupling module is configured to decouple the optimization objective function according to the semi-quadratic splitting algorithm to obtain physical fidelity constraint terms, spectral low-rank constraint terms, and depth prior constraint terms. The physical degradation and phase update module includes a Fourier phase-first amplitude hybrid processing model. The physical degradation and phase update module is configured to optimize and solve the physical fidelity constraint terms based on the Fourier phase-first amplitude hybrid processing model, and obtain and update the first auxiliary variable Z. The first auxiliary variable Z is configured to process data fidelity and phase guidance. The spectral low-rank projection module includes a truncated singular value decomposition model. The spectral low-rank projection module is configured to optimize and solve the spectral low-rank constraint terms based on the truncated singular value decomposition model, and obtain and update the second auxiliary variable S. The second auxiliary variable S is used as a spectral low-rank prior. The dual-path feature reconstruction module includes a dual-branch proximal mapping network model, which comprises a bidirectional spectral fusion unit and an orientation texture perception attention unit. The dual-path feature reconstruction module is configured to solve the depth prior constraint term based on the preset dual-branch proximal mapping network model, and update the target hyperspectral image X of the current loop by combining the first auxiliary variable Z and the second auxiliary variable S. The output module is configured to use the target hyperspectral image X output in the last iteration loop as the high-resolution hyperspectral reconstructed image when the number of iterations reaches a threshold.

[0016] In summary, the hyperspectral super-resolution reconstruction method and system that integrates phase prior and degradation sensing provided in this application have at least the following advantages: (1) Significantly improved structural fidelity: The explicit injection of Fourier phase prior effectively compensates for the loss of geometric structure caused by physical degradation. Especially on the Harvard dataset, this method shows good comprehensive error suppression ability, effectively avoids local spatial blurring, and improves the distortion of complex structures such as building window outlines.

[0017] (2) High spectral consistency: The two-way spectral fusion mechanism breaks down the one-way information barrier.

[0018] (3) Physically Degenerate Interpretable Expansion Architecture: The semi-quadratic splitting algorithm (HQS) is used to decouple the severely underdetermined spatial spectrum reconstruction objective function into three alternating optimization sub-problems: physical fidelity, low spectral rank, and depth prior. Furthermore, this architecture explicitly embeds physical imaging mechanisms such as high-frequency phase features into the end-to-end network iteration, effectively enhancing the interpretability and robustness of the super-resolution reconstruction process. Attached Figure Description

[0019] Figure 1 This is a schematic flowchart of a hyperspectral super-resolution reconstruction method that integrates phase prior and degradation sensing, provided in an embodiment of this application.

[0020] Figure 2 This is a schematic diagram of the execution logic of steps S4 to S6 in the hyperspectral super-resolution reconstruction method that integrates phase prior and degradation perception provided in an embodiment of this application.

[0021] Figure 3 This is a schematic diagram of the execution logic of a bidirectional spectral fusion unit within a bi-branch proximal mapping network model provided in an embodiment of this application.

[0022] Figure 4 This is a schematic diagram of the execution logic of the orientation texture perception attention unit in the hyperspectral super-resolution reconstruction method that integrates phase prior and degradation perception provided in an embodiment of this application.

[0023] Figure 5 This is a schematic diagram of the structure of a hyperspectral super-resolution reconstruction system that integrates phase prior and degradation sensing according to an embodiment of this application.

[0024] Figure 6 This is a schematic diagram showing the specific error comparison on the CAVE test set "superballs" image during the experiment of the hyperspectral super-resolution reconstruction method that integrates phase prior and degradation perception provided in an embodiment of this application.

[0025] Figure 7 This is a schematic diagram comparing the reconstruction error of the img1 image based on the Harvard dataset during an experiment using the hyperspectral super-resolution reconstruction method that integrates phase prior and degradation perception provided in an embodiment of this application.

[0026] Figure label: 100. Hyperspectral super-resolution reconstruction system integrating phase prior and degradation perception; 110. Acquisition module; 120. Construction module; 130. Decoupling module; 140. Physical degradation and phase update module; 150. Spectral low-rank projection module; 160. Dual-path feature reconstruction module; 170. Output module. Detailed Implementation

[0027] The embodiments of this application are described in detail below, with examples of these embodiments illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0028] refer to Figure 1 This is a flowchart illustrating a hyperspectral super-resolution reconstruction method that integrates phase prior and degradation sensing, provided in an embodiment of this application. The hyperspectral super-resolution reconstruction method that integrates phase prior and degradation sensing provided in this application includes the following steps: S1. Based on the observed image, obtain the spectral response function matrix R corresponding to the observed image.

[0029] In this context, the observed image typically refers to a low-resolution hyperspectral image (HSI) or its paired high-resolution multispectral image (MSI) acquired by an imaging device. The spectral response function matrix R describes the response characteristics of the imaging system in different spectral bands and serves as a physical bridge connecting the real scene and the observed data. Step S1 provides necessary prior information for subsequent physical model construction, ensuring that the reconstruction process conforms to the physical laws of the imaging system and avoiding potential physical inconsistencies that may arise with purely data-driven methods.

[0030] S2, Based on the spectral response function matrix R, construct an optimization objective function. The optimization objective function includes at least a data fidelity term and a spatial-spectral joint prior term; the data fidelity term is used to constrain the physical consistency between the reconstructed result and the observed data; the spatial-spectral joint prior term is used to introduce the inherent structural characteristics of the image itself (such as spectral low-rank, spatial smoothness, or texture structure).

[0031] S3. Based on the semi-quadratic splitting algorithm, the optimization objective function is decoupled to obtain the physical fidelity constraint term corresponding to the data fidelity term, the spectral low-rank constraint term corresponding to the spatial-spectral joint prior term, and the depth prior constraint term.

[0032] In this process, the physical fidelity constraint term corresponds to the data fidelity term, while the spectral low-rank constraint term and the depth prior constraint term correspond to the spatial-spectral joint prior term. In other words, step S3 utilizes a semi-quadratic splitting algorithm to decompose the complex original optimization problem into three relatively independent sub-problems: the physical fidelity constraint term (corresponding to data fidelity), the spectral low-rank constraint term, and the depth prior constraint term (both of which correspond to the spatial-spectral joint prior). This significantly reduces the difficulty of solving the problem, allowing each sub-problem to be solved efficiently using the most suitable strategy, thereby improving the overall algorithm's convergence speed and computational efficiency.

[0033] S4. Based on the preset Fourier phase-first-first-second hybrid processing model, the physical fidelity constraint term is optimized and solved to obtain and update the first auxiliary variable Z. The first auxiliary variable Z is configured to process data fidelity and phase guidance.

[0034] Therefore, the physical fidelity constraint term can be processed in the frequency domain, the calculation can be accelerated using the Fast Fourier Transform (FFT), and the structural and energy information of the image can be effectively separated and processed, thereby accurately updating the first auxiliary variable Z and ensuring the accuracy of the reconstruction results under the physical observation model.

