Frequency domain difference image reconstruction method and system based on SwinIR model

Abstract

The invention discloses a frequency domain difference image reconstruction method and system based on a SwinIR model, and belongs to the technical field of image processing. The method comprises the following steps: preprocessing a low-resolution image; fourier transform is carried out on the preprocessed low-resolution image, the image is converted from a spatial domain to a frequency domain, and image spectrum representation is obtained; inputting the image spectrum representation into a differential mode generator to obtain a differential mode signal image spectrum; inputting the differential mode signal image frequency spectrum into a pre-trained SwinIR model, and outputting to obtain a high-resolution reconstructed differential mode image frequency spectrum; performing differential output on the high-resolution reconstructed differential mode image frequency spectrum to obtain a high-resolution reconstructed image frequency spectrum; inverse Fourier transform is carried out on the frequency spectrum of the high-resolution reconstructed image, and the high-resolution reconstructed image is output and obtained; according to the method, through hierarchical feature extraction of the SwinIR model and a frequency domain difference strategy, artifact and noise suppression in the image reconstruction process is effectively realized, and the reconstruction quality is improved.

Description

Technical Field

[0001] The present invention relates to a frequency-domain differential image reconstruction method and system based on the SwinIR model, belonging to the technical field of image processing. Background Art

[0002] With the rapid development of artificial intelligence and computer vision technologies, image super-resolution reconstruction has become one of the important research directions in the field of image processing. The super-resolution technology is to solve the problem of insufficient image resolution. Especially in the fields of medical imaging, satellite remote sensing, and surveillance, high-resolution images are very important for detail analysis and decision-making. Traditional methods such as interpolation algorithms are simple and fast, but details are easily lost. The super-resolution technology based on signal processing has achieved certain development, but its effect in single-image super-resolution reconstruction is limited and it is difficult to meet the actual application requirements. The introduction of deep learning has brought a breakthrough to the super-resolution technology. Especially the super-resolution reconstruction method based on convolutional neural network (CNN) proposed by the SRCNN model in 2014, and subsequent methods such as VDSR, ESPCN, and SRGAN have greatly improved the image reconstruction effect.

[0003] Although deep learning can adaptively extract features and process large-scale data, it also faces some challenges. For example, the generated images may have artifacts, unnatural textures, and noise. In addition, the model is highly dependent on training data, and the computational complexity also limits its practical applications.

[0004] Researchers at home and abroad have proposed some solutions. For example, GAN combined with perceptual loss can generate more realistic details, but it is easy to introduce false artifacts in the high-frequency region, resulting in unnatural texture structures; regularization methods can reduce noise, but they will cause the loss of image details, making the image too smooth. Multi-scale techniques and attention mechanisms can better capture image details, but they require high computational resources, limiting their applications in real-time processing and resource-constrained environments. The adaptive attention mechanism has also been applied to super-resolution reconstruction to enhance image details and global consistency and effectively suppress irrelevant noise. By adaptively selecting important regions in the image, the attention mechanism can more intelligently allocate computational resources and improve the reconstruction effect. However, the increased network complexity and computational burden make this method challenging in practical applications.

[0005] Therefore, how to reduce artifacts and noise and improve the generalization ability of the model under the condition of limited data and computational resources is an important research topic in current image super-resolution reconstruction. Summary of the Invention

[0006] The object of the present invention is to overcome the deficiencies of the prior art and provide a frequency-domain differential image reconstruction method and system based on the SwinIR model. Through the hierarchical feature extraction and frequency-domain differential strategy of the SwinIR model, the suppression of artifacts and noise in the image reconstruction process is effectively realized, the reconstruction quality is improved. At the same time, this method makes full use of frequency-domain information, reduces computational redundancy, and enhances the adaptability and generalization ability of the model in different data scenarios.

