Superresolution reconstruction method for ancient murals based on the stable enhanced generative adversarial network

A stable enhanced superresolution generative adversarial network (SESRGAN) algorithm was proposed in this study to address the low-resolution and blurred texture details in ancient murals. This algorithm makes improvements on the basis of GANs, which use dense residual blocks to extract image features. After two upsampling steps, the feature information of the image is input into the high-resolution (HR) image space to realize an improvement in resolution, and the reconstructed HR image is finally generated. The discriminator network uses VGG as its basic framework to judge the authenticity of the input image. This study further optimized the details of the network model. In addition, three loss optimization models, i.e., the perceptual loss, content loss, and adversarial loss models, were integrated into the proposed algorithm. The Wasserstein GAN-gradient penalty (WGAN-GP) theory was used to optimize the adversarial loss of the model when calculating the perceptual loss and when using the preactivation feature information for calculation purposes. In addition, public data sets were used to pretrain the generative network model to achieve a high-quality initialization. The simulation experiment results showed that the proposed algorithm outperforms other related superresolution algorithms in terms of both objective and subjective evaluation indicators. A subjective perception evaluation was also conducted, and the reconstructed images produced by our algorithm were more in line with the general public’s visual perception than those produced by the other compared algorithms.


Introduction
Ancient Chinese murals once boasted a glorious history. After thousands of years of accumulation and deposition over different dynasties, splendid art classics such as Dunhuang murals have emerged. Over a long period, most of the artistic research on ancient Chinese murals has been based on the discovery, exploration and summarization of traditional painting techniques. Reproducing the grandeur of these previous works has become the main direction of research. Because ancient murals were previously subject to sabotage and weathering, the original smooth and clear images have been obscured by a layer of mist, and the texture details of the murals have to overfitting or underfitting. In 2008, Yang et al. [12] used sparse signals to propose a reconstruction algorithm based on sparse representation. This method requires learning and understanding much information about the relationship between HR images and LR images, establishing a complete dictionary, finding LR images and their corresponding matrix arrays and coefficients, and finally completing the reconstruction by weighting the corresponding HR matrix array. The incompleteness of the dictionary used in this method leads to low detail levels in the reconstructed image edges.
In 2014, Dong et al. [13] proposed the "superresolution using a convolutional neural network" (SRCNN) algorithm. The SRCNN algorithm was the pioneering work of deep learning in the field of superresolution. BI was used for the first time to enlarge LR images to the size of the original image. Only a three-layer convolutional network and nonlinear mapping were used to produce HR images. They interpreted the three-layer convolutional structure in three steps, i.e., image block extraction and feature representation, nonlinear mapping of the feature representation, and final reconstruction, and their method had a better effect than those of the common traditional methods. In 2016, Dong et al. [14] improved the SRCNN algorithm. They used the deconvolutional layer to enlarge the image size in the last layer and change the feature dimension and used a smaller convolution kernel and more mapping layers than did Dong et al. Furthermore, a shrinking layer and an expansion layer were added, and the data set was enhanced. Tong et al. [15] proposed a superresolution dense skip connections network (SRDenseNet) algorithm. The dense block was used to input the features of each layer into all subsequent layers so that the features of all layers were connected in series. This structure alleviated the disappearance of gradients, enhanced the transfer of features, and reduced the number of parameters. In 2016, Anagun et al. [6], using a variety of loss functions combined with the Adam optimizer, selected the loss function with the best convergence, which increased the residual module of the network and improved the model performance, and used the Charbonnier or L1 loss functions to reduce the time cost of building the model. In 2017, Zhang et al. [16] proposed a superresolution reconstruction method based on transfer learning and deep learning. This method can not only obtain high-quality, HR images but also reduce the time cost of building the model. Kim et al. [17] proposed a deep-recursive convolutional network (DRCN) by including a recurrent neural network in the overall network, which greatly reduces the number of network parameters. In 2017, Lim et al. [18] proposed the enhanced deep superresolution (EDSR) algorithm, which eliminates batch standardization, reduces the space used during training, removes the unnecessary modules in the conventional residual error network, and achieves good superresolution reconstruction results. In 2017, Ledig et al. [19] proposed the superresolution generative adversarial network (SRGAN) algorithm and applied GANs to solve the superresolution problem. They used the perceived loss and adversarial loss to alleviate the loss of high-frequency details and image smoothness so that images could give good visual perception. However, the peak signal-to-noise ratio (PSNR) obtained based on this strategy was not sufficiently high. In 2017, Arjovsky et al. [20] used the Wasserstein GAN (WGAN) to solve the issue of instability during GAN training; they used the Wasserstein distance instead of JS divergence to measure the distance between the real image and the reconstructed image. Due to the weight pruning strategy, however, there are still issues with this method, such as gradient explosion and disappearance. In 2018, Wang et al. [21] improved the SRGAN algorithm. They used dense residual blocks for feature extraction from the generative network with the relativistic discriminator as the discriminator. The generator could generate more real texture details and retain more image feature information than could the original SRGAN algorithm. Although all the abovementioned deep-learning-based algorithms have improved the reconstruction results compared with traditional machine learning algorithms, their effects are unsatisfactory when directly applied in mural data set processing. Additionally, during the network model training process, they become unstable. Due to the unclear texture details, lost smoothness and undesired reconstruction effects of the reconstructed images, their research value is low.
Based on the abovementioned literature review, we propose a stable enhanced SRGA N (SESRGAN) algorithm in this study, which is based on the GAN. The main contributions of this study are as follows: 1. A new SESRGAN model is proposed. This model expands the deep learning algorithm and may have reference value for the stable training of other GANs. It utilizes the GAN as its framework and integrates the residual dense blocks with residual scaling (RS-RDB) structure in the generative network to fully capture the feature information of the image and therefore to increase the generalization capacity and robustness of the model. For perceived loss calculation, the SESR GAN model uses the feature information before activation and utilizes the WGAN-gradient penalty (WGAN-GP) to counter loss, thereby enhancing its training stability. 2. The proposed SESRGAN model is applied in the superresolution reconstruction of ancient mural images and improves the overall esthetic and artistic values of the images. In this study, the proposed model completes the superresolution reconstruction of ancient mural images based on the idea of deep learning. It provides a new technical route for ancient mural image restoration, breaks through the existing technical bottleneck of ancient mural digital protection, and provides a technical demonstration of the image content restoration of similar information in the field of cultural heritage digitization.