[0035] S5. Based on the preset truncated singular value decomposition model, the spectral low-rank constraint term is optimized and solved to obtain and update the second auxiliary variable S, which is used as the spectral low-rank prior.

[0036] In other words, the truncated singular value decomposition model retains the main singular values ​​and their corresponding singular vectors while removing the small singular values ​​corresponding to noise, thereby performing low-rank approximation of the data. This effectively taps into the strong correlation (i.e., low-rank characteristics) of hyperspectral images in the spectral dimension. It can maintain the integrity of spectral information while denoising, thus accurately updating the second auxiliary variable S and providing a reliable spectral prior for the reconstruction results.

[0037] S6. Based on the preset dual-branch proximal mapping network model, the depth prior constraint term is solved, and the target hyperspectral image X of the current cycle is updated by combining the first auxiliary variable Z and the second auxiliary variable S. The dual-branch proximal mapping network model includes a bidirectional spectral fusion unit and an orientation texture perception attention unit.

[0038] In other words, the bi-branch proximal mapping network model receives a first auxiliary variable Z and a second auxiliary variable S as input. Through the network's internal nonlinear mapping capabilities (including a bidirectional spectral fusion unit and an orientation-texture-aware attention unit), it learns complex image priors, capturing intricate textures and structural details that traditional manual priors cannot describe. The bidirectional spectral fusion unit enhances the interaction of spectral information, while the orientation-texture-aware attention unit specifically enhances the orientation texture of the image. The combination of these two significantly improves the texture clarity and spectral fidelity of the reconstructed image.

[0039] Repeat steps S4 to S6 until the number of iterations reaches the threshold. Then, use the target hyperspectral image X output from the last iteration as the high-resolution hyperspectral reconstructed image.

[0040] Finally, through multiple iterations, physical constraints, low-rank priors, and deep priors interact and refine each other during the optimization process, gradually bringing the target hyperspectral image X closer to the optimal solution. The final output image achieves a high level of quality in both spatial detail and spectral accuracy.

[0041] In summary, the hyperspectral super-resolution reconstruction method merging phase prior and degradation perception provided in this application decouples the complex optimization problem into three sub-problems—physical fidelity, spectral low-rank, and depth prior—through a semi-quadratic splitting algorithm. These sub-problems are then efficiently solved using Fourier phase-first-first-secondary mixed processing, truncated singular value decomposition, and a bi-branch proximal mapping network, respectively. This method cleverly combines the interpretability of the physical model with the powerful feature representation capabilities of deep learning. Through iterative optimization, it significantly enhances spatial texture details while maintaining spectral fidelity, achieving high-quality, high-resolution image reconstruction.

[0042] In some embodiments, step S3 may include the following steps: According to the preset semi-quadratic splitting algorithm, the optimization objective function is transformed to obtain a multivariate unconstrained penalty function, which includes: a physical fidelity constraint term, a first penalty term, a second penalty term, a depth prior constraint term, and a regularization term.

[0043] Wherein, the physical fidelity constraint term is used to constrain the physical degradation relationship between the observed image and the first auxiliary variable Z; the first penalty term is used to constrain the difference between the target hyperspectral image X and the first auxiliary variable Z; the second penalty term is used to constrain the difference between the target hyperspectral image X and the second auxiliary variable S; the regularization term is used to characterize the spectral low-rank characteristics of the second auxiliary variable S, and the regularization term and the second penalty term together constitute the spectral low-rank constraint term; the depth prior constraint term is used to characterize the joint depth space-spectral prior.

[0044] In the execution of the hyperspectral super-resolution reconstruction method that integrates phase prior and degradation sensing provided in this application, the input or acquired observation image can first be defined as... (When b=3, Y is an RGB image); then, the corresponding hyperspectral image (HSI) is solved using a preset imaging physics model, and HSI is defined as... The observed image can also be called a multispectral image (MSI). H and W represent the height and width of the spatial dimension, respectively; b is the number of spectral bands in the MSI; B is the number of bands in the HSI image.

[0045] It should be noted that the constraint relationship between the multispectral image and the hyperspectral image is expressed by the following formula: (1) In the formula: Y is the input or acquired observation image; It is the spectral response function matrix, and n is additive noise.

[0046] In this embodiment, the hyperspectral super-resolution reconstruction method that integrates phase prior and degradation sensing can employ a Bayesian modeling algorithm, and based on the maximum a posteriori probability (MAP) theory, Equation 1 is reconstructed to obtain Equation 2: (2) In the formula: This is the predicted estimate of the target variable.

[0047] Based on Bayes' theorem and logarithmic function Given a monotonically increasing relationship, maximizing the original function is equivalent to maximizing its logarithm, leading to Formula 3: (3) Since the observed image Y is a known constant, its marginal probability P(Y) is independent of the variable X to be solved. Therefore, when optimizing X, logP(Y) can be omitted, and maximizing a function is equivalent to minimizing its negative.

[0048] (4) To obtain the final optimization objective function, we need to physically model the probability distribution. Corresponding to the data fidelity term, assuming the additive noise n follows a Gaussian distribution, the likelihood term... Equivalent to minimizing the Frobenius norm of the reconstruction error Furthermore, regarding the regularization term, since hyperspectral images (HSI) simultaneously contain rich spatial structure and spectral features, a single prior distribution cannot perfectly characterize their complex physical properties. Therefore, this application uses prior probabilities... The negative logarithmic term is equivalent to the spatial prior. With spectral priors The combination of .

[0049] Substituting the above equivalent form into the maximum a posteriori (MAP) estimation framework, we obtain the final minimization form of the optimization objective function: (5) In the formula: and The weights are the weights of the prior terms.

[0050] Furthermore, this application utilizes a half-quadratic splitting (HQS) algorithm to introduce a first auxiliary variable Z and a second auxiliary variable S, setting Z=X and S=X. A penalty parameter is also introduced. and Prior weights and The optimization problem with equality constraints (Equation 5) is transformed into a multivariable unconstrained penalty function: (6) In the formula: X is the target hyperspectral image; Z is the first auxiliary variable; S is the second auxiliary variable; This represents the rank of the matrix after the second auxiliary variable S is flattened along the spectral dimension. This represents the joint prior of depth space and spectrum.

[0051] Among them, the Spectral redundancy and noise can be effectively suppressed by penalizing non-zero singular values.

[0052] refer to Figure 2 This is an execution logic diagram of steps S4 to S6 provided in an embodiment of this application. Step S4 may include the following steps: The observed image or the target hyperspectral image X from the previous iteration is processed and transformed to obtain a reference signal.

[0053] Specifically, the input is selected from either the observed image (providing real physical observation information) or the image X generated in the previous iteration (or providing intermediate information from the previous iteration loop). Processing transformations may include denoising, normalization, or specific linear transformations, designed to prepare a high-quality input signal for subsequent frequency domain analysis.

