Hyperspectral image super-resolution reconstruction method based on multi-scale cavity convolution guidance

Abstract

The invention discloses a hyperspectral image super-resolution reconstruction method based on multi-scale cavity convolution guidance, and the method comprises the steps: carrying out the space downsampling of HrHSI to generate LrHSI, and carrying out the spectrum degradation to generate first LrMSI; after the HrHSI generates HrMSI through a spectral response function, performing space degradation to generate second LrMSI; constructing an initialized image generation module by adopting a double-branch network comprising multi-stage cascaded CCEs (Control Channel Element), and generating high-resolution initial estimation; a dual-path cavity cooperative enhancement module DDCA is constructed, a main path reinforces local details, an auxiliary path compresses global information, and feature calibration and residual fusion are realized through a gating mechanism; wherein the multi-scale cavity fusion module integrates a channel and a space attention mechanism so as to enhance context and detail information extraction capability; a depth image generation network of a double U-Net architecture is constructed based on DDCA, and reconstruction is realized through joint optimization. According to the invention, the feature distinguishing capability and the detail recovery capability are enhanced.

Description

Technical Field

[0001] This invention relates to the fields of computer vision and remote sensing image processing technology, and in particular to a method for super-resolution reconstruction of hyperspectral images based on multi-scale dilated convolution. Background Technology

[0002] Hyperspectral images (HSI), with their continuous narrow-band spectral resolution, enable precise identification of surface material composition, offering irreplaceable advantages in environmental monitoring, precision agriculture, and mineral exploration. However, due to limitations in sensor physical characteristics, HSI faces an inherent trade-off between spatial resolution and signal-to-noise ratio during acquisition, resulting in insufficient spatial detail and severely restricting refined application scenarios. Therefore, super-resolution reconstruction (HISR) by fusing high spatial resolution multispectral images (MSI) has become a core technological approach for economically acquiring high-resolution HSI (HrHSI). Traditional methods are mainly divided into two categories: frequency domain fusion based on generalized sharpening extension (such as wavelet transform) and optimization models based on matrix / tensor decomposition. The former, while not requiring degenerate model priors and being computationally efficient, is prone to spectral distortion, especially in complex terrain scenes where edge detail recovery is insufficient. The latter constructs optimization models by designing low-rank, sparse, and other regularization terms, which can partially preserve spectral characteristics, but relies on artificial prior assumptions, resulting in poor universality and low computational efficiency when dealing with large-scale data. Both types of methods struggle to balance spatial-spectral feature fidelity with computational efficiency, failing to meet the needs of practical scenarios.

[0003] With the rise of deep learning technology, supervised learning methods based on convolutional neural networks (CNNs) and Transformer architectures have significantly improved super-resolution reconstruction accuracy, achieving deep fusion of spatial-spectral features through end-to-end mapping learning. However, these methods heavily rely on large-scale pairwise training data (HrHSI-HrMSI-LrHSI triples), while high-resolution hyperspectral data is difficult to obtain in real-world scenarios, forcing models to rely on simulated degraded data for training, resulting in degradation of generalization ability and spectral distortion risks in practical applications. Furthermore, mainstream network designs often employ black-box structures, ignoring the physical constraints of the degraded model, leading to insufficient interpretability and difficulty in adapting to multi-sensor scenarios. In recent years, unsupervised methods (such as deep image priors and zero-shot learning) have partially alleviated the data dependency problem by introducing random noise input and degraded model constraints; however, random noise lacks spatial-spectral correlation information of the target scene, and the simple U-Net architecture struggles to fully capture complex high-order features, limiting the ability to reconstruct details. Traditional cross-attention guided modules are limited by a fixed receptive field during feature fusion, making it difficult to effectively capture spatial context information at different scales in images and affecting the detail recovery capability of super-resolution reconstruction. Therefore, how to construct an unsupervised network architecture guided by degradation models to achieve synergistic optimization of physical laws and data-driven approaches has become a key direction for overcoming the current technological bottlenecks. Summary of the Invention

[0004] To address the problems of insufficient multi-scale feature extraction and limited detail recovery capabilities in existing technologies, this invention proposes a hyperspectral image super-resolution reconstruction method guided by multi-scale dilated convolution.

[0005] The specific technical solution is as follows:

[0006] A hyperspectral image super-resolution reconstruction method guided by multi-scale dilated convolution includes the following steps:

[0007] Step 1: Spatially downsample the high-resolution hyperspectral image HrHSI to generate a low-resolution hyperspectral image LrHSI, and use a spectral degradation path to generate a first low-resolution multispectral image LrMSI; the HrHSI is used to generate a high-resolution multispectral image HrMSI through a spectral response function, and a second LrMSI is generated from it using a spatial degradation path.

[0008] Step 2: Construct an initial image generation module with a dual-branch network structure. The inputs to the two branches are the first LrMSI and the second LrMSI, respectively. Each branch includes multiple cascaded cross-channel correlation enhancement modules and subsequent deconvolution layers. The weighted average of the outputs of the two branches generates a high-resolution initial estimated image X. input ;

[0009] Step 3: Construct the dual-path hole collaborative enhancement module DDCA for dual-path processing, with the main path processing X... input The corresponding X branch is used to enhance local details; the auxiliary path processes the Z branch corresponding to HrMSI to compress global information. The two paths achieve weight feature calibration through Sigmoid gating. After the main path features and the auxiliary path weight map are multiplied element-wise, the original input is fused through residual connection to achieve spatial-spectral feature fusion. Both paths use the multi-scale hole fusion module MDFA to capture local to global spatial features, and utilize multiple hole rates and integrate channel attention and spatial attention mechanisms to enhance the ability to extract context and detail information.

[0010] Step 4: Construct a deep image generation network using a dual U-Net architecture, with DDCA embedded in the main and auxiliary paths throughout the entire link. The deep image generation network includes a downsampling stage, an upsampling stage, and a skip connection module between the two stages. In both the downsampling and upsampling stages, a multi-level feature refinement mechanism is constructed using the same number of cascaded DDCAs. Adaptive alignment of cross-resolution features is achieved at the skip connections. The input to the deep image generation network is X. input The output of the upsampling stage, along with HrMSI, is processed by a 1×1 convolution and a sigmoid activation function to obtain a reconstructed image that incorporates both spatial and spectral information.