Generative adversarial networks
The GAN [22] has become a popular deep learning model in recent years and is one of the most promising methods for unsupervised learning with complex distributions. The generative network first captures the distribution of random noise in an image and then uses the distribution of this noise to generate a sample similar to the real data as the input of the discriminator network, which functions to estimate the probability that a sample comes from the training data to judge whether the input data come from the real data or the generated sample. During the process of training the network, the generative network continuously improves its ability to generate real samples to deceive the discriminator network, while the discriminator network continuously improves its ability to discern the authenticity of samples. Through continuous learning in the mutual game between the generative network and the discriminator network, the model is optimized. As time elapses, the generative network and the adversarial network are continuously trained and optimized, and finally, the two networks reach a dynamic equilibrium: the generated sample approximates the distribution of the real sample, and the discrimination probability of the discriminator network for a given sample is 0.5. The loss formula of the GAN is as follows: where X represents the real image data, z represents the noise image data, P X represents the probability distribution of the real image data, p z (z) represents the probability distribution of the generated data, G(z) represents the reconstructed image data, and D(x) represents the probability that the discriminator network correctly judges whether the image data are real or fake. D(G(z)) represents the probability that the discriminator network correctly judges whether the reconstructed image data are real or fake, log D(x) represents the judgment of the discriminator network on the real image data, and log (1 -D(G(z))) represents the judgment on the reconstructed image data. The structure of the generative adversarial network is shown in Fig. 1.

Residual network and dense network
The residual network (ResNet) [23] addresses the fact that the gradient is prone to diffuse or disappear and that the training accuracy and test accuracy decrease due to the saturated and degraded network performance when the convolutional neural network becomes deeper. The ResNet structure is shown in Fig. 2. Suppose that the output of the previous layer is the input x of the current layer; then, the residual of the current layer is F(x), and the output of the next layer is H(x). x is passed on to the next layer H(x) by means of a skip connection. Then, H(x) = F(x) + x. The residual of this layer can be expressed as F(x) = H(x)-x. This residual structure can improve the performance of a relatively deep network [24]. Therefore, this paper introduces the residual block as a part of the generative network. The dense network (DenseNet) [25] commits itself to improving the performance of a network from the perspective of feature reuse. It is a convolutional neural network with dense and close connections between any two layers. Each layer of the DenseNet receives input from all previous layers and then outputs its feature mapping to all subsequent layers, thereby improving the transmission efficiency of information and gradients in the network. The merits of this structure are that it can realize the reuse of features, alleviate the disappearance of gradients, strengthen feature transmission, and substantially reduce the number of parameters. The DenseNet structure is shown in Fig. 3.