[0054] According to the preset frequency domain transformation algorithm, the reference signal is transformed in the frequency domain to obtain the structural components.

[0055] Specifically, the reference signal is transformed from the spatial domain to the frequency domain using Fourier Transform (FFT). In the frequency domain, the phase information of the signal typically corresponds to the edges, contours, and geometric structures of the image. Therefore, the extracted "structural component" mainly refers to the phase spectrum containing key spatial structural information. This allows for the separation of image structure and energy; that is, by extracting phase information as the structural component, the algorithm can accurately capture high-frequency details and edge features of the image, avoiding the blurring effect that traditional spatial domain methods easily produce when processing edges, and providing a core basis for subsequent "phase guidance."

[0056] According to the frequency domain transformation algorithm, the target hyperspectral image or observation image of the previous iteration is transformed in the frequency domain to obtain the amplitude component.

[0057] Specifically, the amplitude component reflects the energy distribution characteristics of the spectrum and space. This component can be used to prevent energy anomalies or spectral distortions during the enhancement of details (structure) and maintain the global visual features of the image.

[0058] Based on the structural components and amplitude components, the guiding features are calculated.

[0059] Specifically, mathematical operations (such as weighted combination, complex reconstruction, or cross-attention mechanisms) are performed on the structural and amplitude components to generate a comprehensive "guided feature." This allows for complementary enhancement of multi-dimensional information. By mixing phase and amplitude information, the generated guided feature contains both clear edge structures and retains accurate energy distribution. This hybrid feature is more robust than a single spatial domain feature and can more effectively guide subsequent optimization processes, addressing the coexistence of "texture blurring" and "contrast loss."

[0060] Based on the guiding features and the physical fidelity constraints, the first auxiliary variable Z for the current stage is updated through an iterative optimization algorithm.

[0061] Specifically, guiding features are incorporated as priors or regularization terms into the optimization formula for physical fidelity constraints. Iterative algorithms such as gradient descent or proximal gradient are used to solve for the first auxiliary variable Z, which satisfies both the physical observation model and the guiding feature constraints. This not only ensures that the first auxiliary variable Z is physically faithful to the observed image (data fidelity) but also corrects the update direction using frequency domain guiding features. This means that the updated first auxiliary variable Z, while removing noise and blur, can accurately recover high-frequency details of the image, significantly improving the clarity and accuracy of super-resolution reconstruction.

[0062] Further, the step of processing and transforming the observed image or the target hyperspectral image X from the previous iteration to obtain the reference signal includes: Based on a pre-defined inverse projection matrix algorithm, the observed image or the target hyperspectral image X from the previous iteration is projected into the hyperspectral space to obtain a reference signal.

[0063] Furthermore, the step of calculating the guiding features based on the structural components and the amplitude components includes: The structural components and amplitude components are combined in the frequency domain to construct a complex spectrum; Based on the inverse Fourier transform algorithm, the complex spectrum is transformed and guided features are generated.

[0064] In some embodiments, the step of updating the first auxiliary variable Z for the current stage through an iterative optimization algorithm based on the guiding features and the physical fidelity constraint term includes: Using the guiding feature as the initial value, and combining it with the physical fidelity constraint, the gradient descent method is used to perform a single-step iterative update to obtain the first auxiliary variable Z.

[0065] In other words, during the execution of step S4, the inverse projection matrix is ​​first used. Projecting the MSI signal into the hyperspectral space yields a reference signal with blurred spectral information but a clear spatial structure. : (7) Then, in the Fourier domain, the amplitude of the previous iteration is... Phase with reference signal Perform aliasing, then obtain the result through inverse Fourier transform. : (8) In this application, the objective constraint is dynamically replaced with a phase-guided constraint term, and the objective function with fixed X, S, and Z is: (9) The first term is the physical fidelity constraint term, and the second term is the structural penalty term. Since this is a quadratic continuously differentiable function (Equation 9), we take the partial derivative of Z to obtain Equation 10: (10) Furthermore, this application employs gradient descent as the iterative algorithm for updates to avoid the high computational cost of matrix inversion. The step size is... : (11) In the formula: k is the number of iterations; This is the first auxiliary variable in the Kth iteration loop; It should be noted that in this application, the threshold number of iterations can be set as needed, such as 5 times, 10 times, etc., which will not be elaborated here.

[0066] In some embodiments, step S5 may include the following steps: The target hyperspectral image X or the observed image corresponding to the previous iteration is used as the input tensor and flattened in the spatial dimension to obtain a two-dimensional matrix; The two-dimensional matrix is ​​standardized to obtain the mean vector, standard deviation vector, and standardized signal matrix. The standardized signal matrix is ​​used as a high-dimensional signal. It is extracted and a low-rank orthogonal basis is constructed by truncating singular value decomposition. The high-dimensional signal is then projected onto the low-rank orthogonal basis for reconstruction, resulting in a reconstructed spectral low-rank matrix. The reconstructed spectral low-rank matrix is ​​denormalized based on the mean vector, the standard deviation vector, and the outer product operation algorithm, and then reshaped back to the original tensor dimension to obtain the updated second auxiliary variable.

[0067] Further, the step of using the standardized signal matrix as a high-dimensional signal, extracting and constructing a low-rank orthogonal basis through truncated singular value decomposition, and projecting the high-dimensional signal onto the low-rank orthogonal basis for reconstruction to obtain the reconstructed spectral low-rank matrix includes: The standardized signal matrix is ​​processed according to the economic singular value decomposition algorithm to obtain the left singular vector matrix, the singular value matrix, and the right singular vector matrix. Based on the preset low-rank constraint parameters, the first t largest singular values ​​and their corresponding left and right singular vectors are extracted to form a low-rank orthogonal basis. The inner product of the normalized signal matrix and the low-rank orthogonal basis is calculated, and redundant noise in the spectral dimension is eliminated by reconstruction to obtain a pure low-rank spectral matrix.

[0068] Specifically, the input tensor is flattened into a matrix in the spatial dimension, and the spatial mean and standard deviation of each band are calculated for standardization. Economy Singular Value Decomposition (SVD) is performed on the standardized matrix, and the components corresponding to the top t largest singular values ​​are extracted to form a low-rank orthogonal basis. The high-dimensional signal is projected onto this low-dimensional subspace to reconstruct a pure spectral low-rank matrix. Then, an inverse normalization operation is performed using the outer product to introduce the mean and standard deviation, reshaping the tensor back to its original dimension to obtain auxiliary variables. .

[0069] During the execution of step S5, since hyperspectral images usually have extremely high spectral dimensions, using singular value decomposition (SVD) to truncate smaller singular values ​​can project the original data into a low-dimensional pure subspace, thereby greatly suppressing spectral distortion and noise during the reconstruction process.

