Method for improving spectral resolution based on generative adversarial network and variational autoencoder

Abstract

A method for improving spectral resolution based on generative adversarial networks (GANs) and variational autoencoders (VAEs) provides an integrated network for generating medium-resolution spectra from low-resolution spectra. This integrated network includes a degradation network based on a VAE and a generative network based on a GAN. The degradation network learns the degradation process from medium-resolution to low-resolution spectra, and this learned degradation process is used to train the generative network. The degradation network employs the encoder structure of a VAE. The generative network transforms low-resolution spectra into medium-resolution spectra and consists of a generator and a discriminator. The generator is responsible for generating medium-resolution spectra from low-resolution spectra, while the discriminator determines whether the generated medium-resolution spectra closely approximate the true medium-resolution spectra. The generator and discriminator interact and train together.

Description

Technical Field

[0001] This invention belongs to the field of astronomy, and specifically relates to a method for improving low-resolution spectra to medium-resolution spectra. Background Technology

[0002] In astronomy, spectroscopy is an indispensable tool for astronomers studying celestial bodies. A spectrum is like a celestial body's "identity card," revealing its absorption and emission lines. By analyzing the characteristics and positions of these lines, the age and metallicity of celestial bodies can be deduced. The Guo Shoujing Telescope (LAMOST) is China's most efficient telescope in terms of spectral acquisition. Currently, it has two survey projects: a low-resolution spectroscopic survey and a medium-resolution spectroscopic survey. The low-resolution survey obtains low-resolution spectra, characterized by a wider wavelength range, but at the cost of reduced resolution. The medium-resolution survey obtains medium-resolution spectra, characterized by a smaller wavelength range than the low-resolution survey, but with very high resolution, revealing more detailed spectral line features. For problems such as celestial body subclassification and the discovery of special celestial bodies, medium-resolution spectroscopy is a valuable tool. Currently, the amount of data from low-resolution spectroscopy (tens of millions) is far greater than that from medium-resolution spectroscopy (millions). Theoretically, if medium-resolution spectra could be generated from low-resolution spectra, we would obtain medium-resolution spectral data of the same order of magnitude as the low-resolution spectra, which would be invaluable for astronomical research. In astronomy, signal processing or recovery tasks primarily involve deblurring or denoising signals (image data, one-dimensional spectral data, etc.), while tasks related to spectrum generation remain largely unexplored. Therefore, providing a method to improve spectral resolution—that is, to generate medium-resolution spectra from low-resolution spectra—is a pressing issue that needs to be addressed in current technology. Summary of the Invention

[0003] To address the problems mentioned in the background, the technical solution provided by this invention is as follows:

[0004] A method for improving spectral resolution based on generative adversarial networks and variational autoencoders is proposed by providing an integrated network to generate medium-resolution spectra from low-resolution spectra. The integrated network includes a degenerate network based on variational autoencoders and a generative network proposed based on generative adversarial networks.

[0005] The degradation network based on variational autoencoder is used to learn the degradation process from medium resolution spectrum to low resolution spectrum. The degradation process learned by the degradation network is used to train the generator network. The degradation network adopts the encoder structure of variational autoencoder because the encoder can realize the transformation of high-dimensional features to low-dimensional features, so the degradation network can degrade medium resolution spectrum to low resolution spectrum.

[0006] The generative adversarial network (GAN) is used to transform low-resolution spectra into medium-resolution spectra. The GAN consists of a generator and a discriminator. The generator is responsible for generating medium-resolution spectra from low-resolution spectra, while the discriminator is responsible for judging whether the generated medium-resolution spectra are close to the real medium-resolution spectra. The generator and discriminator compete with each other and train together.

[0007] The method for improving spectral resolution based on generative adversarial networks and variational autoencoders, further...

[0008] The degenerate network is based on an encoder structure and consists of linear layers. These linear layers can perceive every feature in the spectrum and possess a global receptive field. The calculation formula for the linear layer is shown below, where input is the input to the linear layer, weights and bias are parameters to be learned, and output is the output of the linear layer:

[0009] output = input × weights + bias

[0010] The method for improving spectral resolution based on generative adversarial networks and variational autoencoders further includes a generator consisting of three parts: a shallow feature extraction structure, a deep feature extraction structure, and an upsampling structure.