WGAN-GP
The WGAN-GP theory [20,26] was proposed to solve problems with the WGAN, such as the difficulty in training and slow convergence speed in the real experimental process. Compared with the conventional GAN, its improvement in terms of effects is not obvious. Therefore, the WGAN-GP approach pinpoints the root cause of WGAN defects: the WGAN directly adopts weight clipping in the process of addressing the Lipschitz limitation condition. Every time the parameters of the discriminator are updated once, the condition is then checked to see whether the absolute values of all parameters in the discriminator exceed a threshold n. If any exceed the threshold, these parameters are clipped back to the range of [− n, n]. By ensuring that all parameters of the discriminator are bounded during the training process, the approach ensures that there is not a large difference in the discrimination of two slightly different samples by the discriminator; therefore, the Lipschitz condition is realized indirectly. However, this leads to most weights approximating the two extremes. Therefore, the WGAN-GP approach uses a gradient penalty and adopts the Adam optimizer to replace the RMSprop optimizer, which increases Gaussian noise in the generated image. Compared with the WGAN, this method can train the GAN model more stably, requires almost zero repeated adjustments of the superparameters, can enable the model to converge quickly, and can generate images of good quality.

Stable enhanced generative adversarial network algorithm
The designed GAN can better reconstruct HR images than can other networks. Its architecture is shown in Fig. 4. The generative network takes an LR mural image as input, extracts features through the dense ResNet, reconstructs the image through upsampling and convolution, and outputs the HR mural image. The HR and real HR are input into the discriminator network together. Finally, the discriminator network is responsible for determining whether the input images are real or fake.

Residual dense blocks with residual scaling
To extract as many features of the murals as possible and restore the image quality well, this study makes the following adjustments to the generative network: residual dense blocks with residual scaling (RS-RDB) is used to replace the original residual block (RB) for extracting the deep features of the input image. Since increased numbers of layers and connections always improve the performance of a network, the combination of residual networks and dense connections increases the depth of the network used in this study. The structure of the RS-RDB is shown in Fig. 5. To extract the maximum number of image features and prevent overfitting caused by overly deep networks, we use 23 RDBs in this study, which are helpful for restoring the image texture and eliminating noise. One RDB is composed of 3 dense blocks, and residual scaling is introduced. The residual is multiplied by a numerical value β in (0, 1) to increase the stability of the trained deep network. Among them, the dense block is composed of 4 convolutional layers and 4 leaky ReLU layers. For the sake of the consistency, stability and generalizability of the model, the BN layer in the dense block module is removed to reduce the computational complexity and memory usage. For different PSNR-based tasks, such as superresolution and deblurring, removal of the BN layer has been demonstrated to improve the effect of the model and reduce its computational complexity; the BN layer is prone to generating undesired artifacts, thereby limiting the generalization ability of the model [27]. The dense block is shown in Fig. 6. The input image features are extracted through the abovementioned residual dense blocks, and then HR images are generated. Two subpixel convolutional layers (pixel shufflers) are used to enlarge the size of the image, and finally, a 3*3 convolutional layer is used to output a 3-channel HR image.

Design of the discriminator network
The discriminator network first uses a 64-channel convolutional layer to extract shallow features from the input image and then uses 8 convolutional layers, each of which contains a BN layer. Leaky ReLU is used as the activation function. Because the WGAN-GP approach uses the Wasserstein distance instead of JS divergence to measure the distance between the real sample and the generated sample, the task corresponds to a regression model. Therefore, the following adjustments are made in this study: The sigmoid activation function designed by the original discriminator network is not used. Instead, two fully connected layers are used to directly output the real probability of the image. Details about the discriminator network are shown in Table 1.