[0011] Step 5, Joint Optimization and Reconstruction: Construct a multi-level loss constraint system, compare the reconstructed image with the initial high-resolution hyperspectral image HrHSI, and construct the loss function L2; when the loss function L2 is minimized, the corresponding reconstructed image is the desired reconstructed super-resolution hyperspectral image.

[0012] Furthermore, in step one, the HrHSI is blurred using a Gaussian blur kernel, and then LrHSI is generated by bicubic downsampling; the HrHSI matrix is ​​multiplied by the spectral response function matrix to generate HrMSI.

[0013] Furthermore, in step one, the spectral degradation path is multiplied by LrHSI and the learnable matrix of the spectral response function, and the spectral dimension of LrHSI is reduced to the multispectral dimension through linear transformation to obtain the first LrMSI; the learnable matrix of the spectral response function implicitly learns the weighted summation relationship of the multispectral bands to the hyperspectral bands, which is used to simulate the curve shape of the real spectral response function.

[0014] Furthermore, in step one, the spatial degradation path simulates the spatial blurring effect of the point spread function on HrMSI through a trainable depthwise separable convolution operation, and spatially degrades to generate a second LrMSI; specifically, the HrMSI is subjected to channel-wise depthwise separable convolution with the learnable parameter matrix of the point spread function, and the convolution results of each spectral channel are added together to obtain the LrMSI.

[0015] Furthermore, step two is specifically implemented through the following sub-steps:

[0016] (2.1) The input feature map of each level of cross-channel association enhancement module is F. in ∈R H×W×C H represents the height of the HrHSI, W represents the width of the HrHSI, and C represents the number of spectral channels of the HrHSI. The input feature map of the first-level cross-channel correlation enhancement module of the first branch is the first LrMSI, and the input feature map of the first-level cross-channel correlation enhancement module of the second branch is the second LrMSI. The output of the current-level cross-channel correlation enhancement module is used as the input of the next-level cross-channel correlation enhancement module until the cascading ends. The output of the first branch after passing through multiple cascaded cross-channel correlation enhancement modules is F1, and the output of the second branch after passing through multiple cascaded cross-channel correlation enhancement modules is F2.

[0017] (2.2) Upsample F1 and F2 using a deconvolutional layer with shared weights, and use them as the outputs of this branch:

[0018] X s1 =Deconv(F1)

[0019] X s2 =Deconv(F2)

[0020] (2.3) The outputs of the first branch and the second branch are weighted and averaged to generate a high-resolution initial estimate, as shown in the following expression:

[0021]

[0022] Furthermore, in each level of the cross-channel association enhancement module, F is applied along the channel dimension. in Divide the data into three equal groups: G1, G2, and G3, where G1, G2, and G3 ∈ R. H×W×C / 3 Cross-channel information transmission is achieved through cascaded feature fusion. The first group of processing:

[0023] G′1=Conv 3×3 (LeakyReLU(G1))

[0024] Second group of interactions:

[0025] G′2=Conv3×3 (LeakyReLU(G2+G′1))

[0026] Third group fusion:

[0027] G′3=Conv 3×3 (LeakyReLU(G3+G′1+G′2))

[0028] The three processed outputs are concatenated along the channel to obtain:

[0029] F cat =[G′1, G′2, G′3]∈R H×W×C

[0030] Channel attention weights are generated using 1×1 convolution and Softmax:

[0031] W = Softmax(Conv) 1×1 (F cat ))∈R 1×1×3

[0032] The three sets of outputs are weighted and summed according to the channel attention weights:

[0033] F weithted =W1·G′1+W2·G′2+W3·G′3

[0034] Based on the residual learning mechanism, feature enhancement is performed, and then the weighted features are increased in dimensionality through 1×1 convolution to obtain:

[0035] F processed =Conv 1×1 (LeakyReLU(F weighted ))

[0036] Using jump connections to connect F processed With the original input F in The components are added together to preserve the undegraded spectral information, yielding the output of this level of cross-channel correlation enhancement module, expressed as follows:

[0037] F out =F processed +F in

[0038] The output F of the last-level cross-channel association enhancement module of the first branch out F1 is the output F of the last-level cross-channel association enhancement module in the second branch. out It is F2.

[0039] Furthermore, step three is specifically implemented through the following operations:

[0040] The main path processes the X branch: This path introduces a feature preprocessing module at the front end; the feature preprocessing module includes: ① using a 5×5 kernel-sized depthwise separable convolution to extract features from the input image to capture local spatial structure features; ② performing batch normalization on the convolution output; ③ introducing the LeakyReLU activation function to enhance nonlinear expressive power; ④ capturing local to global spatial features through MDFA; obtaining the output of the current DDCA main path, expressed as follows:

[0041] X m_p =MDFA(LeakyReLU(BN(Conv) 5×5 (X input_p ))))

[0042] In the formula, X m_p X represents the main path output of the p-th level DDCA. input_p This represents the main path input of the p-th level DDCA;

[0043] Meanwhile, the auxiliary path also introduces a feature preprocessing module at the front end to process the Z branch. The expression output by this path is as follows:

[0044] Z p =MDFA(LeakyReLU(BN(Conv) 5×5 (Z input_p ))))

[0045] In the formula, Z p Z represents the output of the Z branch of the p-th level DDCA. input_p This represents the secondary path input for the p-th level DDCA;

[0046] For Z p The lightweight compression process includes: extracting channel-level global features using average pooling, reducing dimensionality through 1×1 convolution, enhancing key feature responses through ReLU activation, increasing dimensionality again through 1×1 convolution to restore channel dimensions, and obtaining adaptive channel weights for the p-th level DDCA using the sigmoid function, as shown in the following expression:

[0047] W attn_p =σ(Conv 1×1 (ReLU(Conv 1×1 (AvgPool(Z p )))))

[0048] In the formula, σ represents the Sigmoid function, with a weight range of [0, 1];

[0049] Weighted feature calibration: Adjusting X m_p With W attn_p Element-wise multiplication yields the output X of the X branch of the p-th level DDCA.p .

