# A Deep Residual Star Generative Adversarial Network for multi-domain Image
Super-Resolution

Rao Muhammad Umer  Dept. of Computer Science
University of Udine
Udine, Italy
<EMAIL_ADDRESS>Asad Munir  Dept. of Computer Science
University of Udine
Udine, Italy
<EMAIL_ADDRESS>Christian Micheloni  Dept. of Computer Science
University of Udine
Udine, Italy
<EMAIL_ADDRESS>
###### Abstract

Recently, most of state-of-the-art single image super-resolution (SISR)
methods have attained impressive performance by using deep convolutional
neural networks (DCNNs). The existing SR methods have limited performance due
to a fixed degradation settings, _i.e._ usually a bicubic downscaling of low-
resolution (LR) image. However, in real-world settings, the LR degradation
process is unknown which can be bicubic LR, bilinear LR, nearest-neighbor LR,
or real LR. Therefore, most SR methods are ineffective and inefficient in
handling more than one degradation settings within a single network. To handle
the multiple degradation, _i.e._ refers to multi-domain image super-
resolution, we propose a deep Super-Resolution Residual StarGAN
(SR${}^{2~{}*}$GAN), a novel and scalable approach that super-resolves the LR
images for the multiple LR domains using only a single model. The proposed
scheme is trained in a StarGAN like network topology with a single generator
and discriminator networks. We demonstrate the effectiveness of our proposed
approach in quantitative and qualitative experiments compared to other state-
of-the-art methods.

###### Index Terms:

Single Image Super-Resolution, Multi-domain SR, Deep Learning, and GAN.

##  I Introduction

The goal of the single image super-resolution (SISR) is to reconstruct the
high-resolution (HR) image from its low-resolution (LR) image counterpart.
SISR problem is a fundamental low-level vision and image processing problem
with various practical applications in satellite imaging, medical imaging,
video enhancement and security and surveillance imaging as well. With the
increasing amount of HR images / videos data on the internet, there is a great
demand for storing, transferring, and sharing such large sized data with low
cost of storage and bandwidth resources. Moreover, the HR images are usually
downscaled to easily fit into display screens with different resolutions while
retaining visually plausible information. The downscaled LR counterpart of the
HR can efficiently utilize lower bandwidth, save storage, and easily fit to
various digital displays. However, some details are lost and sometimes visible
artifacts appear when users downscale and upscale the digital contents.

Figure 1: The visualization of our proposed approach where a single generator
$\mathbf{G}$ learns the mappings among multiple domains _i.e._ LR/HR to LR/HR.

Usually, the SISR is described as a linear forward observation model [1, 2, 3]
by the following image degradation process:

${\bf y}={\bf H}*\tilde{{\bf x}}+\eta,$ (1)

where ${\bf y}$ is an observed LR image, ${\bf H}$ is a _down-sampling
operator_ that convolves with an HR image $\tilde{{\bf x}}$ and resizes it by
a scaling factor $s$, and $\eta$ is considered as an additive white Gaussian
noise with standard deviation $\sigma$. However, in real-world settings,
$\eta$ also accounts for all possible errors during the image acquisition
process that include inherent sensor noise, stochastic noise, compression
artifacts, and the possible mismatch between the forward observation model and
the camera device. In most of existing SR methods, the operator ${\bf H}$ is
usually known / fixed _i.e._ bicubic. But in real-world settings, the operator
${\bf H}$ is unknown that can be bicubic, bilinear, nearest, and real
degradation kernel.

Recently, numerous works have been addressed toward the task of SISR that are
based on DCNNs for their powerful feature representation capabilities either
on PSNR values [4, 5, 6, 7, 8, 9, 10] or on visual quality [11, 12, 13, 14, 1,
2]. The SR methods mostly rely on the single degradation (_i.e._ usually
bicubic) with paired LR and HR images in the supervised training. In the real-
world settings, the input LR image contains more complex degradation. As the
bicubic, bilinear, and nearest LR degradation are rarely suitable for the real
LR images, but these degradations can be used for data augmentation and are
indeed a good choice for clean and sharp image super-resolution. Moreover, the
_Real LR_ domain in the proposed method contains the LR/HR image pairs that
follow the realistic physical image model instead of artificial ones. Due to
such different degradation settings, the most SR methods often fail to produce
convincing SR results or train their model independently for every pair of
image domains.