[0070] That is, with X and Z fixed, the objective function of S in the kth iteration becomes: (12) In the formula: Let S be the rank of the matrix after the second auxiliary variable S is flattened along the spectral dimension.

[0071] Adjustments can be made during execution. and The proportion, that is, setting a hard rank constraint threshold, allows the soft penalty problem to be equivalently transformed into a proximal mapping problem with rank constraints: (13) Then, the tensor Flattened into a matrix in spatial dimension (in ), calculate the spatial mean for each band. and standard deviation The standardized matrix is ​​obtained. During the calculation, a 1×N all-1 row vector was introduced. This facilitates matrix operations. During operation, let... To maintain a minimal constant for numerical stability, the normalization process is formulated as follows: (14) Furthermore, because the number of bands in a hyperspectral image is much smaller than the number of spatial pixels ( To avoid memory overflow, for Perform Economy Singular Value Decomposition (ESVD): (15) Wherein, the left singular matrix is The singular value diagonal matrix is The right singular matrix is .

[0072] According to the low-rank approximation theorem (Eckart-Young-Mirsky theorem), the optimal solution consists of the components corresponding to the first t largest singular values. Extracting the first t columns of U forms a low-rank orthogonal basis. The high-dimensional signal is then projected onto this subspace to calculate the coordinate matrix. And reconstruct a pure spectral low-rank matrix. : (16) (17) Finally, the mean and standard deviation are broadcast to the same dimension as the original matrix using the outer product, and then... The transformation reshapes it back to the original tensor dimension, yielding the following formula: (18) (19) refer to Figure 3 This is a schematic diagram of the execution logic of a bidirectional spectral fusion unit within a dual-branch proximal mapping network model provided in an embodiment of this application. Step S6 may include the following steps: The first auxiliary variable Z and the second auxiliary variable S are input into the bidirectional spectral fusion unit. The forward branch is used to model the global long-range dependence of the spectral sequence, and the reverse branch is used to extract multi-scale band-specific absorption features. The spectral enhancement features are obtained through fusion. The spectral enhancement features are input into the orientation texture perception attention unit, and the directional perception attention weights are generated through the spatial coordinate attention branch. The high-frequency directional texture is adaptively enhanced through the learnable Gabor filter branch, and the texture perception features are obtained through residual fusion. The target hyperspectral image X for the current cycle is obtained by updating the texture-aware features.

[0073] Further, the steps of inputting the first auxiliary variable Z and the second auxiliary variable S into the bidirectional spectral fusion unit, using the forward branch to model the global long-range dependence of the spectral sequence, and using the reverse branch to extract multi-scale band-specific absorption features, and obtaining spectral enhancement features through fusion include: Use the observed image or the target hyperspectral image obtained from the previous iteration as the input feature map. In the forward branch of the bidirectional spectral fusion unit, the input feature map is flattened into a sequence vector according to the band dimension; according to the preset spectral multi-head self-attention mechanism, feature mapping is performed on different bands, modeling and obtaining the global long-range dependency features of the spectral sequence. In the reverse branch of the bidirectional spectral fusion unit, the input feature map is mirrored and flipped in reverse order according to the spectral dimension. The spatial dimension is compressed by global average pooling, and multi-scale band-specific absorption features are extracted by using one-dimensional convolution kernels of various sizes. Attention weights are generated to reweight the reversed features by channel and then flipped back to the forward order to obtain channel-reweighted features. The global long-range dependency feature and the channel reweighted feature are fused element-wise to obtain the fused spectral enhancement feature.

[0074] Furthermore, the steps of inputting the spectral enhancement features into the orientation texture-aware attention unit, generating directional awareness attention weights through a spatial coordinate attention branch, adaptively enhancing high-frequency directional textures through a learnable Gabor filter branch, and obtaining texture-aware features through residual fusion include: A one-dimensional adaptive average pooling kernel is used to encode global context information along the horizontal and vertical spatial coordinate axes of the input feature map, generating two independent channel description vectors. The channel description vectors are then merged through a concatenation operation and processed by a convolutional layer and activation function to generate a spatial attention weight matrix with directional awareness. The input feature map is convolved using a pre-defined complex Gabor filter bank to adaptively enhance high-frequency directional texture features and suppress low-frequency noise components under joint constraints in the frequency and spatial domains. The spatial frequency, orientation rotation angle, and axial standard deviation of the Gaussian envelope within the complex Gabor filter bank are all set as trainable network parameters. The input feature map is multiplied element-wise with the spatial attention weight matrix, and the result is concatenated channel-wise with the texture feature map output by the learnable Gabor filter branch. The target hyperspectral image X of the current loop is then output through the residual connection structure.

[0075] In other words, in the forward branch of the bidirectional spectral fusion unit: the input feature map is flattened into a sequence by band, and a multi-head self-attention mechanism (SMSA) is used to map features to different bands, modeling the global long-range dependency of the spectral sequence. In the reverse branch of the bidirectional spectral fusion unit: the input features are mirrored and reversed along the spectral dimension, the spatial dimension is compressed by global average pooling, and then multi-scale band-specific absorption features are extracted using one-dimensional convolutional kernels of various sizes. Attention weights are generated to reweight the reversed features by channel and flip them back to the forward order. Finally, the output features of the forward and reverse branches are fused element-wise.

[0076] The orientation texture-aware attention unit comprises a parallel spatial coordinate attention branch and a learnable Gabor filter branch. The spatial coordinate attention branch encodes channel information along the horizontal and vertical directions using a one-dimensional pooling kernel, and then generates a orientation-aware attention weight matrix through convolution and activation functions after merging. The learnable Gabor filter branch constructs a Gabor filter convolution kernel with learnable parameters for spatial frequency, orientation rotation angle, and axial standard deviation. During training, it adaptively enhances high-frequency directional textures and suppresses low-frequency noise. The input features of this module are multiplied by the coordinate attention weights and then residually fused with the Gabor filter features.

[0077] In this application, the theoretical optimal solution of X can be transformed into a Proximal Operator Network (Proximal Operator Network). Perform mapping solution: (20) The proximal operator First, utilize learnable weights. and It will have physical fidelity. and low-rank pure spectrum Information fusion is performed to obtain Formula 21. , All of them are learnable parameters that are greater than zero.

[0078] (twenty one) Fusion features After 3×3 embedding, the data are fed into the bidirectional spectral fusion unit and the orientation texture awareness attention unit, respectively.

[0079] The bidirectional spectral fusion unit contains two parallel attention streams (forward branch and backward branch). The forward branch uses spectral multi-head self-attention (SMSA) in the spectral dimension to extract global spectral associations, while the backward branch can extract multi-scale 1D convolutional module (MSCM) features after flipping the spectral dimension.

[0080] (twenty two) (twenty three) In the formula: It is a 3x3 convolution.