[0011] The generator operation includes the following steps:

[0012] 1.1) The low-resolution spectral data is processed through four shallow feature extraction structures to extract four shallow features, and the four shallow features are fused to obtain the fused feature data.

[0013] 1.2) Extract deep-level feature data from the fused feature data obtained in step 1.1) using a deep feature extraction structure;

[0014] 1.3) The deep feature data obtained in step 1.2) is upsampled through an upsampling structure. The deep feature data is finally mapped into a medium resolution spectrum through the upsampling structure.

[0015] The method for improving spectral resolution based on generative adversarial networks and variational autoencoders further includes four groups of shallow feature extraction structures, each with a different receptive field. These shallow feature extraction structures are used to extract spectral features. Each group of shallow feature extraction structures extracts features from the input low-resolution spectral data. Each group of shallow feature extraction structures includes a convolutional normalization module and a downsampling module. The convolutional normalization module performs two convolutional processes on the input low-resolution spectral data and one normalization process to obtain feature data. The downsampling module performs downsampling processing on the feature data and then processes the downsampled feature data through the ReLU activation function. Finally, the four groups of features extracted by the four groups of shallow feature extraction structures are stacked and fused, and the fused feature data is output as a group of shallow feature data.

[0016] The ReLU activation function is expressed by the following formula:

[0017]

[0018] The method for improving spectral resolution based on generative adversarial networks and variational autoencoders further includes a deep feature extraction structure composed of four convolutional modules. Each convolutional module consists of a convolutional layer, a normalization layer, a pooling layer, and an activation function. The deep feature extraction structure uses these four convolutional modules to further mine features from the fused feature data output in step 1.1), finally outputting a set of deep-level feature data extracted by each convolutional module.

[0019] The discriminator consists of three parts: a global feature extractor, a local feature extractor, and a feature fusion unit. The operation of the discriminator includes the following steps:

[0020] 2.1) The medium-resolution spectral data output from step 1.3) is used as input data and processed by a global feature extractor.

[0021] 2.2) The medium-resolution spectral data output from step 1.3) is used as input data and processed by a local feature extractor.

[0022] 2.3) The feature data obtained in steps 2.1) and 2.2) are processed together through the feature fusion machine. If the final output is 1, it is judged as true; if the output is 0, it is judged as false.

[0023] In step 2.1), the global feature extractor is composed of fully connected layers, which can extract features from the global medium-resolution spectral data.

[0024] In step 2.2), the local feature extractor consists of three convolutional feature extraction modules and one convolutional layer. Each convolutional feature extraction module consists of a convolutional layer, a downsampling layer and an activation function. The input data is processed by the three convolutional feature extraction modules and the convolutional layer in sequence to extract features from the local medium-resolution spectral data.

[0025] In step 2.3), the feature fusion unit consists of two fully connected layers and an activation function. The feature fusion unit fuses the features extracted by the global feature extractor and the local feature extractor using two fully connected layers, and then uses the activation function to map the result to obtain a 0 or 1 value, which is used to determine whether the generated medium resolution spectrum is real. A value of 0 means that the generated medium resolution spectrum is very similar to the real medium resolution spectrum, and a value of 1 means that the generated medium resolution spectrum is very similar to the real medium resolution spectrum.

[0026] The activation function is the sigmoid function, which can be expressed as follows:

[0027]

[0028] The method for improving spectral resolution based on generative adversarial networks and variational autoencoders further includes the following steps in training the ensemble network:

[0029] S1: Training the degenerate network: using labeled samples (X) i ,Y i The training process is performed to obtain the weight parameters of the trained model, where X... i Let Y represent a 1×n medium resolution spectrum. i This represents the corresponding 1×m low-resolution spectrum, where i represents the i-th sample, i = 1, 2, 3...x, and x is the total number of training samples;

[0030] S2: Train the generator network using the labeled samples (Y). i ,X i The system is trained using the degenerate network in S1, and the generated medium-resolution spectrum is simultaneously used to verify whether it can be degraded to a low-resolution spectrum, where X... i Let Y represent a 1×n medium resolution spectrum. i This represents the corresponding 1×m low-resolution spectrum, where i represents the i-th sample, i = 1, 2, 3...x, and x is the total number of training samples.

[0031] The method for improving spectral resolution based on generative adversarial networks and variational autoencoders further utilizes the generator in the generative network determined in S2 to generate medium-resolution spectra from low-resolution spectra.