Figure 2: Visualizes the structure of the our proposed SR${}^{2~{}*}$GAN
setup. $\mathbf{G}$ takes an input as both the source image (${\bf y}$) and
target domain label and generates a fake target image ($\hat{{\bf y}}$).
$\mathbf{G}$ tries to reconstruct the fake source image (${\bf y}^{\prime}$)
from the fake target image ($\hat{{\bf y}}$) given the source domain label.
$\mathbf{D}$ learns to discriminate between real and fake target images and
classify the real target images to its corresponding domain. In this way, the
$\mathbf{G}$ tries to generate fake target images indistinguishable from real
target images and classifiable as target domain images by the $\mathbf{D}$.

Instead of learning a fixed degradation setting (e.g., bicubic LR), the
proposed SR${}^{2~{}*}$GAN takes as inputs both an image and a domain label,
and learns to generate the image into the corresponding domain (LR/HR). The
domain labels are encoded in binary or one-hot vector to represent domain
information. Fig. 1 illustrates an overview of our proposed SISR approach,
where a single network $\mathbf{G}$ learns the mappings among the multiple
domains _i.e._ Bicubic LR, Bilinear LR, Nearest LR, Real LR, and HR. During
the training phase, we translate the source domain images into the target
domain images by randomly generate target domain labels. At the testing phase,
we fix the target domain as HR domain to generate the SR images from any blind
LR domain. The proposed scheme is inspired by the recent success of StarGAN
[15] for multi-domain image-to-image translation applications. The proposed
approach (refers to the section III for more details) allows us to
simultaneously train for multiple domains with in a unified network.

Our contributions in this paper are as follows:

  * •

We propose SR${}^{2~{}*}$GAN for multi-domain image super-resolution task. In
contrast to the existing deep SISR methods, our method learns the mappings
among multiple domains with in a single model.

  * •

The proposed scheme requires a single generator and discriminator networks to
train efficiently for the images of multiple domains.

  * •

We provide both qualitative and quantitative results on SR benchmarks to show
its superiority over existing SR methods.

##  II Related Work

Recently, numerous works addressed the task of SISR using deep CNNs for their
powerful feature representation capabilities. A preliminary CNN-based method
to solve SISR is a super-resolution convolutional network with three layers
(SRCNN) [16]. Kim  _et al._[4] proposed a very deep SR (VDSR) network with a
residual learning approach. Lim _et al._[5] proposed an enhanced deep SR
(EDSR) network by taking advantage of the residual learning. In [17], the
authors proposed SRWDNet to solve the joint deblurring and super-resolution
task by following the realistic degradation. In [3], the authors proposed the
ISRResCNet to solve the SISR in an iterative manner. These methods mostly rely
on the PSNR-based metric by optimizing the $\mathcal{L}_{1}$/$\mathcal{L}_{2}$
losses in a supervised way by the LR/HR paired data.

For the perception SR task, a preliminary attempt was made by Ledig _et
al._[11] who proposed the SRGAN method to produce perceptually more pleasant
results. To further enhance the performance of the SRGAN, Wang _et al._[12]
proposed the ESRGAN model to achieve the state-of-art perceptual performance.
Despite their success, the previously mentioned methods are trained with LR/HR
image pairs with the bicubic downsampling and thus they have limited
performance in the real-world settings. Recently, in the real-world SR
challenge series [18, 19, 20], the authors have described the effects of
bicubic downsampling. More recently, in [1, 2], the authors proposed GAN-based
SR methods to solve the real-world SR problem. However, the above SR methods
have different models to be independently built for every LR degradation. Our
approach takes into account the different LR degradation within a single
network by greatly increasing its applicability in practical scenarios.

##  III Proposed Method

###  III-A Multi-domain training strategy

Our goal is to train a single network $\mathbf{G}$ that super-resolves the LR
images from multiple LR domains. To achieve this objective, we train the
generator $\mathbf{G}$ to translate an input source image ${\bf y}$ into an
output target image $\hat{{\bf y}}$ conditioned on the target domain labels
$\mathbf{\ell}$ as $\mathbf{G}({\bf y},\mathbf{\ell})\rightarrow\hat{{\bf
y}}$. The domain labels $\mathbf{\ell}$ are encoded in binary or one-hot
vector to represent domain information. We randomly generate the target domain
labels $\mathbf{\ell}$ so that the network $\mathbf{G}$ flexibly translates
the source domain images into the target domain images. The discriminator
network $\mathbf{D}$ learns to distinguish between real/fake images and also
tries to minimize the domain classification error only associated with the
known domain label. The discriminator $\mathbf{D}$ (_i.e._ adapted from
StarGAN [15]) produces the probability distributions over both target images
and target domain labels, $\mathbf{D}:{\bf
x}\rightarrow\\{\mathbf{D}_{trg}({\bf x}),\mathbf{D}_{cls}({\bf x})\\}$. Fig.
2 illustrates the training strategy of the proposed SR${}^{2~{}*}$GAN.