[0081] Then, the forward spectral dependence and the inverse spectral local continuous features are added together, and the result is obtained by performing a Fusion Conv (1×1 convolution and GELU) operation. : (twenty four) Similarly, another branch obtains it through Orientation and Texture-Aware Attention (OTAA). It captures global dependencies while preserving complex texture details, significantly improving the overall expressive power of the target outline.

[0082] (25) Finally, the initial fused features and the output features of the two branches are combined. and Perform residual connections to obtain the final reconstructed HSI feature map for this iterative stage. .

[0083] (26) In summary, the hyperspectral super-resolution reconstruction method fusion of phase prior and degradation perception provided in this application effectively overcomes the shortcomings of traditional unidirectional modeling in spectral reconstruction through a bidirectional spectral fusion unit, and solves the pain point in hyperspectral image processing where it is difficult to simultaneously consider global spectral long-range dependence and local continuous spectral similarity features. Figure 3 As shown, the bidirectional spectral fusion unit adopts an asymmetric dual-branch architecture: the forward branch uses spectral multi-head self-attention mechanism (SMSA) and depthwise separable convolution to efficiently extract global spectral features; the reverse branch applies cascaded multi-scale 1D convolution to the reverse spectral sequence to accurately capture the band-specific absorption micro-details under different receptive fields.

[0084] The forward branch aims to capture the global long-range dependencies of the spectral sequence while simultaneously injecting local spatial features. Specifically, the forward branch uses S-MSA proposed by the MST++ network, treating the complete two-dimensional spatial feature map of each band as an independent token. This design reduces the computational complexity of self-attention from... Significantly reduced to First, the input features... Perform layer normalization, flatten the spatial dimension H×W, and then reshape the feature map into a new sequence. ,in .

[0085] (27) Spectral relationships are modeled using N independent attention heads that process Q, K, and V projections in parallel, allowing the network to simultaneously focus on different spectral features along the spectral dimension. It is a learnable scalar parameter used to adjust the attention weights between different bands. The specific operation is shown in the formula: (28) (29).

[0086] Then, all N heads are concatenated and projected using a linear projection matrix. Further fusion is performed, followed by the addition of positional embeddings P(V) consisting of two 3×3 depthwise separable convolutions (DWConv). Finally, the SMSA feature dimensions are reshaped back to the same dimensions as the input features. (30) (31) To compensate for the local spatial information lost during serialization, the feature map undergoes channel mapping, local spatial feature extraction, channel restoration, and residual fusion to obtain the output of the forward branch.

[0087] (32) (33) (34) (35) The reverse branch extracts band-specific absorption features by disrupting the forward spectral order and utilizing multi-scale receptive fields. First, the input X is flipped along the spectral dimension to obtain the reverse-order features. Subsequently, the spatial dimension is compressed using global average pooling (GAP), and the vector is reshaped into a 1D spectral vector. : (36) (37) Subsequently, 1D convolution kernels of different sizes (K=1,3,5,7) were used to extract multi-scale spectral dependence features: (38) (39) (40) (41) After concatenating the features from the four scales along the spectral dimension, inverse spectral attention weights are generated by fusing convolution and the Sigmoid activation function. Then, the attention weights are expanded to B×1×1, and then the reversed feature maps are reweighted channel by channel. Finally, they are flipped back to the forward order. It is the Sigmoid activation function (S-type function).

[0088] (42) (43) Finally, the global spectral features extracted from the forward branch are... Local fine spectral enhancement features extracted with reverse branch Adding elements one by one, the final feature Y of the output module is: (44).

[0089] refer to Figure 4 This is a schematic diagram of the execution logic of the orientation texture perception attention unit in a hyperspectral super-resolution reconstruction method that integrates phase prior and degradation perception according to an embodiment of this application. The orientation texture perception attention unit adopts a dual-branch decoupled feature fusion architecture, such as... Figure 4 As shown in the diagram, the right branch is responsible for the precise spatial localization and long-distance dependent capture positional attention mechanism, while the left branch is a learnable directional Gabor filter that excels at extracting fine spatial features, allowing the network to "accurately identify key regions" while also "seeing complex textures," thereby significantly improving its comprehensive ability to express the target contour and detailed features.

[0090] The orientation texture-aware attention unit has a spatial coordinate attention branch and a learnable Gabor filter branch. Input features Where B is the number of spectral bands, and H and W are the height and width of the space, respectively.

[0091] The spatial coordinate attention branch consists of coordinate information embedding and coordinate attention generation. Coordinate information embedding involves encoding channel information in the input feature image X using pooling kernels of size (H,1) and (1,W) along the horizontal and vertical directions, respectively, thus obtaining a two-dimensional feature image. This allows for the capture of long-range features along one spatial direction while preserving precise location information along the other. As shown in the following formula: (45) (46) in, This represents the output of the b-th channel at height h; This represents the output of the b-th channel at height w.

[0092] In the process of generating coordinate attention, the first step is to merge... and Then, the directional spatial feature map f is obtained through a 1×1 convolution mapping function and an activation function, as shown in the following formula.

[0093] (47) Next, f is split into and Two tensors are transformed into tensors with the same number of spectral bands as the input X-rays through a 1×1 convolution, and then converted using the Sigmoid function. Generate attention weights in two directions. and Finally, the module's input feature map is multiplied element-wise with the two attention weights to obtain the module's output Y1, as shown below.

[0094] (48) (49) (50) In this application, the learnable Gabor filter branch can use a learnable Gabor filter, corresponding to the real-valued convolutional kernel in deep learning networks. This effectively solves the problems of traditional Gabor filters, which suffer from redundant feature extraction and an inability to automatically evolve during training to match complex image features due to the high dependence of their parameters on manual experience in selecting several directions and scales, and the lack of data adaptation capabilities. The formula for the learnable Gabor filter in this application is as follows: (51) In the formula, X,y represent pixel space coordinates; It is the standard deviation; Used to control the rotation direction of the Gabor convolution kernel; This represents the spatial aspect ratio of a Gaussian ellipse; This represents a fixed phase offset value; It is the wavelength of a sine wave, and the Gabor filter is a sine wave with a variable window; and Represents the learnable direction Rotated coordinates, using learnable spatial frequencies To capture texture features at different scales, and These represent the standard deviations that can be dynamically learned on the X and y axes, respectively.

[0095] This learnable Gabor filter enables a shift from "human experience-driven" to "data-driven"; it can dynamically optimize kernel parameters during training using the backpropagation algorithm, adaptively enhance high-frequency structural details in complex textures, and effectively suppress low-frequency background noise, significantly improving feature extraction accuracy while retaining the good physical interpretability of the Gabor filter operator.