[0050] Furthermore, in step four, both paths employ the Multi-Scale Hollow Fusion Module (MDFA) to capture local to global spatial features, specifically achieved through the following operations:

[0051] (1) MDFA adopts a five-way parallel convolutional branch structure and achieves multi-scale feature capture of the input through differentiated dilation rate design;

[0052] Branch 1 is used for local detail extraction, employing a 1×1 standard convolution with a dilation rate of 1, and is expressed as follows:

[0053]

[0054] In the formula, X represents the convolution operation. in This represents the current input to the MDFA;

[0055] Branch 2 is used for medium receptive fields, employing a 3×3 standard convolution with a dilatation rate of 6, as shown in the following expression:

[0056]

[0057] Branch 3 is used for a wide range of contexts, employing a standard 3×3 convolution with a dilation rate of 12, and is expressed as follows:

[0058]

[0059] Branch 4 uses the widest receptive field, employing a 3×3 standard convolution with a dilatation rate of 18, as shown in the following expression:

[0060]

[0061] Branch 5 is the global average pooling branch, used to extract global contextual features. It employs a 3×3 standard convolution with a dilation rate of 18, and the expression is as follows:

[0062] F gap =AvgPool2d(X in )

[0063] The five features are concatenated and weighted along the channel dimension to obtain the comprehensive feature map F. fused The expression is as follows:

[0064]

[0065] In the formula, the weight α k Weights set by humans;

[0066] (2) Employing channel attention mechanism and spatial attention mechanism to synthesize feature map Ffused Perform channel and spatial dimension recalibration.

[0067] Channel dimension: for F fused Global average pooling is performed on each channel to generate a channel description vector Z. c The expression is as follows:

[0068]

[0069] In the formula, Z c ∈R 1×1×5C , C represents the number of spectral channels of HrHSI; H represents the height of HrHSI, W represents the width of HrHSI, and c represents the number of spectral channels of HrMSI.

[0070] Channel importance weights W are generated using a 1×1 convolutional layer and a non-linear activation function. c The expression is as follows:

[0071] W c =σ(FC2(ReLU(FC1(Z)) c ))))∈R 1×1×5C

[0072] In the formula, σ represents the Sigmoid function, with a weight range of [0, 1];

[0073] Weight W c With the comprehensive feature map F fused Multiply by each channel to obtain the channel attention output F. channwl ;

[0074] Spatial dimension: along f fused Global max pooling and average pooling are performed along the channel dimension to generate a spatial feature map Z. s The expression is as follows:

[0075]

[0076] Then, a spatial attention map W is generated by 1×1 convolution and sigmoid activation. s The expression is as follows:

[0077] W s =σ(Conv 1×1 (Z s ))∈R H×W×1

[0078] Finally, the weights are multiplied position-by-position by the comprehensive feature map to obtain the spatial attention output f. spatial ;

[0079] (3) Feature fusion and dimensionality reduction: The channel attention and spatial attention outputs are superimposed on the original features to preserve the original information. The expression is as follows:

[0080] F att =F fused +F channel +F spatial ∈R H×W×5C

[0081] Finally, the channel dimension is compressed using a 1×1 convolution to generate the final output, as shown in the following expression:

[0082]

[0083] In the formula, C out The target number of channels is X. in One-fifth of the number of channels.

[0084] Furthermore, in step four, during the downsampling phase, X is input into the main path of the first-level DDCA. input_1 =X input Secondary path input Z input_1 =z, to obtain X1 and Z1; after average pooling downsampling of X1 and z1, input them into the second-level DDCA to obtain X2 and z2; after average pooling downsampling of X2 and Z2, input them into the third-level DDCA to obtain X3 and Z3;

[0085] The operations performed by the skip connection module include: 1×1 convolution to compress feature channels, batch normalization, and LeakyReLU activation function to enhance nonlinear expressive power;

[0086] During the upsampling phase, X3 and Z3 are upsampled to obtain X. 3_up , Z 3_up Input X2 and Z2 into the jump connection module to generate s1 and s2, wherein s1 and s2 are respectively connected to X 3_up , Z 3_up Perform feature concatenation to generate Then, input it into the fourth level DDCA to obtain X4 and Z4;

[0087] Upsampling X4 and Z4 yields X 4_up , Z 4_up Input X1 and Z1 into the jump connection module to generate s3 and s4, where s1 and s2 are respectively connected to X. 4_up , Z 4_up Perform feature concatenation to generate Then, input it into the fourth level DDCA to get X5 and Z6;

[0088] The output X6 from the upsampling stage is then processed by a 1×1 convolution and a sigmoid activation function to obtain the reconstructed image.

[0089] Furthermore, in step five, a multi-level loss constraint system is constructed. Through the synergistic optimization of the spectral response function, point spread function, and data-driven approach, unsupervised hyperspectral image reconstruction is achieved. The loss function is as follows:

[0090]

[0091] In the formula, Φ SRF This represents the spectral response function SRF, with parameter θ. SRF , Φ PSF This represents the point spread function (PSF), with parameter θ. PSF When the loss function L2 is minimized, the corresponding reconstructed image is the desired reconstructed super-resolution hyperspectral image.

[0092] The beneficial effects of this invention are:

[0093] (1) This invention constructs a multi-scale dilated fusion attention (MDFA) module, which significantly improves the comprehensiveness and robustness of feature representation. This module uses a multi-branch parallel dilated convolutional structure to cover multiple levels of receptive fields, from local details to global semantics, simultaneously capturing spatial-spectral features at different scales. Combined with a dynamic weight fusion mechanism and dual-domain attention calibration, it effectively enhances feature discrimination capabilities and solves the problems of detail loss and insufficient contextual information in traditional methods. The multi-branch parallel design balances computational efficiency and accuracy, significantly improving image quality.

[0094] (2) This invention designs a dual-dilated cooperative attention (DDCA) module to achieve efficient fusion and calibration of cross-modal features. Through a dual-path cooperative mechanism that enhances local detail extraction via the main path and extracts global guiding signals via the auxiliary path, combined with Sigmoid-gated dynamic interaction, optimized calibration of spatial-spectral features is achieved. Residual connections preserve original information, enhancing model stability and training convergence speed. The deep image generation network built based on DDCA achieves multi-level feature adaptive alignment through a symmetrical design of upsampling and downsampling, combined with a cross-scale skip connection module, effectively preserving high-frequency details; and constructs a multi-level loss constraint system to achieve unsupervised blind reconstruction.

[0095] (3) This invention achieves high-precision and high-efficiency hyperspectral image super-resolution reconstruction through multi-module collaborative innovation. Its lightweight architecture and end-to-end optimization framework significantly reduce the dependence on hardware resources and are applicable to real-time scenarios such as remote sensing monitoring and environmental analysis. Attached Figure Description

[0096] Figure 1 This is a flowchart of a hyperspectral image super-resolution reconstruction method guided by multi-scale dilated convolution in an embodiment of the present invention.