[0007] To achieve the above object / To solve the above technical problems, the present invention is implemented by the following technical solutions: First aspect: A frequency-domain differential image reconstruction method based on the SwinIR model, the method includes: Preprocess the low-resolution image; Perform Fourier transform on the preprocessed low-resolution image to convert the image from the spatial domain to the frequency domain, and obtain the image spectrum representation; Input the image spectrum representation into the differential mode generator to obtain the differential mode signal image spectrum; Input the differential mode signal image spectrum into the pre-trained SwinIR model, and output the high-resolution reconstructed differential mode image spectrum; Perform differential output on the high-resolution reconstructed differential mode image spectrum to obtain the high-resolution reconstructed image spectrum; Perform inverse Fourier transform on the high-resolution reconstructed image spectrum, and output the high-resolution reconstructed image.

[0008] Optionally, the SwinIR model includes a shallow feature extraction layer, a deep feature extraction layer, and a high-quality image spectrum reconstruction layer. The shallow feature extraction layer includes a convolutional network layer and a LeakyReLU activation layer. Among them, the number of input channels of the convolutional network layer is the number of channels of the low-resolution image spectrum, and the number of output channels is the dimension of the shallow feature tensor. The deep feature extraction layer includes 6 RSTB modules and 1 3×3 convolutional network layer; the high-quality image spectrum reconstruction layer includes 1 skip connection module, 1 upsampling module, and 1 convolutional network layer. The skip connection module directly adds the shallow feature tensor and the deep feature tensor; the number of input channels of the convolutional network layer is the dimension of the shallow feature tensor, and the number of output channels is the number of channels of the high-resolution image spectrum.

[0009] Optionally, the processing process of the deep feature extraction layer is as follows: The residual block module processes the input signal, extracts features through the window multi-head self-attention mechanism. The window multi-head self-attention mechanism divides the extracted features into windows of a fixed size of 7×7, and independently calculates the self-attention within each window to capture detailed features; The captured detailed features enter the shifted window multi-head self-attention mechanism, where the position of the window is shifted by 3×3 in adjacent layers; the input features and the features processed by the attention mechanism are added through a multi-layer perceptron module, and through the alternating cycle of the window multi-head self-attention mechanism and the shifted window multi-head self-attention mechanism, the features are integrated through a 3×3 convolutional network layer to obtain a set of deep features.

[0010] Optionally, the step of inputting the image spectrum representation into the differential mode generator to obtain the differential mode signal image spectrum includes: The differential mode generator performs differential mode processing on the Fourier-transformed low-resolution image spectrum to obtain two low-resolution image spectra, one of which is the original low-resolution image spectrum and the other is the anti-low-resolution image spectrum for inputting into the SwinIR model. The anti-low-resolution image refers to mapping all pixels of the original image according to the relationship for one-to-one mapping.

[0011] Optionally, the preprocessing of the low-resolution image includes: Performing image normalization preprocessing on the input low-resolution image.

[0012] Optionally, the image normalization preprocessing includes mapping the range of pixel values to 0 to 1.

[0013] Optionally, the step of performing differential output on the high-resolution reconstructed differential mode image spectrum to obtain the high-resolution reconstructed image spectrum includes: Performing differential output on the high-resolution reconstructed differential mode image spectrum to remove the common mode noise, where the differential output means subtracting the anti-low-resolution image spectrum of the differential mode output from the high-resolution reconstructed differential mode image spectrum.

[0014] Optionally, the training process of the SwinIR model includes: Preprocessing the DIV2K dataset containing high- and low-resolution images. The preprocessing includes normalizing the input images, mapping the range of pixel values to 0 to 1, and dividing the processed dataset into a training set and a test set; Performing Fourier transform on the dataset images to obtain low-resolution image spectra and high-resolution image spectra; Inputting the low-resolution image spectrum into the differential mode generator to obtain the differential mode signal image spectrum; Inputting the differential mode signal image spectrum and the corresponding high-resolution image spectrum into the SwinIR model network for training; Using the backpropagation algorithm to continuously optimize the model parameters to obtain the trained SwinIR model.

[0015] Optionally, the training further includes: By comparing the differences between the high-resolution image spectrum output by the SwinIR model and the target high-resolution image spectrum, the loss value is calculated using a pixel-level L1 loss function; The SwinIR model uses the calculated loss value to layer-by-layer pass the error gradient back to each parameter of the SwinIR model through the backpropagation algorithm; The optimizer is used to update each parameter according to the learning rate, making the generated high-resolution spectrum approach the true target spectrum. The loop continues until the loss curve becomes stable and the metrics on the validation set reach the optimal, indicating the convergence and completion of the model training.