[0096] In summary, the hyperspectral super-resolution reconstruction method that integrates phase prior and degradation sensing provided in this application has at least the following advantages: (1) Significantly improved structural fidelity: The explicit injection of Fourier phase prior effectively compensates for the loss of geometric structure caused by physical degradation. Especially on the Harvard dataset, this method has good comprehensive error suppression ability, effectively avoids local spatial blurring, and improves the distortion of complex structures such as building window outlines.

[0097] (2) High spectral consistency: The two-way spectral fusion mechanism breaks down the one-way information barrier. Research by technical personnel has found that after introducing two-way interaction, the SAM index, which measures spectral distortion, drops significantly, and can more accurately fit the small high-frequency abrupt changes in the real spectrum.

[0098] (3) Physically Degenerate Interpretable Deployment Architecture: The severely underdetermined spatial-spectral reconstruction objective function is decoupled into three alternating optimization subproblems: physical fidelity, low spectral rank, and depth prior, using the semi-quadratic splitting algorithm (HQS). This architecture explicitly embeds physical imaging mechanisms such as high-frequency phase features into the end-to-end network iteration, effectively enhancing the interpretability and robustness of the super-resolution reconstruction process.

[0099] also, Figure 1 The flowchart illustrating the hyperspectral super-resolution reconstruction method based on fused phase prior and degradation sensing shown in the diagram is merely a representation of the logical order provided by one of the many embodiments of this invention. This order is intended to clearly illustrate the execution flow of the method in a specific application scenario. However, in practical applications, the flexibility and scalability of this invention allow those skilled in the art to adjust the order of the above steps according to different practical needs and environmental conditions, such as having parallel or concurrent relationships between some steps, which will not be elaborated upon here.

[0100] Based on the same inventive concept, such as Figure 5As shown, this application also provides a hyperspectral super-resolution reconstruction system 100 that integrates phase prior and degradation perception, which includes an acquisition module 110, a construction module 120, a decoupling module 130, a physical degradation and phase update module 140, a spectral low-rank projection module 150, a dual-path feature reconstruction module 160, and an output module 170. Data transmission between these modules can be achieved via communication lines.

[0101] The acquisition module 110 is configured to acquire the observed image and the corresponding spectral response function matrix R. The construction module 120 is configured to construct an optimization objective function based on the spectral response function matrix R, wherein the optimization objective function includes at least a data fidelity term and a spatial-spectral joint prior term. The decoupling module 130 incorporates a semi-quadratic splitting algorithm, and is configured to decouple the optimization objective function according to the semi-quadratic splitting algorithm to obtain a physical fidelity constraint term, a spectral low-rank constraint term, and a depth prior constraint term.

[0102] The physical degradation and phase update module 140 is equipped with a Fourier phase-first amplitude hybrid processing model. The physical degradation and phase update module 140 is configured to optimize and solve the physical fidelity constraint terms based on the Fourier phase-first amplitude hybrid processing model, and obtain and update the first auxiliary variable Z. The first auxiliary variable Z is configured to process data fidelity and phase guidance.

[0103] The spectral low-rank projection module 150 is equipped with a truncated singular value decomposition model. The spectral low-rank projection module 150 is configured to optimize and solve the spectral low-rank constraint terms based on the truncated singular value decomposition model, and obtain and update the second auxiliary variable S. The second auxiliary variable S is used as a spectral low-rank prior.

[0104] The dual-path feature reconstruction module 160 is equipped with a dual-branch proximal mapping network model, which includes a bidirectional spectral fusion unit and an orientation texture perception attention unit. The dual-path feature reconstruction module 160 is configured to solve the depth prior constraint term based on the preset dual-branch proximal mapping network model, and update the target hyperspectral image X of the current cycle by combining the first auxiliary variable Z and the second auxiliary variable S.

[0105] The output module 170 is configured to use the target hyperspectral image X output in the last iteration loop as the high-resolution hyperspectral reconstructed image when the number of iterations reaches a threshold.

[0106] Furthermore, it should be noted that the hyperspectral super-resolution reconstruction system 100, which integrates phase prior and degradation sensing, may also include a memory and a controller. The memory stores machine-readable instructions executable by the processor. When the machine-readable instructions are executed by the processor, they perform the steps in the hyperspectral super-resolution reconstruction method integrating phase prior and degradation sensing provided in any of the above embodiments.

[0107] The implementation principle and technical effects of the hyperspectral super-resolution reconstruction system 100 based on the fusion of phase prior and degradation perception are the same as those of the aforementioned hyperspectral super-resolution reconstruction method based on the fusion of phase prior and degradation perception. For the sake of brevity, any parts not mentioned in the system embodiment can be referred to the corresponding content in the aforementioned hyperspectral super-resolution reconstruction method based on the fusion of phase prior and degradation perception.

[0108] In the experimental implementation of the hyperspectral super-resolution reconstruction method integrating phase prior and degradation perception provided in this application, technicians can use two hyperspectral datasets to evaluate the effectiveness of the proposed model. The first dataset, CAVE, contains 32 scenes covering five representative real-world material categories. This dataset was acquired using a cooled CCD camera, has a spatial resolution of 512×512 pixels, and includes 31 spectral bands with wavelengths ranging from 400 to 700 nm, spaced 10 nm apart.

[0109] The second dataset, known as Harvard, comprises 50 hyperspectral images (HSI) of indoor and outdoor scenes. These images were captured using a hyperspectral imaging system equipped with liquid crystal (Nuance FX, CRI, Inc.) with a spatial resolution of 1040 × 1392 pixels, a spectral range spanning 420–720 nm, and also include 31 spectral bands and a spectral step size of 10 nm.

[0110] This experiment was built using the PyTorch 2.2.0 deep learning framework and CUDA 12.1 environment. All network models were trained on a hardware platform equipped with an NVIDIA GeForce RTX 4090 D graphics card. Regarding hyperparameter configuration, the initial learning rate was set to 0.0005, and the total training epochs were 200.

[0111] In addition, during the execution of the hyperspectral super-resolution reconstruction method, different batch sizes were adopted for different datasets: the batch size for the CAVE and Harvard datasets was uniformly set to 64, while the batch size for the Chikusei remote sensing dataset was set to 16.

[0112]

[0113] As shown in Table 1, on the CAVE dataset, the PSNR value of the hyperspectral super-resolution reconstruction method provided in this application is 41.4637 dB, which is 0.3133 dB higher than the second-best MSFN algorithm. Regarding spectral distortion evaluation, the SAM value of the hyperspectral super-resolution reconstruction method provided in this application is 5.1925, which is 0.0749 lower than the second-best MST++ algorithm. Overall, the hyperspectral super-resolution reconstruction method provided in this application demonstrates good performance in both spatial detail recovery and spectral fidelity.