[0097] Figure 2 This is a schematic diagram of the structure of the image generation module initialization in an embodiment of the present invention, wherein (a) is a calculation flowchart in the image generation module initialization, and (b) is a calculation flowchart of the single-level cross-channel association enhancement module CCE.

[0098] Figure 3 This is a schematic diagram of the structure of the Dual-Path Hole Co-enhancement Module (DDCA) in an embodiment of the present invention.

[0099] Figure 4 This is a schematic diagram of the structure of the multi-scale void fusion module MDFA in an embodiment of the present invention.

[0100] Figure 5 This is a schematic diagram of the structure of the depth image generation network in an embodiment of the present invention. Detailed Implementation

[0101] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The objectives and effects of the present invention will become clearer as a result. The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0102] like Figure 1 As shown, a hyperspectral image super-resolution reconstruction method based on multi-scale dilated convolution includes the following steps:

[0103] S1: Data Preprocessing: Spatial-spectral downsampling. The high-resolution hyperspectral image (HrHSI) is spatially downsampled (Gaussian blur kernel and downsampling) to generate a low-resolution hyperspectral image (LrHSI), and then a high-resolution multispectral image (HrMSI) is generated using the Spectral Response Function (SRF). This is achieved through the following sub-steps:

[0104] (S1.1) Spatial downsampling: The HrHSI is blurred using a Gaussian blur kernel, and then LrHSI is generated by bicubic downsampling, as shown in the following expression:

[0105]

[0106] In the formula, G is the Gaussian kernel. Represents a convolution operation; X∈R H×W×C Represents HrHSI, where H is the height of HrHSI, W is the width of HrHSI, and C is the number of spectral channels of HrHSI; Y∈R h×w×C Let LrHSI be the height of LrHSI and w be the width of LrHSI.

[0107] (S1.2) Using the SRF matrix, HrMSI is generated through matrix multiplication, as shown in the following expression:

[0108] Z = X·S

[0109] In the formula, Z∈R H×W×c Let S represent HrMSI, where c is the number of spectral channels of HrMSI; S∈R C×c This represents the SRF matrix.

[0110] (S1.1) and (S1.2) can be performed simultaneously.

[0111] S2: Construct a degradation information learning module and adopt dual-path degradation modeling to obtain two types of low-resolution multi-spectral images (LrMSI). The dual paths are spatial degradation path and spectral degradation path.

[0112] Spatial Degradation Path: By using trainable depthwise separable convolution operations, the spatial blurring effect of the point spread function (PSF) on HrMSI is simulated, resulting in spatial degradation to LrMSI, as expressed below:

[0113] K2=Z⊙W PSF

[0114] In the formula, W PSF ∈R k×k×1 The matrix represents the learnable parameters, where k represents the kernel size and ⊙ represents channel-wise depth-separable convolution, where each spectral channel is spatially convolved independently and then summed.

[0115] Spectral degradation path: By fitting the SRF through pointwise convolutional layers, another LrMSI is generated from the LrHSI spectral degradation. Specifically, a learnable parameter matrix W is constructed. SRF ∈R C×c By using a linear transformation, the spectral dimension of LrHSI is reduced from C to the multispectral dimension c, resulting in LrMSI, as expressed below:

[0116] K1 = Y·W SRF

[0117] W SRF The weighted summation relationship between the multispectral bands and the hyperspectral bands is implicitly learned to simulate the shape of the real SRF curve. A joint optimization objective for the degradation parameters is established: minimizing the difference between the two LrMSI values, corresponding to the constructed loss function expression:

[0118] L1 = ||K1-K2||1

[0119] In the formula, ||·||1 represents the mean absolute error function.

[0120] S3: Construct the initial image generation module, such as Figure 2 As shown, this module has a symmetrical dual-branch network structure to achieve parallel processing of dual inputs. Each branch contains multiple cascaded Channel Correlation Enhancement (CCE) modules and deconvolution layers, establishing cross-band correlations through progressive feature fusion. The weighted average of the dual-branch outputs yields a high-resolution initial estimated image X. input Specifically, this is achieved through the following sub-steps:

[0121] (S3.1) As Figure 2As shown in (a), the initial image generation module has a symmetrical dual-branch network structure. The inputs to the two branches are the low-resolution multispectral images K1 (degraded by LrHSI spectral degradation) and K2 (degraded by HrMSI spatial degradation) obtained by S2, respectively. Each branch contains multi-level cascaded CCEs, and cross-band associations are established through progressive feature fusion. In this embodiment, a three-level cascade is used to perform feature extraction and fusion step by step. The input of the first branch is K1, which generates intermediate feature F1 through the three-level cascaded CCEs. The input of the second branch is K2, which also generates intermediate feature F2 through the three-level cascaded CCEs.

[0122] like Figure 2 As shown in (b), cross-layer skip connections are used in each level of CCE to preserve the original degradation feature information.

[0123] CCE enhances the network's ability to model complex spectral features in hyperspectral images through cross-channel feature interaction and dynamic weight allocation mechanisms. Its core objectives are to eliminate channel redundancy, adaptively distinguish important channels, suppress noise interference, and capture cross-band nonlinear spectral correlations. The input feature map for each CCE level is F. in ∈R H×W×C (Initial F) in (For K1 or K2), along the channel dimension, F in Divide into three equal groups: G1 = G2 = G3 = split(F in That is, G1, G2, G3∈R H×W×C / 3 Cross-channel information transmission is achieved through cascaded feature fusion. The first group of processing:

[0124] G′1=Conv 3×3 (LeakyReLU(G1))

[0125] Second group of interactions:

[0126] G′2=Conv 3×3 (LeakyReLU(G2+G′1))

[0127] Third group fusion:

[0128] G′3=Conv 3×3 (LeakyReLU(G3+G′1+G′2))

[0129] The three processed outputs are concatenated along the channel to obtain:

[0130] F cat =[G′1, G′2, G′3]∈R H×W×C

[0131] Next, channel attention weights are generated using 1×1 convolution and Softmax:

[0132] W = Softmax(Conv) 1×1 (F cat ))∈R 1×1×3

[0133] Next, the three sets of features are summed according to their weights:

[0134] F weighted =W1·G′1+W2·G′2+W3·G′3

[0135] Based on the residual learning mechanism, feature enhancement is performed, and then the weighted features are increased in dimensionality through 1×1 convolution to obtain:

[0136] F processed =Conv 1×1 (LeakyReLU(F weighted ))

[0137] Using jump connections to connect F processed With the original input F in The spectra are added together to preserve the undegraded spectral information, yielding the output of this level of CCE:

[0138] F out =F processed +F in

[0139] The input to the first-level CCE is K1 or K2, and the output of the current-level CCE is used as the input to the next-level CCE, until the cascading ends.