Loss function
A loss function is used to judge whether the image reconstructed by the model is good or not. To generate a genuine visual effect for the reconstructed image, the perceptual loss and content loss are used to optimize the generative network, and the adversarial loss is used to optimize the adversarial network. The final calculation formula for the loss function is as follows: where λ 1 and λ 2 represent the coefficients used to balance the different losses. First, the content loss is introduced. To ensure the accuracy of the reconstructed image and the original image information, the mean squared error (MSE) loss is taken as the content loss of the generative network. The spatial error between the generated image pixels and the real image pixels is calculated to determine the pixel-level loss. The formula for determining the pixel-level MSE loss is: Then, the perceptual loss is introduced. The MSE loss enables the reconstructed image to have a very high PSNR. However, high-frequency content is absent in the  image, which blurs the details of the image. In the generative network, the perceptual loss in the VGG [23] network is also introduced, and the feature information before activation (instead of after activation) is used for calculation purposes. To calculate the VGG loss, the generated HR image and the real HR image are input into the VGG19 network for feature extraction, and then the RMSE is used to calculate the Euclidean distance on the extracted feature map. The calculation formula for the VGG is: where φ i, j represents the feature map obtained between the jth convolution (before activation) and the ith pooling layer of the VGG19 network. Then, we define the VGG loss as the feature of the reconstructed image, representing the Euclidean distance between G θ G (I LR ) and the reference image I HR . W i, j and H i, j are the dimensions of the corresponding feature map in the VGG network. Finally, the adversarial loss is introduced. To make the model training process more stable, we introduce the WGAN-GP [14] method proposed by researchers at Monterey University to further improve the objective function of the model on the basis of the WGAN. The gradient penalty is applied to the discriminator network. The formula for calculating the loss function of the WGAN is: The added Lipschitz condition is: When the input sample does not change significantly after the input sample changes, K is generally set to 1. Through the weighting and merging of the original discriminator loss, the formula to calculate the adversarial loss of the WGAN-GP discriminator can be derived as:

Training process of the SESRGAN algorithm
The specific process of the superresolution generative adversarial network (SESRGAN) algorithm proposed in this study is described as follows: Input: the LR image data set and the corresponding HR image data set. Output: the generative network G and the adversarial network D.
Step 1: Feed the LR image to the generative network G and output the generative HR image HR g obtained after reconstruction.
Step 2: Calculate the MSE between the HR image and HR g image and update the parameters of the generative network.
Step 3: Repeat step 1-step 2 n 1 times to obtain and save the pretrained generative network model l adv .
Step 4: Input the LR image into l adv and output the generated HR image l adv .
Step 5: Input HR 1 and the corresponding HR into the adversarial network D, calculate the adversarial loss l adv , and update the parameters of the adversarial network D. Step 6: Input HR 1 and the corresponding HR into the pretrained VGG network, and then use the eigenvalues before activation to calculate the perceptual loss l VGG .
Step 7: Calculate the content loss l MSE between HR 1 and the corresponding HR.
Step 8: Calculate the total loss l g , and update and save the generative network G and the adversarial network D.
Step 9: Repeat step 3-step 8 n 2 times, and continuously update and save the generative network G and the adversarial network D.
The training process of the SESRGAN algorithm is shown in Fig. 7.

Experimental environment and design
The hardware environment set up for the experiment was as follows: an Intel Corei7-7700K CPU, 16 GB of memory, and an NVIDIA GeForce GTX1080Ti graphics card. The software environment set up in the experiment was as follows: CUDA version 9.0, cuDNN version 7.0, and the Windows 10 operating system. Python 3.6 and the PyTorch framework were used to write the experimental test. The software compiler was pycharm2019_3.1_x64. The training data set used in the experiment consisted of 800 DIV2K images, 2650 Flickr2K images, and 90 mural images. The test data set was made up of 30 mural images. The mural data set in this study consisted of murals of different styles and types. First, the data set was expanded. The data were enhanced by flipping them and rotating them 180°, as shown in Fig. 8. The downsampling factor for the HR and LR images was 4. To increase the input and output speeds during training, the LR images were clipped to a size of 120*120, and the HR images were clipped to a size of 480*480; all the images were then fed into the model. The optimizer used was the Adam optimizer, with β 1 = 0.9 and β 2 = 0.99. The initial learning rate was set to 0.0001, and the attenuation parameter of the learning rate was 0.5. The residual scaling strategy was introduced in the generative network model, where β = 0.2. This study, incorporating the idea of second transfer learning proposed by Yuan [15], used the DIV2K data set to pretrain a generator on the generative network, which was used to initialize the parameters to obtain high-quality images and fast convergence speeds. Then, the Flickr2K images were fed into the network for training, and finally, the mural data set was fed into the network to complete the training process. The generator and discriminator models were updated alternatively, and finally, the experimental results were obtained and analyzed.