[0032] This invention is the first to apply an integrated network based on generative adversarial networks and variational autoencoders to spectral generation. It provides a powerful tool for astronomical research, filling a gap in the field of spectral generation. The method provided by this invention can upscale large amounts of low-resolution spectral data to medium-resolution spectral data, which is highly significant for those seeking to use medium-resolution spectral data for celestial subclassification or identification of specific celestial objects. Attached Figure Description

[0033] Figure 1 This is a basic flowchart of the method for improving spectral resolution based on generative adversarial networks and variational autoencoders provided by the present invention;

[0034] Figure 2 This is a schematic diagram of the training process of the generative network and the degradation network in the method for improving spectral resolution based on generative adversarial networks and variational autoencoders provided by the present invention.

[0035] Figure 3 This is a schematic diagram of the generator in the generative network of the method for improving spectral resolution based on generative adversarial networks and variational autoencoders provided by the present invention.

[0036] Figure 4 This is a schematic diagram of the discriminator in the generator network of the method for improving spectral resolution based on generative adversarial networks and variational autoencoders provided by the present invention. Detailed Implementation

[0037] The invention will now be further described in conjunction with the accompanying drawings.

[0038] Example

[0039] like Figure 1 The flowchart shown illustrates a method for improving spectral resolution based on generative adversarial networks and variational autoencoders. It primarily provides an integrated network to generate medium-resolution spectra from low-resolution spectra. This integrated network comprises a degenerate network based on a variational autoencoder and a generative network based on a generative adversarial network.

[0040] The degradation network based on variational autoencoder is used to learn the degradation process from medium resolution spectrum to low resolution spectrum. The degradation process learned by the degradation network is used to train the generator network. The degradation network adopts the encoder structure of variational autoencoder because the encoder can realize the transformation of high-dimensional features to low-dimensional features, so the degradation network can degrade medium resolution spectrum to low resolution spectrum.

[0041] The generative adversarial network (GAN) is used to transform low-resolution spectra into medium-resolution spectra. The GAN consists of a generator and a discriminator. The generator is responsible for generating medium-resolution spectra from low-resolution spectra, while the discriminator is responsible for judging whether the generated medium-resolution spectra are close to the real medium-resolution spectra. The generator and discriminator compete with each other and train together.

[0042] The method for improving spectral resolution based on generative adversarial networks and variational autoencoders, further...

[0043] The degenerate network is based on an encoder structure and consists of linear layers. These linear layers can perceive every feature in the spectrum and possess a global receptive field. The calculation formula for the linear layer is shown below, where input is the input to the linear layer, weights and bias are parameters to be learned, and output is the output of the linear layer:

[0044] output = input × weights + bias

[0045] The method for improving spectral resolution based on generative adversarial networks and variational autoencoders further includes a generator consisting of three parts: a shallow feature extraction structure, a deep feature extraction structure, and an upsampling structure.

[0046] The generator operation includes the following steps:

[0047] 1.1) The low-resolution spectral data is processed through four shallow feature extraction structures to extract four shallow features, and the four shallow features are fused to obtain the fused feature data.

[0048] 1.2) Extract deep-level feature data from the fused feature data obtained in step 1.1) using a deep feature extraction structure;

[0049] 1.3) The deep feature data obtained in step 1.2) is upsampled through an upsampling structure. The deep feature data is finally mapped into a medium resolution spectrum through the upsampling structure.

[0050] The method for improving spectral resolution based on generative adversarial networks and variational autoencoders further includes four groups of shallow feature extraction structures, each with a different receptive field. These shallow feature extraction structures are used to extract spectral features. Each group of shallow feature extraction structures extracts features from the input low-resolution spectral data. Each group of shallow feature extraction structures includes a convolutional normalization module and a downsampling module. The convolutional normalization module performs two convolutional processes on the input low-resolution spectral data and one normalization process to obtain feature data. The downsampling module performs downsampling processing on the feature data and then processes the downsampled feature data through the ReLU activation function. Finally, the four groups of features extracted by the four groups of shallow feature extraction structures are stacked and fused, and the fused feature data is output as a group of shallow feature data.

[0051] The ReLU activation function is expressed by the following formula:

[0052]

[0053] The method for improving spectral resolution based on generative adversarial networks and variational autoencoders further includes a deep feature extraction structure composed of four convolutional modules. Each convolutional module consists of a convolutional layer, a normalization layer, a pooling layer, and an activation function. The deep feature extraction structure uses these four convolutional modules to further mine features from the fused feature data output in step 1.1), finally outputting a set of deep-level feature data extracted by each convolutional module.