[0140] (S3.2) Upsample F1 and F2 using a deconvolutional layer with shared weights, and use them as the outputs of this branch:

[0141] X s1 =Deconv(F1)

[0142] X s2 =Deconv(F2)

[0143] (S3.3) Perform a weighted average on the dual outputs to generate a high-resolution initial estimated image, as shown in the following expression:

[0144]

[0145] S4: Construct the Dual-Path Hollow Collaborative Enhancement Module (DDCA), such as Figure 3As shown, DDCA also employs a dual-path processing flow. The main path enhances local details, while the auxiliary path compresses global information. The dual paths utilize Sigmoid gating for feature calibration. After element-wise multiplication of the main path features with the weight map, the original input is fused through residual connections, resulting in cross-scale, cross-modal feature enhancement and achieving efficient fusion of spatial-spectral features. Specifically, a multi-scale hole fusion module (MDFA) is used, leveraging various hole rates and integrating channel and spatial attention mechanisms to enhance feature representation while capturing detailed information and broad contextual information in the image. This is achieved through the following sub-steps:

[0146] (S4.1) Main Path Processing X Branch: This path introduces a feature preprocessing module at the front end. The feature preprocessing module includes: ① using a 5×5 kernel-sized depthwise separable convolution to extract features from the input image to capture local spatial structure features; ② batch normalizing the convolution output to accelerate training and stabilize gradients; ③ introducing the LeakyReLU activation function to enhance nonlinear expressive power; ④ capturing local to global spatial features through MDFA to obtain the output of the current DDCA main path, the formula of which is as follows:

[0147] X m_p =MDFA(LeakyReLU(BN(Conv) 5×5 (X input_p ))))

[0148] In the formula, X m_p X represents the main path output of the p-th level DDCA. input_p This represents the main path input of the p-th level DDCA.

[0149] Simultaneously, the auxiliary path handles the Z branch: This path also introduces a feature preprocessing module at the front end, using a 5×5 kernel-sized depthwise separable convolution to extract features from the input image to capture local spatial structure features. The convolution output is batch normalized to accelerate training and stabilize gradients. Subsequently, the LeakyReLU activation function is introduced to enhance non-linear expressive power. Then, MDFA is used to capture local to global spatial features, with the following formula:

[0150] Z p =MDFA(LeakyReLU(BN(Conv) 5×5 (Z input_p ))))

[0151] In the formula, Z p Z represents the output of the Z branch of the p-th level DDCA. input_p This represents the secondary path input for the p-th level DDCA.

[0152] Next, a lightweight compression process is used to generate low-dimensional spectral features. This process includes: ① average pooling to extract channel-level global features; ② 1×1 convolution for dimensionality reduction; ③ introducing the ReLU activation function to enhance the response of key features; ④ 1×1 convolution for dimensionality increase to restore channel dimensions and retain core information; and ⑤ generating adaptive channel weights using the sigmoid function. The output of the current DDCA auxiliary path is then obtained, as shown in the following formula:

[0153] W attn_p =σ(Conv 1×1 (ReLU(Conv 1×1 (AvgPool(Z p )))))

[0154] In the formula, W attn_p σ represents the adaptive channel weights of the p-th level DDCA; σ represents the Sigmoid function with a weight range of [0, 1].

[0155] (S4.2) Weight feature calibration: Adjust X m_p With W attn_p Element-wise multiplication is used to achieve dynamic weighting of features, enhancing the response intensity of important regions, and obtaining the X branch output of the p-th level DDCA, as shown in the following formula:

[0156]

[0157] In the formula, This indicates element-wise multiplication.

[0158] In the process of processing the X branch of the main path and the Z branch of the secondary path in S4.1, local to global spatial features are captured through MDFA, such as... Figure 4 As shown, MDFA is implemented through the following operations:

[0159] (1) MDFA has a multi-branch parallel dilated convolution design: it adopts a five-way parallel convolution branch structure and achieves multi-scale feature capture of MDFA input through differential dilation design.

[0160] Branch 1 is used for local detail extraction, employing a 1×1 standard convolution with a dilation rate of 1, and its formula is as follows:

[0161]

[0162] In the formula, X in This represents the current input to the MDFA.

[0163] Branch 2 is used for a medium receptive field, employing a 3×3 standard convolution with a dilatancy of 6, and its formula is as follows:

[0164]

[0165] Branch 3 is used for a wide range of contexts, employing a standard 3×3 convolution with a dilation rate of 12, and its formula is as follows:

[0166]

[0167] Branch 4 is used for the widest receptive field, employing a 3×3 standard convolution with a dilatation rate of 18, as shown in the following formula:

[0168]

[0169] Branch 5 is an additional global average pooling branch used to extract global contextual features, enhancing the MDFA model's understanding of the overall layout. It employs a 3×3 standard convolution with a dilation rate of 18, and its formula is as follows:

[0170] F gap =AvgPoll2d(X in )

[0171] The five features are concatenated and weighted along the channel dimension to obtain the comprehensive feature map F. fused The formula is as follows:

[0172]

[0173] In the formula, the weight α k Weights set by humans.

[0174] (2) Employing channel attention mechanism and spatial attention mechanism to synthesize feature map F fused By recalibrating the channel and spatial dimensions, the two attention mechanisms can be performed simultaneously.

[0175] Channel attention mechanism: for F fused Each channel undergoes global average pooling (GAP) to generate a channel description vector Z. c The formula is as follows:

[0176]

[0177] Where the output vector dimension is: Z c ∈R 1×1×5C ,

[0178] Channel importance weights W are generated using a 1×1 convolutional layer and a non-linear activation function. c The formula is as follows:

[0179] W c =σ(FC2(ReLU(FC1(Z)) c ))))∈R1×1×5C

[0180] Finally, the weight W is... c With the comprehensive feature map F fused Multiplying each channel sequentially yields the channel attention output, as shown in the following formula:

[0181] F channel =W c ×F fused

[0182] In the formula, × represents channel-by-channel multiplication.