[0016] Second aspect: A frequency-domain differential image reconstruction system based on the SwinIR model, the system includes: An image processing module for preprocessing the low-resolution image; An image conversion module for performing Fourier transform on the preprocessed low-resolution image to convert the image from the spatial domain to the frequency domain, obtaining an image spectrum representation; A generation module for inputting the image spectrum representation into a differential mode generator to obtain a differential mode signal image spectrum; A differential mode image spectrum reconstruction module for inputting the differential mode signal image spectrum into a pre-trained SwinIR model and outputting a high-resolution reconstructed differential mode image spectrum; A differential processing module for performing differential output on the high-resolution reconstructed differential mode image spectrum to obtain a high-resolution reconstructed image spectrum; A high-resolution reconstruction module for performing inverse Fourier transform on the high-resolution reconstructed image spectrum and outputting a high-resolution reconstructed image.

[0017] Compared with the prior art, the beneficial effects achieved by the present invention: The present invention is used for the extraction and optimization of frequency-domain features, enhances the expression ability of frequency-domain features through a deep learning network, effectively solves the problems of noise interference and artifacts, and finally realizes the efficient reconstruction of low-resolution images to high-resolution images; Through the hierarchical feature extraction and frequency-domain differential strategy of the SwinIR model, the present invention effectively suppresses artifacts and noise during the image reconstruction process, improves the reconstruction quality, and is applicable to image denoising, super-resolution reconstruction, and image restoration related to frequency-domain analysis. Especially, it has important application value in fields with high demand for high-quality image reconstruction. Description of the Drawings

[0018] Figure 1 It is the method flowchart of the embodiment of the present invention; Figure 2 It is the structure diagram of the SwinIR model of the embodiment of the present invention; Figure 3This is the flowchart for training the SwinIR model according to an embodiment of the present invention. Detailed implementation manners

[0019] To make the technical means, creative features, achieved purposes and effects of the present invention easy to understand, the present invention will be further described below in conjunction with specific implementation manners.

[0020] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise stated, the meaning of "plurality" is two or more.

[0021] In the description of the present invention, it should be noted that unless otherwise clearly defined and limited, the terms "installed", "connected", "connected" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected, or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific situations.

[0022] Embodiment 1, as Figure 1 shown, discloses a frequency-domain differential image reconstruction method based on the SwinIR model, including: Step 1: Input a low-resolution image, and use the low-resolution image to be processed as the input.

[0023] Step 2: Image preprocessing, perform a normalization preprocessing operation on the input image.

[0024] Step 3: Perform Fourier transform, perform Fourier transform on the preprocessed image, convert the image from the spatial domain to the frequency domain, and obtain the image spectrum representation for subsequent processing.

[0025] Step 4: Input a differential mode generator to obtain the differential mode signal (image) spectrum, and use the differential mode generator to extract the differential mode signal (image) spectrum from the input spectrum.

[0026] Step 5: The differential-mode signal (image) spectrum is input into the SwinIR model. The differential-mode signal (image) spectrum is used as the input and fed into the SwinIR model to obtain the high-resolution reconstructed differential-mode image spectrum.

[0027] In the specific implementation process of this embodiment, for Step 2, image normalization preprocessing is performed on the input low-resolution image, and the range of pixel values is mapped to 0-1 to ensure that the image data has a unified scale and range in the subsequent processing process, thereby improving the stability and efficiency of the algorithm and eliminating the interference caused by differences in brightness, contrast, etc. between different images.

[0028] In the specific implementation process of this embodiment, for Step 4, the differential-mode generator first performs differential-mode processing on the Fourier-transformed low-resolution image spectrum to obtain two low-resolution image spectra, one of which is the original low-resolution image spectrum and the other is the anti-low-resolution image spectrum, for input into the SwinIR model. The anti-low-resolution image refers to mapping all pixels of the original image according to the relationship.