[0114] Figure 6 The comparison of specific errors of each algorithm on the CAVE test set "superballs" images is shown. In the error visualization, the closer the color is to dark blue, the smaller the reconstruction error; the closer it is to red, the larger the error. At the red arrow, the HSCNN+ algorithm has the largest bounding box error when reconstructing the first two squares from top to bottom. Compared to the other comparison algorithms, the hyperspectral super-resolution reconstruction method provided in this application has the best performance in reconstructing the bounding boxes of the first three squares from top to bottom. At the green arrow, the DRCR network significantly reduces the error of the balloon's outer boundary arc; the MST++ network reconstructs the balloon arc with a relatively large overall background error. Compared to MSFN, the hyperspectral super-resolution reconstruction method provided in this application has better performance in reconstructing texture and edge information.

[0115] As shown in Table 2, the hyperspectral super-resolution reconstruction method of this application achieves optimal values ​​for the three core indicators, SAM (3.9209), PSNR (42.5983 dB), and SSIM (0.9793), on the Harvard test set. Compared with the suboptimal MST++ algorithm, this method improves PSNR by 0.1633 dB and reduces SAM error by 0.022. Furthermore, the overall results fully demonstrate that the hyperspectral super-resolution reconstruction method of this application can better balance accurate restoration of spatial details with high-fidelity reconstruction of spectral information.

[0116]

[0117] like Figure 7 As shown, on img1 of the Harvard test set, HSCNN+ and EDSR exhibit high global background errors in the snow-covered area of ​​the eaves. The MSFN network still shows local distortion in the window outline of the red box. However, the hyperspectral super-resolution reconstruction method that integrates phase prior and degradation perception provided in this application demonstrates the best comprehensive error suppression capability, effectively avoiding the local spatial blurring that is prone to occur in other advanced algorithms.

[0118] It needs to be made clear that, Figure 1The flowchart illustrating the hyperspectral super-resolution reconstruction method fusing phase prior and degradation sensing shown in the document is merely a representation of the logical order provided by one of the many embodiments of this application. This order is intended to clearly illustrate the execution flow of the method in a specific application scenario. However, in practical applications, the flexibility and scalability of this application allow those skilled in the art to adjust the order of the above steps according to different actual needs and environmental conditions, such as having parallel or concurrent relationships between some steps, which will not be elaborated upon here.

[0119] Furthermore, those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0120] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 A means for a process or multiple processes and / or a block diagram (one or more blocks) specifying the functions.

[0121] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 A process or multiple processes and / or a block diagram (one or more blocks) specifying the functions.

[0122] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0123] Additionally, any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

Claims

1. A hyperspectral super-resolution reconstruction method integrating phase prior and degradation perception, characterized in that, Includes the following steps: S1, Based on the observed image, obtain the spectral response function matrix R corresponding to the observed image; S2, Based on the spectral response function matrix R, construct the optimization objective function; S3, according to the semi-quadratic splitting algorithm, the optimization objective function is decoupled to obtain the physical fidelity constraint term, the spectral low-rank constraint term, and the depth prior constraint term; S4, Based on the preset Fourier phase-first-first-second hybrid processing model, the physical fidelity constraint term is optimized and solved to obtain and update the first auxiliary variable Z. The first auxiliary variable Z is configured to process data fidelity and phase guidance. S5. Based on the preset truncated singular value decomposition model, the spectral low-rank constraint term is optimized and solved to obtain and update the second auxiliary variable S, which is used as the spectral low-rank prior. S6, based on the preset dual-branch proximal mapping network model, the depth prior constraint term is solved, and the target hyperspectral image X of the current cycle is updated by combining the first auxiliary variable Z and the second auxiliary variable S. The dual-branch proximal mapping network model includes a bidirectional spectral fusion unit and an orientation texture perception attention unit. Repeat steps S4 to S6 until the number of iterations reaches the threshold. Then, use the target hyperspectral image X output from the last iteration as the high-resolution hyperspectral reconstructed image.

2. The hyperspectral super-resolution reconstruction method fusing phase prior and degradation sensing according to claim 1, characterized in that, The step S3, which decouples the optimization objective function according to the semi-quadratic splitting algorithm to obtain the physical fidelity constraint, the spectral low-rank constraint, and the depth prior constraint, includes: According to the semi-quadratic splitting algorithm, the optimization objective function is transformed to obtain a multivariate unconstrained penalty function, which includes: a physical fidelity constraint term, a first penalty term, a second penalty term, a depth prior constraint term, and a regularization term. Wherein, the physical fidelity constraint term is used to constrain the physical degradation relationship between the observed image and the first auxiliary variable Z; the first penalty term is used to constrain the difference between the target hyperspectral image X and the first auxiliary variable Z; the second penalty term is used to constrain the difference between the target hyperspectral image X and the second auxiliary variable S; the regularization term is used to characterize the spectral low-rank characteristics of the second auxiliary variable S, and the regularization term and the second penalty term together constitute the spectral low-rank constraint term; the depth prior constraint term is used to characterize the joint depth space-spectral prior.

3. The hyperspectral super-resolution reconstruction method fusing phase prior and degradation sensing according to claim 1, characterized in that, The step S4, which optimizes and solves the physical fidelity constraint term based on a preset Fourier phase-first-image hybrid processing model to obtain and update the first auxiliary variable Z, includes: The observed image or the target hyperspectral image X from the previous iteration is processed and transformed to obtain a reference signal; According to a preset frequency domain transformation algorithm, the reference signal is transformed in the frequency domain to obtain structural components; The frequency domain transformation algorithm is used to perform a frequency domain transformation on the target hyperspectral image or observation image of the previous iteration to obtain the amplitude component. Based on the structural components and the amplitude components, the guiding features are calculated; Based on the guiding features and the physical fidelity constraints, the first auxiliary variable Z for the current stage is updated through an iterative optimization algorithm.

4. The hyperspectral super-resolution reconstruction method fusing phase prior and degradation sensing according to claim 3, characterized in that, The step of processing and transforming the observed image or the target hyperspectral image X from the previous iteration to obtain the reference signal includes: Based on the preset inverse projection matrix algorithm, the observed image or the target hyperspectral image X from the previous iteration is projected into the hyperspectral space to obtain the reference signal; And / or, the step of calculating the guiding features based on the structural components and the amplitude components includes: The structural components and amplitude components are combined in the frequency domain to construct a complex spectrum; Based on the inverse Fourier transform algorithm, the complex spectrum is transformed and guided features are generated; And / or, the step of updating the first auxiliary variable Z for the current stage through an iterative optimization algorithm based on the guiding features and the physical fidelity constraint term includes: Using the guiding feature as the initial value, and combining it with the physical fidelity constraint term, the gradient descent method is used to perform a single-step iterative update to obtain the first auxiliary variable Z.