[0183] Spatial attention mechanism: along F fused Global Max Pooling (GMP) and Average Pooling (GAP) are performed along the channel dimension to generate a spatial feature map Z. s The formula is as follows:

[0184]

[0185] Next, a spatial attention map is generated using a 1×1 convolution and a sigmoid activation, as shown in the following formula:

[0186] W s =σ(Conv 1×1 (Z s ))∈R H×W×1

[0187] Finally, the weights are multiplied position-by-position by the comprehensive feature map to obtain the spatial attention output, the formula of which is as follows:

[0188]

[0189] In the formula, This indicates positional multiplication.

[0190] (3) Feature fusion and dimensionality reduction: The channel and spatial attention outputs are superimposed on the original features to preserve the original information. The formula is as follows:

[0191] F att =F fused +F channel +F spatial ∈R H×W×5C

[0192] Finally, the channel dimension is compressed using a 1×1 convolution to generate the final output, as shown in the following formula:

[0193]

[0194] In the formula, C out Indicates the target number of channels (X is the input of MDFA).in One-fifth of the number of channels).

[0195] S5. Constructing a Deep Image Generation Network: The deep image generation network adopts a symmetrical dual-U-Net architecture. The main and auxiliary branches embed DDCA throughout the entire link and achieve dynamic interaction through the cross-modal attention mechanism of DDCA. Specifically, the deep image generation network includes a downsampling stage (i.e., the encoder stage), an upsampling stage (i.e., the decoder stage), and skip connections between the two. In the downsampling and upsampling stages, a multi-level feature refinement mechanism is constructed through cascaded DDCA, and adaptive alignment of cross-resolution features is achieved at the skip connections.

[0196] During the downsampling phase, X is input into the main path of the first-level DDCA (corresponding to the first layer of the encoder). input_1 =X input Secondary path input Z input_1 =Z, output X1 and Z1, the expression is as follows:

[0197] X1, Z1 = DDCA1(X input_1 Z input_1 )

[0198] Downsampling X1 and Z1 yields X 1_down and Z 1_down The formula is as follows:

[0199] X 1_down Z 1_down =AvgPool1(X1, Z1)

[0200] X 1_down and Z 1_down Inputting the second-level DDCA (corresponding to the second layer of the encoder) yields X2 and Z2, with the following formulas:

[0201] X2, Z2 = DDCA2(X 1_down Z 1_down )

[0202] Downsampling X2 and Z2 yields X 2_down and Z 2_dowm The formula is as follows:

[0203] X 2_down Z 2_down =AvgPool2(X2, Z2)

[0204] Next, X 2_down and Z 2_down Inputting the third-level DDCA yields X3 and Z3, achieving global feature aggregation, as shown in the following formula:

[0205] X3, Z3 = DDCA3(X2_down Z 2_down )

[0206] Skip connections: Skip connection modules can preserve high-frequency details (such as edges and textures) from the encoder stage. Their operations include: compressing feature channels through 1×1 convolution to achieve cross-channel information fusion; stabilizing feature distribution and suppressing noise interference through batch normalization; and finally enhancing nonlinear expressive power using the LeakyReLU activation function. The formula is as follows:

[0207] s q =LeakyReLU(BN(Conv 1×1 (F l )))

[0208] In the formula, F l This represents the l-th layer features of the encoder, with the first layer corresponding to X1 and Z1, and the second layer corresponding to X2 and Z2.

[0209] During the upsampling phase, the outputs X3 and Z3 from the previous layer are upsampled to obtain X. 3_up and Z 3_up The formula is as follows:

[0210] X 3_up Z 3_up =BilinearUp1(X3, Z3)

[0211] The upsampling stage achieves multi-resolution optimization through multi-level skip connections and dynamic feature fusion. X2 and Z2, through the skip connection module, generate s1 and s2 respectively with X... 3_up , Z 3_up Feature splicing generation The formula is as follows:

[0212]

[0213] Will Inputting the fourth level DDCA yields X4 and Z4, with the following formulas:

[0214]

[0215] Upsampling X4 and Z4 yields X 4_up and Z 4_up The formula is as follows:

[0216] X 4_up Z 4_up =BilinearUp2(X4, Z4)

[0217] X1 and Z1 generate s3 and s4 through the jump connection module, respectively, which are connected to X... 4_up and Z 4_upFeature splicing generation The formula is as follows:

[0218]

[0219] Will Inputting the fourth-level DDCA yields X5 and Z5, with the following formulas:

[0220]

[0221] Finally, X5 obtains the output value of the depth image generation network through a 1×1 convolutional kernel and a sigmoid activation function. The formula is as follows:

[0222]

[0223] S6. Joint Optimization and Reconstruction: Constructing a multi-level loss constraint system. It is a reconstructed image generated by a depth image generation network, containing fused spatial and spectral information. The essence of the feedback network is to build a joint optimization multi-objective training mechanism, so that the network can simultaneously meet the requirements of physical degradation modeling, structural alignment and reconstruction accuracy at multiple levels, thereby further improving the quality and robustness of super-resolution hyperspectral images. By combining model-driven loss and data-driven optimization, it ensures that the reconstruction results meet both physical constraints and visual quality requirements.

[0224] A multi-level loss constraint system is constructed, and unsupervised hyperspectral image reconstruction is achieved through the synergistic optimization of the physical degradation model and data-driven approaches. The loss function formula is as follows:

[0225]

[0226] Where, Φ SRF This represents the spectral response function SRF, with parameter θ. SRF , Φ PSF This represents the point spread function (PSF), with parameter θ. PSF When the loss function L2 is minimized, the corresponding reconstructed image is the desired reconstructed super-resolution hyperspectral image.