[0029] Please see Figure 2 , in Step 5, in the specific implementation process of this embodiment, the SwinIR model consists of a shallow feature extraction layer, a deep feature extraction layer, and a high-quality image spectrum reconstruction layer. The shallow feature extraction layer includes a convolutional network layer and a LeakyReLU activation layer, where the number of input channels of the convolutional network layer is the number of channels of the low-resolution image spectrum, and the number of output channels is the dimension of the shallow feature tensor. The deep feature extraction layer includes 6 RSTB modules and 1 3×3 convolutional network layer. The high-quality image spectrum reconstruction layer includes 1 skip connection module, 1 upsampling module, and 1 convolutional network layer. The skip connection module directly adds the shallow feature tensor and the deep feature tensor. The number of input channels of the convolutional network layer is the dimension of the shallow feature tensor, and the number of output channels is the number of channels of the high-resolution image spectrum.

[0030] For further elaboration on Step 5, the processing process of the deep feature extraction layer is as follows: The residual block module processes the input signal, extracts features through the window multi-head self-attention mechanism. The window multi-head self-attention mechanism divides the extracted features into windows of a fixed size of 7×7, calculates self-attention independently within each window, and captures detailed features; The captured detailed features enter the shifted window multi-head self-attention mechanism, and the position of the window is shifted by 3×3 in adjacent layers; the input features and the features processed by the attention mechanism are added through the multi-layer perceptron module. Through the alternating cycle of the window multi-head self-attention mechanism and the shifted window multi-head self-attention mechanism, the features are integrated through the 3×3 convolutional network layer to obtain a set of deep features.

[0031] See Figure 3 ,In one embodiment, the SwinIR model is a trained SwinIR model; the training process includes the following sub-steps: Step S5.1, use the DIV2K dataset containing high and low resolution images; In one embodiment, the DIV2K dataset contains various types of image scenes, including natural landscapes, buildings, objects, etc. This diversity enables the trained and tested models to better generalize to different actual application scenarios, rather than just performing well in a single scenario. At the same time, DIV2K is a standard dataset in the field of image super-resolution and is widely used in academic research and industrial applications. The experimental results using the DIV2K dataset can be conveniently compared fairly with other research works to measure the superiority and performance of the method.

[0032] Step S5.2, preprocess the dataset; In one embodiment, the preprocessing, including normalizing the input images, is to map the range of pixel values to 0-1, and then divide the processed dataset into a training set and a test set; Step S5.3, perform Fourier transform on the dataset images to obtain the low-resolution image spectrum and the high-resolution image spectrum; Step S5.4, input the low-resolution image spectrum into a differential mode generator to obtain the differential mode signal (image) spectrum; In one embodiment, the differential mode generator first performs differential mode on the Fourier-transformed low-resolution image spectrum to obtain two low-resolution image spectra, one of which is the original low-resolution image spectrum and the other is the inverse low-resolution image spectrum, for input into the SwinIR model. The inverse low-resolution image refers to mapping all the pixels of the original image according to the relationship.

[0033] Step S5.5, input the differential mode signal (image) spectrum and the corresponding high-resolution image spectrum into the SwinIR model network for training; Step S5.6, continuously optimize the model parameters using the backpropagation algorithm; In one embodiment, the training process uses the SwinIR model for training. By comparing the difference between the high-resolution image spectrum output by the model and the target high-resolution image spectrum, the loss value is calculated using the pixel-level L1 loss function. The model uses the calculated loss value and, through the backpropagation algorithm, passes the error gradient layer by layer back to each parameter of the model, including the convolutional layer weights of the shallow feature extraction module, the weights and biases of the attention mechanism in the RSTB of the deep feature extraction module, etc. The optimizer updates these parameters according to the learning rate, making the generated high-resolution spectrum gradually approach the true target spectrum. This process is repeated until the loss curve flattens out and the metrics on the validation set reach the optimal value, indicating the convergence and completion of the model training.

[0034] Among them, the SwinIR model is the same as the SwinIR model structure described in step 4.