[0054] The discriminator consists of three parts: a global feature extractor, a local feature extractor, and a feature fusion unit. The operation of the discriminator includes the following steps:

[0055] 2.1) The medium-resolution spectral data output from step 1.3) is used as input data and processed by a global feature extractor.

[0056] 2.2) The medium-resolution spectral data output from step 1.3) is used as input data and processed by a local feature extractor.

[0057] 2.3) The feature data obtained in steps 2.1) and 2.2) are processed together through the feature fusion machine. If the final output is 1, it is judged as true; if the output is 0, it is judged as false.

[0058] In step 2.1), the global feature extractor is composed of fully connected layers, which can extract features from the global medium-resolution spectral data.

[0059] In step 2.2), the local feature extractor consists of three convolutional feature extraction modules and one convolutional layer. Each convolutional feature extraction module consists of a convolutional layer, a downsampling layer and an activation function. The input data is processed by the three convolutional feature extraction modules and the convolutional layer in sequence to extract features from the local medium-resolution spectral data.

[0060] In step 2.3), the feature fusion unit consists of two fully connected layers and an activation function. The feature fusion unit fuses the features extracted by the global feature extractor and the local feature extractor using two fully connected layers, and then uses the activation function to map the result to obtain a 0 or 1 value, which is used to determine whether the generated medium resolution spectrum is real. A value of 0 means that the generated medium resolution spectrum is very similar to the real medium resolution spectrum, and a value of 1 means that the generated medium resolution spectrum is very similar to the real medium resolution spectrum.

[0061] The activation function is the sigmoid function, which can be expressed as follows:

[0062]

[0063] The training of the aforementioned ensemble network includes the following steps:

[0064] S1: Training of the Degenerate Network Based on Variational Autoencoder: Based on the encoder function of the variational autoencoder, a degenerate network is designed. This network learns the process of degenerating a medium-resolution spectrum into a low-resolution spectrum. The learned degenerate process is used to supervise and guide the generator network, enabling it to better complete the generation task. Using selected samples (X...) i ,Y i The training process is performed to obtain the weight parameters of the trained model, where X... i Let Y represent a 1×n medium resolution spectrum. i This represents the corresponding 1×m low-resolution spectrum, where i represents the i-th sample, i = 1, 2, 3...x, and x is the total number of training samples, which includes 190,000 low-resolution spectra (each low-resolution spectrum contains both red and blue ends) and 380,000 medium-resolution spectra (190,000 red ends and 190,000 blue ends respectively).

[0065] S2: Training of the Generative Network Based on Generative Adversarial Networks (GANs): The generative network consists of a generator and a discriminator. The generator performs specific generation tasks, and the discriminator checks and evaluates the generated data. Based on GANs, low-resolution spectra are generated into medium-resolution spectra. Furthermore, the degradation process learned by the degradation network is used to make the generated medium-resolution spectra more similar to the real medium-resolution spectra. Using well-selected samples (Y... i ,X iThe training process is performed to obtain the weight parameters of the trained model, where X... i Let Y represent a 1×n medium resolution spectrum. i This represents the corresponding 1×m low-resolution spectrum, where i represents the i-th sample, i = 1, 2, 3...x, and x is the total number of training samples, which includes 190,000 low-resolution spectra (each low-resolution spectrum contains both red and blue ends) and 380,000 medium-resolution spectra (190,000 red ends and 190,000 blue ends).

[0066] Finally, using the generation network determined by S2, medium-resolution spectra are generated from low-resolution spectra.

[0067] The training process of generative and degenerate networks is illustrated in the diagram below. Figure 2 As shown, there are two parts. First, the generation network consists of a generator and a discriminator. The generator is mainly responsible for generating a medium-resolution spectrum from a low-resolution spectrum; the discriminator is responsible for determining whether the generated medium-resolution spectrum is fake. In other words, the generator needs to fool the discriminator, while the discriminator needs to distinguish between real and fake. Finally, the discriminator judges whether the medium-resolution spectrum generated by the generator is real or fake. At this point, the discriminator can no longer distinguish between real and fake, reaching a dynamic equilibrium.