Evaluation indexes
To demonstrate the effectiveness of our algorithm, we use both reference and noreference indexes to assess the quality of the reconstructed image, with the former type including the PSNR, structural similarity index method (SSIM), multiscale structural similarity index method (MS-SS), and Firchet inception distance (FID) and the latter including the natural image quality evaluator (NIQE). A higher PSNR value (unit: dB) between the two images indicates less distortion between the reconstructed image and the HR image, that is, a higher-quality reconstructed image; the SSIM reflects the similarity of the reconstructed image to the real image in terms of the brightness, contrast and structure. The closer the SSIM is to 1, the higher the similarity between the two images, indicating that the generated image better conforms to the visual perceptual effects of the public. MS-SSIM is the average obtained from the calibration procedures of image assessments with different resolution scales. IS is the scoring system for the generated image in terms of diversity and quality using the training inception-v3 network. A high IS score indicates better diversity and quality of the generated image. FID is a measure of the distance between the feature vector of the authentic image and that of the generated image, based on which the similarity between the authentic image and the generated image is evaluated. A lower FID means a higher similarity. The NIQE does not require distorted images to be visually scored for training. Instead, after calculation of the locally mean subtracted contrast normalized (MSCN) image, part of the image blocks are used as training data according to the local activity. The NIQE takes model parameters that are obtained based on a generalized Gaussian model fitting as the features. It adopts a multivariable Gaussian model to describe the features and assesses the quality of the generated image based on the distance between the model parameter of the image and the pre-established model parameter. A lower NIQE score indicates a higher perception quality of the image. The subjective evaluation standard commonly used at present is the mean opinion score (MOS), which grades images using 5 levels (bad, poor, fair, good, and excellent). To obtain the MOS, we invited 50 evaluators to grade each algorithm from 1 to 5 points on the basis of the overall perception effects and local details/texture of the image, and then we counted the results of each evaluator's score of the image and computed the average score, which was taken as the MOS to evaluate the performance of each algorithm.

Model training loss and analysis
The loss function is a tool to measure the quality of the architecture of a network. During the training process, the SESRGAN algorithm realizes gradient optimization by continuously updating and calculating each parameter. After training the model 160 × 10 3 times, the parameters achieve their optimal values, thereby minimizing the loss function. The various losses are shown in Fig. 9, where Fig. 9a is the content loss, Fig.  9b is the perceptual loss, Fig. 9c is the adversarial loss, and Fig. 9d is the total loss. In Fig. 9, the content loss is stable between 4 × 10 −4 and 5.5 × 10 −4 , indicating that the pixels of the generated images are sufficiently similar to the pixels of the real images, with no excessive pixel errors. The perceptual loss steadily decreases within a range of 0.8-1.2 and finally stabilizes at approximately 0.9, indicating that the error between the feature extraction of the generated image and the feature extraction of the real image is small and demonstrating that the generative model can extract image features well. The adversarial network is stable within a range of 0-0.5. The discriminator loss periodicity begins at a high level and then declines because the discriminator is locked when the generator is being trained, causing the capability of the discriminator to decrease. Then, the generator is locked. The discriminator is continuously optimized during training so that the loss is reduced, indicating that the discriminator finally becomes sophisticated enough that it can successfully judge whether an image is a generated image or a real image. The total loss of the generator is stable within a range of 0.03-0.04, indicating that the generator is relatively mature after training and can successfully generate the reconstructed HR image from the corresponding LR image.