[0227] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for super-resolution reconstruction of hyperspectral images based on multi-scale dilated convolution, characterized in that, Includes the following steps: Step 1: Spatially downsample the high-resolution hyperspectral image HrHSI to generate a low-resolution hyperspectral image LrHSI, and use a spectral degradation path to generate a first low-resolution multispectral image LrMSI; the HrHSI is used to generate a high-resolution multispectral image HrMSI through a spectral response function, and a second LrMSI is generated from it using a spatial degradation path. Step 2: Construct an initial image generation module with a dual-branch network structure. The inputs to the two branches are the first LrMSI and the second LrMSI, respectively. Each branch includes multiple cascaded cross-channel correlation enhancement modules and subsequent deconvolution layers. The weighted average of the outputs of the two branches generates a high-resolution initial estimated image X. input ; Step 3: Construct the dual-path hole collaborative enhancement module DDCA for dual-path processing, with the main path processing X... input The corresponding X branch is used to enhance local details; the auxiliary path processes the Z branch corresponding to HrMSI to compress global information. The two paths achieve weight feature calibration through Sigmoid gating. After the main path features and the auxiliary path weight map are multiplied element-wise, the original input is fused through residual connection to achieve spatial-spectral feature fusion. Both paths use the multi-scale hole fusion module MDFA to capture local to global spatial features, and utilize multiple hole rates and integrate channel attention and spatial attention mechanisms to enhance the ability to extract context and detail information. Step 4: Construct a deep image generation network using a dual U-Net architecture, with DDCA embedded in the main and auxiliary paths throughout the entire link; the deep image generation network includes a downsampling stage, an upsampling stage, and a skip connection module between the two stages. In the downsampling and upsampling stages, a multi-level feature refinement mechanism is constructed through the same number of cascaded DDCAs, and adaptive alignment of cross-resolution features is achieved at the skip connection. The input to the depth image generation network is X. input The output of the upsampling stage, along with HrMSI, is processed by a 1×1 convolution and a sigmoid activation function to obtain a reconstructed image that incorporates both spatial and spectral information. Step 5, Joint Optimization and Reconstruction: Construct a multi-level loss constraint system, compare the reconstructed image with the initial high-resolution hyperspectral image HrHSI, and construct the loss function L2; when the loss function L2 is minimized, the corresponding reconstructed image is the desired reconstructed super-resolution hyperspectral image.

2. The hyperspectral image super-resolution reconstruction method based on multi-scale dilated convolution guided by claim 1, characterized in that, In step one, the HrHSI is blurred using a Gaussian blur kernel, and then LrHSI is generated by bicubic downsampling; the HrHSI matrix is ​​multiplied by the spectral response function matrix to generate HrMSI.

3. The hyperspectral image super-resolution reconstruction method based on multi-scale dilated convolution guided by claim 1, characterized in that, In step one, the spectral degradation path is multiplied by LrHSI and the learnable matrix of the spectral response function, and the spectral dimension of LrHSI is reduced to the multispectral dimension through linear transformation to obtain the first LrMSI; the learnable matrix of the spectral response function implicitly learns the weighted summation relationship of the multispectral bands to the hyperspectral bands, which is used to simulate the curve shape of the real spectral response function.

4. The hyperspectral image super-resolution reconstruction method based on multi-scale dilated convolution guided by claim 1, characterized in that, In step one, the spatial degradation path simulates the spatial blurring effect of the point spread function on HrMSI through a trainable depthwise separable convolution operation, and spatially degrades to generate a second LrMSI. Specifically, the HrMSI is subjected to channel-wise depthwise separable convolution with the learnable parameter matrix of the point spread function, and the convolution results of each spectral channel are added together to obtain the LrMSI.

5. The hyperspectral image super-resolution reconstruction method based on multi-scale dilated convolution guided by claim 1, characterized in that, Step two is specifically implemented through the following sub-steps: (2.1) The input feature map of each level of cross-channel association enhancement module is F. in ∈R H×W×C H represents the height of the HrHSI, W represents the width of the HrHSI, and C represents the number of spectral channels of the HrHSI. The input feature map of the first-level cross-channel correlation enhancement module of the first branch is the first LrMSI, and the input feature map of the first-level cross-channel correlation enhancement module of the second branch is the second LrMSI. The output of the current-level cross-channel correlation enhancement module is used as the input of the next-level cross-channel correlation enhancement module until the cascading ends. The output of the first branch after passing through multiple cascaded cross-channel correlation enhancement modules is F1, and the output of the second branch after passing through multiple cascaded cross-channel correlation enhancement modules is F2. (2.2) Upsample F1 and F2 using a deconvolutional layer with shared weights, and use them as the outputs of this branch: X s1 =Deconv(F1) X s2 =Deconv(F2) (2.3) The outputs of the first branch and the second branch are weighted and averaged to generate a high-resolution initial estimate, as shown in the following expression:

6. The hyperspectral image super-resolution reconstruction method based on multi-scale dilated convolution guided by claim 5, characterized in that, In each level of the cross-channel association enhancement module, F will be along the channel dimension. in Divide the data into three equal groups: G1, G2, and G3, where G1, G2, and G3 ∈ R. H×W×C / 3 Cross-channel information transmission is achieved through cascaded feature fusion. The first group of processing: G′1=Conv 3×3 (LeakyReLU(G1)) Second group of interactions: G′2=Conv 3×3 (LeakyReLU(G2+G′1)) Third group fusion: G′3=Conv 3×3 (LeakyReLU(G3+G′1+G′2)) The three processed outputs are concatenated along the channel to obtain: F cat =[G1′,G2′,G3′]∈R H×W×C Channel attention weights are generated using 1×1 convolution and Softmax: W=Softmax(Conv 1×1 (H cat ))∈R 1×1×3 The three sets of outputs are weighted and summed according to the channel attention weights: F weighted =W1·G′1+W2·G′2+W3·G′3 Based on the residual learning mechanism, feature enhancement is performed, and then the weighted features are increased in dimensionality through 1×1 convolution to obtain: F processed =Conv 1×1 (LeakyReLU(F weighted )) Using jump connections to connect F processed With the original input F in The components are added together to preserve the undegraded spectral information, yielding the output of this level of cross-channel correlation enhancement module, expressed as follows: F out =F processed +F in The output F of the last-level cross-channel association enhancement module of the first branch out F1 is the output F of the last-level cross-channel association enhancement module in the second branch. out It is F2.