[0068] A schematic diagram of the generator structure in a generative network is shown below. Figure 3 As shown, four shallow feature extraction structures extract features from the spectrum. Each shallow feature extraction structure consists of a convolutional normalization module and a downsampling module, and each shallow feature extraction structure has a different receptive field. This allows for better feature extraction from the input at different scales. The four sets of features extracted by the four shallow feature extraction structures are then fused. The fused features are then processed by a deep feature extraction structure for deeper feature mining. The deep feature extraction structure consists of four convolutional modules, which perform feature mining layer by layer to obtain deep features. Finally, the deep features are passed through an upsampling structure, which maps the deep features to a medium-resolution spectrum.

[0069] A schematic diagram of the discriminator structure in the generative network is shown below. Figure 4 As shown, the system consists of a global feature extractor, a local feature extractor, and a feature fusion unit. The global feature extractor, composed of fully connected layers, extracts global features from the input medium-resolution spectral data. The local feature extractor extracts local features from the input medium-resolution spectral data and consists of three convolutional feature extraction modules and one convolutional layer. Each convolutional feature extraction module consists of a convolutional layer, a downsampling layer, and an activation function. The feature fusion unit consists of two fully connected layers and an activation function. The two fully connected layers fuse global and local features, and finally, the sigmoid function, acting as the activation function, maps the result to a 0 or 1 value.

[0070] This invention utilizes an integrated network based on generative adversarial networks and variational autoencoders to demonstrate powerful capabilities in generating medium-resolution spectra. By allowing the degradation network within the integrated network to fully learn the process of medium-resolution spectra degrading to low-resolution spectra, and enabling the generative network to leverage this learned degradation process to generate medium-resolution spectra from low-resolution spectra, this invention ensures that the generative network does not blindly generate medium-resolution spectra but rather achieves a higher similarity to real-world medium-resolution spectra, thus guaranteeing the reliability of medium-resolution spectra generated from low-resolution spectra.

[0071] This invention requires no human intervention and the network exhibits good robustness. Experimental results show that this invention can be used to generate medium-resolution spectra from low-resolution spectra.

[0072] Table 1 compares the medium-resolution spectra generated by the generator network after training in the example with the true medium-resolution spectra, including the blue and red ends.

[0073] Blue End 0.966719 0.023922 0.031349 0.999076 0.001105 Red End 0.970167 0.012607 0.016626 0.999804 0.000311

[0074] Table 2 shows a comparison of the spectral lines of the medium-resolution spectrum generated using this invention with the actual medium-resolution spectrum, including the blue-end Mg absorption line and the red-end Hα absorption line.

[0075]

[0076] In summary, the medium-resolution spectra generated by this invention show a high degree of similarity to real medium-resolution spectra, both in terms of overall spectrum similarity and the similarity of specific spectral lines. Therefore, this method can be used to generate medium-resolution spectra from low-resolution spectra, thereby providing a batch of reliable medium-resolution spectral data for astronomical research and further enhancing the value of big data-driven astronomical research today.

[0077] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for improving spectral resolution based on generative adversarial networks and variational autoencoders, characterized by providing an integrated network to generate medium-resolution spectra from low-resolution spectra, wherein... The integrated network includes a degradation network based on a variational autoencoder and a generative network based on a generative adversarial network. The degradation network based on the variational autoencoder is used to learn the degradation process from medium-resolution spectrum to low-resolution spectrum. The degradation process learned by the degradation network is used to train the generative network. The degradation network adopts the encoder structure of the variational autoencoder. The generative network based on the generative adversarial network is used to transform the low-resolution spectrum into a medium-resolution spectrum. The generative network consists of a generator and a discriminator. The generator is responsible for generating a medium-resolution spectrum from the low-resolution spectrum, and the discriminator is responsible for judging whether the generated medium-resolution spectrum is close to the real medium-resolution spectrum. The generator and the discriminator compete with each other and train together. The training of the integrated network includes the following steps: S1: Training the degenerate network: using labeled samples (X) i ,Y i The model is trained to obtain the weight parameters of the trained model, where X... i Let Y represent a 1×n medium resolution spectrum. i This represents the corresponding 1×m low-resolution spectrum, where i represents the i-th sample, i=1,2,3...x, and x is the total number of training samples; S2: Train the generator network using the labeled samples (Y). i ,X i The system is trained using the degenerate network in S1, and the generated medium-resolution spectrum is simultaneously used to verify whether it can be degraded to a low-resolution spectrum, where X... i Let Y represent a 1×n medium resolution spectrum. i This represents the corresponding 1×m low-resolution spectrum, where i represents the i-th sample, i=1,2,3...x, and x is the total number of training samples; Using the generator in the generator network determined by S2, medium-resolution spectra are generated from low-resolution spectra.