Analysis of the murals reconstructed by the SESRGAN algorithm
To verify the effectiveness of the algorithm in reconstructing the ancient murals, 4 images were randomly selected from the reconstructed 4-fold HR mural images and compared with the corresponding LR mural images, as shown in Fig. 10.
As shown in Fig. 10, the texture details of each LR ancient mural image after reconstruction by the algorithm in this study are relatively ideal. The reason for this is that a deep network was used to extract high-frequency features, and a pretrained VGG network was used to extract feature information before activation rather than after activation. An observation of the LR images is that those that retain more details are clearer after reconstruction than those that retain fewer details, and these images show good consistency in terms of brightness and contrast. In addition, it is clear that after the reconstruction of LR images that retain few details, the restored images are relatively complete, and they are not inferior to other reconstructed mural images in terms of details. As shown in Table 2, the reconstructed images exhibited satisfactory scores in terms of both the reference and no-reference assessment indicators, which indicates that the algorithm proposed in this study exhibits excellent stability.

Comparison experiment and analysis
To ensure the desired effect of this experiment, one mural image from each of six styles of mural images was selected as a representative for comparison, as shown in Fig. 11, in which Fig. 11a is the Yonglegong mural, Fig. 11b is the Baigong mural from the Qing dynasty, Fig. 11c is the Chaoyuan mural, Fig. 11d is the Lushui Temple mural, Fig. 11e is the Landscape mural, and Fig. 11f is the Life mural from the Ming dynasty. The BI algorithm in reference [7], the SRGAN algorithm in reference [19], and the ESRGAN algorithm in reference [21] were employed for the comparison experiment. To observe the contrast effect clearly, the locally reconstructed and enlarged details of these 6 murals were selected, as shown in Fig. 12.
As shown in Fig. 12, for the Yonglegong mural and Baigong mural, each algorithm restores details well. However, the BI and SRGAN algorithms do not perform as well as the algorithm in reference [28], the ESRGAN algorithm and the SESRGAN algorithm proposed in this study in terms of brightness. For the Chaoyuan mural, an examination of the face of the figure in the mural reveals that the image reconstructed by the SESR GAN algorithm is smoother and that the noise elimination effect of the proposed  algorithm is better than those of other algorithms. In the Lushui Temple mural, by observing the accessories of the mural portrait, one can find that the texture details of other algorithms are missing, while the algorithm in this study retains these texture details. In the Landscape and Life murals, the BI algorithm does not take the feature information of the entire image into account, resulting in a lack of high-frequency details. The feature information extracted by the SRGAN algorithm is insufficient because it adopts a rather shallow network. Therefore, their details and textures are poorer than those extracted by the algorithms in references [28][29][30], the ESRGAN algorithm, and the algorithm in this study. The ESRGAN algorithm and that in reference [30] have an excellent restoration effect. However, they introduce some unpleasant noises. In summary, the reconstruction effect of the SESRGAN algorithm is superior to those of the other algorithms in terms of image details. The BI algorithm is inferior to the other algorithms in terms of brightness and detail restoration for various styles of mural images. The SRGAN algorithm restores part of the high-frequency information.
Because both the BI and SRGAN algorithms use few network layers, some highfrequency details are not learned, and the edges are seriously sharpened. The overall effect of the ESRGAN algorithm is better than those of the BI and SRGAN algorithms in terms of the restoration of details, but it adds unpleasant artifacts and noise information. Although the reconstruction effects of the algorithms in references [28][29][30] are satisfactory, they do not perform as well as the SESRGAN algorithm in terms of local details. Therefore, the algorithm proposed in this study is improved to a certain extent in terms of texture details, overall brightness, and resolution compared with the other algorithms.  Figure 13 shows the subjective scores given by the 50 evaluators to the reconstruction effects of different styles of ancient murals in Fig. 12. After evaluation and discussion by the evaluators, it was unanimously agreed that the overall perception of the algorithm proposed in this study conformed more to human visual perception than that of the other algorithms, and it achieved better effects in terms of brightness and image smoothness than did the other algorithms. In terms of local texture details, the evaluators believed that the reconstruction effect achieved by this algorithm was more desirable, and more accurate details were restored in LR images than those obtained by the other algorithms. Through comparison, it is shown that this algorithm is also superior to the other algorithms in terms of the overall perception and local detail texture. Therefore, the proposed algorithm also gives a more persuasive outcome than do the other algorithms in terms of subjective scoring.
To validate the superiority of the SESRGAN model, the averages in terms of the considered assessment indicators that are obtained by different algorithms on the mural data sets are calculated, and the results are summarized in Table 3.
As shown in Table 3, the SESRGAN overperforms all other algorithms in terms of the PSNR, SSIM, FID, and NIQE. However, its performance in terms of the MS-SSIM is poorer than that of the algorithm in reference [29], which may be attributed to more detailed features being extracted by the algorithm used in reference [29] because of the adoption of layered RBs. Therefore, in the future, layered feature extraction will be incorporated into the proposed algorithm to obtain more subtle mural texture features. In addition, the SESRGAN exhibits excellent performance in terms of the IS, being second only to the ESRGAN. In summary, because the SESRGAN adopts the RS-RDB structure in a generative network to fully extract features and calculates the perceived loss before rather than after activation, it exhibits excellent performance in terms of both the reference and no-reference image indicators.