5. The hyperspectral super-resolution reconstruction method fusing phase prior and degradation sensing according to claim 1, characterized in that, The step S5, which optimizes the low-rank constraint term of the spectrum based on a preset truncated singular value decomposition model to obtain and update the second auxiliary variable S, includes: The target hyperspectral image X or the observed image corresponding to the previous iteration is used as the input tensor and flattened in the spatial dimension to obtain a two-dimensional matrix; The two-dimensional matrix is ​​standardized to obtain the mean vector, standard deviation vector, and standardized signal matrix. The standardized signal matrix is ​​used as a high-dimensional signal. It is extracted and a low-rank orthogonal basis is constructed by truncating singular value decomposition. The high-dimensional signal is then projected onto the low-rank orthogonal basis for reconstruction, resulting in a reconstructed spectral low-rank matrix. The reconstructed spectral low-rank matrix is ​​denormalized based on the mean vector, the standard deviation vector, and the outer product operation algorithm, and then reshaped back to the original tensor dimension to obtain the updated second auxiliary variable.

6. The hyperspectral super-resolution reconstruction method fusing phase prior and degradation sensing according to claim 5, characterized in that, The steps of using the standardized signal matrix as a high-dimensional signal, extracting and constructing a low-rank orthogonal basis through truncated singular value decomposition, and projecting the high-dimensional signal onto the low-rank orthogonal basis for reconstruction to obtain the reconstructed spectral low-rank matrix include: The standardized signal matrix is ​​processed according to the economic singular value decomposition algorithm to obtain the left singular vector matrix, the singular value matrix, and the right singular vector matrix. Based on the preset low-rank constraint parameters, the first t largest singular values ​​and their corresponding left and right singular vectors are extracted to form a low-rank orthogonal basis. The inner product of the normalized signal matrix and the low-rank orthogonal basis is calculated, and redundant noise in the spectral dimension is eliminated by reconstruction to obtain a pure low-rank spectral matrix.

7. The hyperspectral super-resolution reconstruction method fusing phase prior and degradation sensing according to claim 1, characterized in that, The step S6, which involves solving the depth prior constraint term based on a preset dual-branch proximal mapping network model and updating the target hyperspectral image X for the current cycle by combining the first auxiliary variable Z and the second auxiliary variable S, includes: The first auxiliary variable Z and the second auxiliary variable S are input into the bidirectional spectral fusion unit. The forward branch is used to model the global long-range dependence of the spectral sequence, and the reverse branch is used to extract multi-scale band-specific absorption features. The spectral enhancement features are obtained through fusion. The spectral enhancement features are input into the orientation texture perception attention unit, and the directional perception attention weights are generated through the spatial coordinate attention branch. The high-frequency directional texture is adaptively enhanced through the learnable Gabor filter branch, and the texture perception features are obtained through residual fusion. The target hyperspectral image X for the current cycle is obtained by updating the texture-aware features.

8. The hyperspectral super-resolution reconstruction method fusing phase prior and degradation sensing according to claim 7, characterized in that, The steps of inputting the first auxiliary variable Z and the second auxiliary variable S into the bidirectional spectral fusion unit, modeling the global long-range dependence of the spectral sequence using the forward branch, extracting multi-scale band-specific absorption features using the reverse branch, and obtaining spectral enhancement features through fusion include: Use the observed image or the target hyperspectral image obtained from the previous iteration as the input feature map. In the forward branch of the bidirectional spectral fusion unit, the input feature map is flattened into a sequence vector according to the band dimension; according to the preset spectral multi-head self-attention mechanism, feature mapping is performed on different bands, modeling and obtaining the global long-range dependency features of the spectral sequence. In the reverse branch of the bidirectional spectral fusion unit, the input feature map is mirrored and flipped in reverse order according to the spectral dimension. The spatial dimension is compressed by global average pooling, and multi-scale band-specific absorption features are extracted by using one-dimensional convolution kernels of various sizes. Attention weights are generated to reweight the reversed features by channel and then flipped back to the forward order to obtain channel-reweighted features. The global long-range dependency feature and the channel reweighted feature are fused element-wise to obtain the fused spectral enhancement feature.

9. The hyperspectral super-resolution reconstruction method fusing phase prior and degradation sensing according to claim 8, characterized in that, The steps of inputting the spectral enhancement features into the orientation texture-aware attention unit, generating directional attention weights through a spatial coordinate attention branch, adaptively enhancing high-frequency directional textures through a learnable Gabor filter branch, and obtaining texture-aware features through residual fusion include: A one-dimensional adaptive average pooling kernel is used to encode global context information along the horizontal and vertical spatial coordinate axes of the input feature map, generating two independent channel description vectors. The channel description vectors are then merged through a concatenation operation and processed by a convolutional layer and activation function to generate a spatial attention weight matrix with directional awareness. The input feature map is convolved using a pre-defined complex Gabor filter bank to adaptively enhance high-frequency directional texture features and suppress low-frequency noise components under joint constraints in the frequency and spatial domains. The spatial frequency, orientation rotation angle, and axial standard deviation of the Gaussian envelope within the complex Gabor filter bank are all set as trainable network parameters. The input feature map is multiplied element-wise with the spatial attention weight matrix, and the result is concatenated channel-wise with the texture feature map output by the learnable Gabor filter branch. The target hyperspectral image X of the current loop is then output through the residual connection structure.

10. A hyperspectral super-resolution reconstruction system integrating phase prior and degradation sensing, characterized in that, include: The acquisition module is configured to acquire the observed image and the corresponding spectral response function matrix R; A construction module is configured to construct an optimization objective function based on the spectral response function matrix R, wherein the optimization objective function includes at least a data fidelity term and a spatial-spectral joint prior term; A decoupling module is provided, which includes a semi-quadratic splitting algorithm. The decoupling module is configured to decouple the optimization objective function according to the semi-quadratic splitting algorithm to obtain physical fidelity constraint terms, spectral low-rank constraint terms, and depth prior constraint terms. The physical degradation and phase update module includes a Fourier phase-first amplitude hybrid processing model. The physical degradation and phase update module is configured to optimize and solve the physical fidelity constraint terms based on the Fourier phase-first amplitude hybrid processing model, and obtain and update the first auxiliary variable Z. The first auxiliary variable Z is configured to process data fidelity and phase guidance. The spectral low-rank projection module includes a truncated singular value decomposition model. The spectral low-rank projection module is configured to optimize and solve the spectral low-rank constraint terms based on the truncated singular value decomposition model, and obtain and update the second auxiliary variable S. The second auxiliary variable S is used as a spectral low-rank prior. The dual-path feature reconstruction module includes a dual-branch proximal mapping network model, which comprises a bidirectional spectral fusion unit and an orientation texture perception attention unit. The dual-path feature reconstruction module is configured to solve the depth prior constraint term based on the preset dual-branch proximal mapping network model, and update the target hyperspectral image X of the current loop by combining the first auxiliary variable Z and the second auxiliary variable S. The output module is configured to use the target hyperspectral image X output in the last iteration loop as the high-resolution hyperspectral reconstructed image when the number of iterations reaches a threshold.

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