[0035] Step 6: The high-resolution reconstructed differential-mode image spectrum is differentially output to remove the common-mode noise and obtain the high-resolution image spectrum.

[0036] In one embodiment, the differential output means subtracting the high-resolution reconstructed differential-mode image spectrum from the anti-low-resolution image spectrum of the differential-mode output to obtain the high-resolution reconstructed image spectrum.

[0037] Step 7: The inverse Fourier transform outputs the high-resolution image.

[0038] In one embodiment, the inverse Fourier transform outputs the high-resolution image by performing an inverse Fourier transform on the high-resolution reconstructed image spectrum to obtain the final high-resolution reconstructed image.

[0039] Embodiment 2 discloses a frequency-domain differential image reconstruction system based on the SwinIR model. The system includes: An image processing module for preprocessing the low-resolution image; An image conversion module for performing a Fourier transform on the preprocessed low-resolution image to convert the image from the spatial domain to the frequency domain and obtain an image spectrum representation; A generation module for inputting the image spectrum representation into a differential-mode generator to obtain a differential-mode signal image spectrum; A differential-mode image spectrum reconstruction module for inputting the differential-mode signal image spectrum into a pre-trained SwinIR model and outputting a high-resolution reconstructed differential-mode image spectrum; A differential processing module for differentially outputting the high-resolution reconstructed differential-mode image spectrum to obtain a high-resolution reconstructed image spectrum; A high-resolution reconstruction module for performing an inverse Fourier transform on the high-resolution reconstructed image spectrum and outputting a high-resolution reconstructed image.

[0040] The present invention is used for the extraction and optimization of frequency-domain features. By means of a deep learning network, the expression ability of frequency-domain features is improved, the problems of noise interference and artifacts are effectively solved, and finally the efficient reconstruction of low-resolution images into high-resolution images is realized; Through the hierarchical feature extraction and frequency-domain difference strategy of the SwinIR model, the present invention effectively suppresses artifacts and noise in the image reconstruction process, improves the reconstruction quality, and is applicable to image denoising, super-resolution reconstruction, and image restoration related to frequency-domain analysis. Especially, it has important application value in the fields with high requirements for high-quality image reconstruction.

[0041] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A frequency-domain differential image reconstruction method based on the SwinIR model, characterized in that The method includes: Preprocessing the low-resolution image; Performing Fourier transform on the preprocessed low-resolution image to convert the image from the spatial domain to the frequency domain, obtaining an image spectrum representation; Inputting the image spectrum representation into a differential mode generator to obtain a differential mode signal image spectrum; Inputting the differential mode signal image spectrum into a pre-trained SwinIR model, and outputting a high-resolution reconstructed differential mode image spectrum; Performing differential output on the high-resolution reconstructed differential mode image spectrum to obtain a high-resolution reconstructed image spectrum; Performing inverse Fourier transform on the high-resolution reconstructed image spectrum, and outputting a high-resolution reconstructed image.

2. The method for reconstructing a frequency-domain differential image based on the SwinIR model according to claim 1, wherein, The SwinIR model includes a shallow feature extraction layer, a deep feature extraction layer, and a high-quality image spectrum reconstruction layer. The shallow feature extraction layer includes a convolutional network layer and a LeakyReLU activation layer. Among them, the number of input channels of the convolutional network layer is the number of channels of the low-resolution image spectrum, and the number of output channels is the dimension of the shallow feature tensor. The deep feature extraction layer includes 6 RSTB modules and 1 3×3 convolutional network layer; the high-quality image spectrum reconstruction layer includes 1 skip connection module, 1 upsampling module, and 1 convolutional network layer. The skip connection module directly adds the shallow feature tensor and the deep feature tensor; the number of input channels of the convolutional network layer is the dimension of the shallow feature tensor, and the number of output channels is the number of channels of the high-resolution image spectrum.