Ablation experiment: influence of modules on model performance
To validate the influence of the modules on the performance of the proposed model, we design the modules, as given in Table 4, to evaluate their influence on the assessment indicators of the model. As shown in Table 4, RS-RDB has the largest influence on the performance of the model. Compared with the model with the classic RDB, that with RS-RDB achieves noticeable improvements in all indicators. The preactivation perceived loss calculation has the second-largest influence, which is primarily manifested in the NIQE. Although the WGAN-GP presents the smallest influence, it improves the performance of the model to some extent.

Ablation experiment: influence of superparameters on model performance
To validate the influence of superparameters on the performance of the proposed model, we design the residual scaling factor (Table 5) and the learning rate (Table 6) to evaluate their influence on the model performance. As shown in Table 5, when β = 0.2 and β = 0.3, the model exhibits excellent performance, and when β = 0.2, the model is in the optimal state. Therefore, β = 0.2 is most suitable for the SESRGAN model. Table 6 shows that when the learning rate is 0.5, the model exhibits satisfactory performance.
The algorithm proposed in this study achieved a good superresolution reconstruction effect for the ancient mural data set. However, during the process of mural reconstruction, mural images whose reconstruction effects were not ideal also existed, as shown in Fig. 14. The image on the left is the generated image, while the image on the right is the HR image. An observation of the facial features and eave texture in the generated image reveals differences from those in the HR image. This is mainly because there was an insufficient number of murals of this style; thus, the model did not learn sufficient feature information about murals of this style and therefore lacked high-frequency detail information. As a result, the model failed to restore the complete murals when reconstructing them.

Conclusions
We proposed the SESRGAN algorithm in this study to reconstruct ancient murals and solve the problems of blurring and low resolution, which are responsible for the low appreciation and research value of ancient murals. In our GAN, the RDB module was  used for extracting deep features, which was beneficial for extracting feature information. Then, the WGAN-GP theory was introduced to improve the adversarial loss. The Wasserstein distance was adopted to calculate the distance between the reconstructed image and the real image. The gradient penalty was applied to the discriminator network to improve the stability of the network training process. The preactivation features were used to calculate the perceptual loss, which was conducive to restoring texture details and a satisfactory level of brightness. Second transfer learning was adopted to train the model, and finally, a stable enhanced mural reconstruction model was obtained. Compared with other superresolution algorithms, the algorithm proposed in this study achieved improvements in terms of different types of objective assessment indicators. In terms of the subjective evaluation index, it outperformed other algorithms in terms of the MOS and obtained a higher score in terms of local detailed texture than that obtained by other algorithms. This model achieved a good reconstruction effect for both the overall mural images and the local mural images. After reconstruction, the HR mural images were clear and bright. The reconstructed images retained rich texture details, and the ornamental and research values of the murals were enhanced to a certain extent. This model can help prevent the loss of ancient mural images. The deficiency of this study lies in the superresolution reconstruction process being carried out only after the murals were enlarged 4 times. However, the reconstruction process was not carried out at multiple scales. Next, the global feature information and local feature information were not fully utilized. In addition, the texture details of some reconstructed murals were not recovered completely, and the training period of the model was long. The main tasks in the next stage of our research include (1) collecting more mural data sets of different styles to adapt to the depth of the generative network and increase the generalizability and stability of the model; (2) conducting multiscale superresolution reconstruction of murals, showing the artistry and research value of murals at different scales; and (3) simplifying the network structure to reduce the training time and integrating the global and local features into the training process to obtain more detailed texture features and higher-quality mural images than before.