2. The method for improving spectral resolution based on generative adversarial networks and variational autoencoders as described in claim 1, characterized in that, The degenerate network is based on an encoder structure and consists of linear layers. These linear layers can sense every feature in the spectrum and have a global receptive field. The calculation formula for the linear layers is as follows: ， The input is the input to the linear layer, the weights and bias are the parameters to be learned, and the output is the output of the linear layer.

3. The method for improving spectral resolution based on generative adversarial networks and variational autoencoders as described in claim 2, characterized in that the generator consists of three parts, namely a shallow feature extraction structure, a deep feature extraction structure, and an upsampling structure; The generator operation includes the following steps: 1.1) The low-resolution spectral data is processed through four shallow feature extraction structures to extract four shallow features, and the four shallow features are fused to obtain the fused feature data. 1.2) Extract deep-level feature data from the fused feature data obtained in step 1.1) using a deep feature extraction structure; 1.3) The deep feature data obtained in step 1.2) is upsampled through an upsampling structure. The deep feature data is finally mapped into a medium resolution spectrum through the upsampling structure.

4. The method for improving spectral resolution based on generative adversarial networks and variational autoencoders as described in claim 3, further comprising four groups of shallow feature extraction structures, each with a different receptive field. These shallow feature extraction structures are used to extract spectral features. Each group of shallow feature extraction structures extracts features from the input low-resolution spectral data. Each group of shallow feature extraction structures includes a convolutional normalization module and a downsampling module. The convolutional normalization module performs two convolutional processes on the input low-resolution spectral data and one normalization process to obtain feature data. The downsampling module performs downsampling on the feature data and processes the downsampled feature data through a ReLU activation function. Finally, the four groups of features extracted by the four shallow feature extraction structures are stacked and fused, and the fused feature data is output as a group of shallow feature data. The ReLU activation function is expressed as follows: .

5. The method for improving spectral resolution based on generative adversarial networks and variational autoencoders as described in claim 4, characterized in that, The deep feature extraction structure consists of four sets of convolutional modules. Each convolutional module consists of a convolutional layer, a normalization layer, a pooling layer, and an activation function. The deep feature extraction structure uses the four sets of convolutional modules to further mine the fused feature data output in step 1.1), and finally outputs a set of deep feature data extracted by each convolutional module.

6. The method for improving spectral resolution based on generative adversarial networks and variational autoencoders as described in claim 3, characterized in that... The discriminator consists of three parts: a global feature extractor, a local feature extractor, and a feature fusion unit. The operation of the discriminator includes the following steps: 2.1) The medium-resolution spectral data output from step 1.3) is used as input data and processed by the global feature extractor; 2.2) The medium-resolution spectral data output from step 1.3) is used as input data and processed by a local feature extractor; 2.3) The feature data obtained in steps 2.1) and 2.2) are processed together through the feature fusion machine. If the final output is 1, it is judged as true; if the output is 0, it is judged as false.

7. The method for improving spectral resolution based on generative adversarial networks and variational autoencoders as described in claim 6, characterized in that: In step 2.1), the global feature extractor is composed of fully connected layers, which can extract features from the global medium-resolution spectral data; In step 2.2), the local feature extractor consists of three convolutional feature extraction modules and one convolutional layer. Each convolutional feature extraction module consists of a convolutional layer, a downsampling layer and an activation function. The input data is processed by the three convolutional feature extraction modules and the convolutional layer in sequence to extract features from the local medium-resolution spectral data. In step 2.3), the feature fusion unit consists of two fully connected layers and an activation function. The feature fusion unit fuses the features extracted by the global feature extractor and the local feature extractor using two fully connected layers, and then uses the activation function to map the result to obtain a 0 or 1 value, which is used to determine whether the generated medium resolution spectrum is real. A value of 0 means that the generated medium resolution spectrum is very similar to the real medium resolution spectrum, and a value of 1 means that the generated medium resolution spectrum is very similar to the real medium resolution spectrum. The activation function is the sigmoid function, which can be expressed as follows: .

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