3. The frequency-domain differential image reconstruction method based on the SwinIR model according to claim 2, wherein The processing process of the deep feature extraction layer is as follows: The residual block module processes the input signal, extracts features through a window multi-head self-attention mechanism. The window multi-head self-attention mechanism divides the extracted features into windows of a fixed size of 7×7, calculates self-attention independently within each window, and captures detailed features; The captured detailed features enter the shifted window multi-head self-attention mechanism, and the position of the window is shifted by 3×3 in adjacent layers; The input features and the features processed by the attention mechanism are added through a multi-layer perceptron module, and the window multi-head self-attention mechanism and the shifted window multi-head self-attention mechanism alternate in a cycle. The features are integrated through a 3×3 convolutional network layer to obtain a set of deep features.

4. The frequency-domain differential image reconstruction method based on the SwinIR model according to claim 1, wherein, The step of inputting the image spectrum representation into a differential mode generator to obtain a differential mode signal image spectrum includes: The differential-mode generator performs differential-mode processing on the spectrum of the low-resolution image after Fourier transform to obtain two low-resolution image spectra, one of which is the original low-resolution image spectrum and the other is the anti-low-resolution image spectrum, which are used as inputs to the SwinIR model. The anti-low-resolution image refers to the one-to-one mapping of all pixels of the original image according to the relationship.

5. The method for reconstructing a frequency-domain difference image based on the SwinIR model according to claim 1, characterized in that, The step of preprocessing the low-resolution image includes: Performing image normalization preprocessing on the input low-resolution image.

6. The frequency-domain differential image reconstruction method based on the SwinIR model according to claim 5, characterized in that, The image normalization preprocessing includes: mapping the range of pixel values to 0-1.

7. The frequency-domain differential image reconstruction method based on the SwinIR model according to claim 1, characterized in that The step of performing differential output on the high-resolution reconstructed differential mode image spectrum to obtain a high-resolution reconstructed image spectrum includes: Performing differential output on the high-resolution reconstructed differential mode image spectrum to remove common-mode noise, where the differential output means subtracting the high-resolution reconstructed differential mode image spectrum from the anti-low-resolution image spectrum of the differential output.

8. The frequency-domain differential image reconstruction method based on the SwinIR model according to claim 1, wherein, The training process of the SwinIR model includes: Preprocessing the DIV2K dataset containing high- and low-resolution images. The preprocessing includes normalizing the input images, mapping the range of pixel values to 0-1, and dividing the processed dataset into a training set and a test set; Perform Fourier transform on the dataset images to obtain the low-resolution image spectrum and the high-resolution image spectrum; Input the low-resolution image spectrum into the differential mode generator to obtain the differential mode signal image spectrum; Input the differential mode signal image spectrum and the corresponding high-resolution image spectrum into the SwinIR model network for training; The backpropagation algorithm continuously optimizes the model parameters to obtain the trained SwinIR model.

9. The frequency-domain differential image reconstruction method based on the SwinIR model according to claim 8, wherein The training also includes: By comparing the difference between the high-resolution image spectrum output by the SwinIR model and the target high-resolution image spectrum, calculate the loss value using the pixel-level L1 loss function; The SwinIR model uses the calculated loss value to pass the error gradient layer by layer back to each parameter of the SwinIR model through the backpropagation algorithm; Use the optimizer to update each parameter according to the learning rate, so that the generated high-resolution spectrum approaches the real target spectrum, and loop until the loss curve tends to be stable and the metrics on the validation set reach the optimal, marking the convergence and completion of the training of the model.

10. A frequency-domain differential image reconstruction system based on the SwinIR model, characterized in that, The system includes: An image processing module for preprocessing the low-resolution image; An image conversion module for performing Fourier transform on the preprocessed low-resolution image to convert the image from the spatial domain to the frequency domain to obtain an image spectrum representation; A generation module for inputting the image spectrum representation into the differential mode generator to obtain the differential mode signal image spectrum; A differential mode image spectrum reconstruction module for inputting the differential mode signal image spectrum into the pre-trained SwinIR model and outputting the high-resolution reconstructed differential mode image spectrum; A differential processing module for performing differential output on the high-resolution reconstructed differential mode image spectrum to obtain the high-resolution reconstructed image spectrum; A high-resolution reconstruction module for performing inverse Fourier transform on the high-resolution reconstructed image spectrum and outputting the high-resolution reconstructed image.

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