7. The hyperspectral image super-resolution reconstruction method based on multi-scale dilated convolution guided by claim 1, characterized in that, Step three is specifically implemented through the following operations: Main path processing X branch: This path introduces a feature preprocessing module at the front end; The feature preprocessing module includes: ① using a 5×5 kernel-sized depthwise separable convolution to extract features from the input image to capture local spatial structure features; ② batch normalizing the convolution output; ③ introducing the LeakyReLU activation function to enhance nonlinear expressive power; ④ capturing local to global spatial features through MDFA; and obtaining the output of the current DDCA main path, expressed as follows: X m_p =MDFA(LeakyReLU(BN(Conv 5×5 (X input_p )))) In the formula, X m_p X represents the main path output of the p-th level DDCA. input_p This represents the main path input of the p-th level DDCA; Meanwhile, the auxiliary path also introduces a feature preprocessing module at the front end to process the Z branch. The expression output by this path is as follows: Z p =MDFA(LeakyReLU(BN(Conv 5×5 (Z input_p )))) In the formula, Z p Z represents the output of the Z branch of the p-th level DDCA. input_p This represents the secondary path input for the p-th level DDCA; For Z p The lightweight compression process includes: extracting channel-level global features using average pooling, reducing dimensionality through 1×1 convolution, enhancing key feature responses through ReLU activation, increasing dimensionality again through 1×1 convolution to restore channel dimensions, and obtaining adaptive channel weights for the p-th level DDCA using the sigmoid function, as shown in the following expression: IN attn_p =σ(Conv 1×1 (ReLU(Conv 1×1 (AvgPool(Z p ))))) In the formula, σ represents the Sigmoid function, with a weight range of [0, 1]; Weighted feature calibration: Adjusting X m_p With W attn_p Element-wise multiplication yields the output X of the X branch of the p-th level DDCA. p .

8. The hyperspectral image super-resolution reconstruction method based on multi-scale dilated convolution guided by claim 1, characterized in that, In step four, both paths employ the Multi-Scale Hollow Fusion Module (MDFA) to capture local to global spatial features, specifically through the following operations: (1) MDFA adopts a five-way parallel convolutional branch structure and achieves multi-scale feature capture of the input through differentiated dilation rate design; Branch 1 is used for local detail extraction, employing a 1×1 standard convolution with a dilation rate of 1, and is expressed as follows: In the formula, X represents the convolution operation. in This represents the current input to the MDFA; Branch 2 is used for medium receptive fields, employing a 3×3 standard convolution with a dilatation rate of 6, as shown in the following expression: Branch 3 is used for a wide range of contexts, employing a standard 3×3 convolution with a dilation rate of 12, and is expressed as follows: Branch 4 uses the widest receptive field, employing a 3×3 standard convolution with a dilatation rate of 18, as shown in the following expression: Branch 5 is the global average pooling branch, used to extract global contextual features. It employs a 3×3 standard convolution with a dilation rate of 18, and the expression is as follows: F gap =AvgPool2d(X in ) The five features are concatenated and weighted along the channel dimension to obtain the comprehensive feature map F. fused The expression is as follows: In the formula, the weight α k Weights set by humans; (2) Employing channel attention mechanism and spatial attention mechanism to synthesize feature map F fused Perform channel and spatial dimension recalibration. Channel dimension: for F fused Global average pooling is performed on each channel to generate a channel description vector Z. c The expression is as follows: In the formula, Z c ∈R 1×1×5C , C represents the number of spectral channels of HrHSI; H represents the height of HrHSI, W represents the width of HrHSI, and c represents the number of spectral channels of HrMSI. Channel importance weights W are generated using a 1×1 convolutional layer and a non-linear activation function. c The expression is as follows: In the formula, σ represents the Sigmoid function, with a weight range of [0, 1]; Weight W c With the comprehensive feature map F fused Multiply by each channel to obtain the channel attention output F. channel ; Spatial dimension: along F fused Global max pooling and average pooling are performed along the channel dimension to generate a spatial feature map Z. s The expression is as follows: Then, a spatial attention map W is generated by 1×1 convolution and sigmoid activation. s The expression is as follows: IN s =σ(Conv 1×1 (WITH s ))∈R H×W×1 Finally, the weights are multiplied position-by-position by the comprehensive feature map to obtain the spatial attention output F. spatial ; (3) Feature fusion and dimensionality reduction: The channel attention and spatial attention outputs are superimposed on the original features to preserve the original information. The expression is as follows: F att =F fused +F channel +F spatial ∈R H×W×5C Finally, the channel dimension is compressed using a 1×1 convolution to generate the final output, as shown in the following expression: In the formula, C out The target number of channels is X. in One-fifth of the number of channels.

9. The hyperspectral image super-resolution reconstruction method based on multi-scale dilated convolution guided by claim 1, characterized in that, In step four, during the downsampling phase, X is input into the main path of the first-level DDCA. input_1 =X input Secondary path input Z input_1 =Z, to obtain X1 and z1; after performing average pooling downsampling on X1 and Z1, input them into the second-level DDCA to obtain X2 and Z2; after performing average pooling downsampling on X2 and Z2, input them into the third-level DDCA to obtain X3 and Z3; The operations performed by the skip connection module include: 1×1 convolution to compress feature channels, batch normalization, and LeakyReLU activation function to enhance nonlinear expressive power; During the upsampling phase, X3 and Z3 are upsampled to obtain X. 3_up , Z 3_up Input X2 and Z2 into the jump connection module to generate s1 and s2, wherein s1 and s2 are respectively connected to X 3_up , Z 3_up Perform feature concatenation to generate Then, input it into the fourth level DDCA to obtain X4 and Z4; Upsampling X4 and Z4 yields X 4_up , Z 4_up Input X1 and Z1 into the jump connection module to generate s3 and s4, where s1 and s2 are respectively connected to X. 4_up , Z 4_up Perform feature concatenation to generate Then, input it into the fourth level DDCA to obtain X5 and Z5; The output X5 from the upsampling stage is then processed by a 1×1 convolution and a sigmoid activation function to obtain the reconstructed image.

10. The hyperspectral image super-resolution reconstruction method based on multi-scale dilated convolution guided by claim 1, characterized in that, In step five, a multi-level loss constraint system is constructed. Through the synergistic optimization of the spectral response function, point spread function, and data-driven approach, unsupervised hyperspectral image reconstruction is achieved. The loss function is as follows: In the formula, Φ SRF This represents the spectral response function SRF, with parameter θ. SRF , Φ PSF This represents the point spread function (PSF), with parameter θ. PSF When the loss function L2 is minimized, the corresponding reconstructed image is the desired reconstructed super-resolution hyperspectral image.

Images