###  III-B Network Architectures

Generator ($\mathbf{G}$): We use the generator $\mathbf{G}$ network as a
_Encoder-Resnet-Decoder_ like structure, adapted from SRResCGAN [1] which
strictly follows the degradation process (1). In the $\mathbf{G}$ network,
both _Encoder_ and _Decoder_ layers have $64$ convolutional feature maps of
$5\times 5$ kernel size with $C\times H\times W$ tensors, where $C$ is the
number of channels of the input image. _Resnet_ consists of $5$ residual
blocks with two Pre-activation _Conv_ layers, each of $64$ feature maps with
kernel support $3\times 3$, and the preactivation is the _Sine_ nonlinearities
layer with $64$ output feature channels. The trainable projection layer [21]
inside the _Decoder_ computes the proximal map with the estimated noise
standard deviation $\sigma$ and handles the data fidelity and prior terms.
Discriminator ($\mathbf{D}$): The discriminator network ($\mathbf{D}$) learns
to distinguish between real and fake images and classify the real images to
its corresponding domain. The discriminator network contains 6 convolutional
layers with kernels that support $4\times 4$ of increasing feature maps from
$64$ to $2048$ followed by the leaky ReLU as done in StarGAN [15].

###  III-C Network Losses

To train the generator $\mathbf{G}$ and discriminator $\mathbf{D}$, we use the
following respective objective loss functions:

$\mathcal{L}_{G}=\mathcal{L}_{\mathrm{per}}+\mathcal{L}_{\mathrm{GAN}}+\mathcal{L}_{tv}+\mathcal{L}_{cls}^{f}+10\cdot\mathcal{L}_{\mathrm{1}}+10\cdot\mathcal{L}_{\mathrm{cyc}},$
(2) $\mathcal{L}_{D}=\mathcal{L}_{GAN}+\mathcal{L}_{cls}^{r},$ (3)

where $\mathcal{L}_{per}$, $\mathcal{L}_{GAN}$, $\mathcal{L}_{tv}$,
$\mathcal{L}_{cls}^{r/f}$, $\mathcal{L}_{1}$, and $\mathcal{L}_{cyc}$ denote
the perceptual (VGG-based) loss, texture/GAN loss, total variation loss,
real/fake classification loss, content loss, and cyclic loss respectively.

##  IV Experiments

###  IV-A Training data

For the training, we use DIV2K [22], Flickr2K [23], and RealSR [24] datasets
that jointly contain 22,430 high-quality HR images for image restoration tasks
with rich and diverse textures. We obtain the LR bicubic, LR bilinear, and LR
nearest images by down-sampling HR images by the scaling factor $\times 4$ of
the DIV2K and Flickr2K datasets using the Pytorch bicubic, bilinear, and
nearest kernel function. The LR real images by the scaling factor $\times 4$
are provided with their corresponding HR images in the RealSR dataset. We
consider the five domains as shown in Fig. 1. We obtain the source domain
images from the three datasets with their corresponding domain labels. We
randomly generate the target domain labels with their corresponding images
from the three datasets. We train our network in RGB color space.

###  IV-B Data augmentation

We augment the training data with random vertical and horizontal flipping, and
$90^{\circ}$ rotations. Moreover, we also consider another effective data
augmentation technique, called mixture of augmentation (MOA) [25] strategy. In
the MOA, a data augmentation (DA) method, among _i.e._ Blend, RGB permutation,
Mixup, Cutout, Cutmix, Cutmixup, and CutBlur is randomly selected and then
applied on the inputs. This MOA technique encourages the network to acquire
more generalization power by partially blocking or corrupting the training
sample.

###  IV-C Training details

At the training time, we set the input image patch size as $128\times 128$. We
train the network for 51000 training iterations with a batch size of 16 using
Adam optimizer with parameters $\beta_{1}=0.9$, $\beta_{2}=0.999$, and
$\epsilon=10^{-8}$ without weight decay for both generator and discriminator
to minimize the loss functions in the Eqs. (2) and (3). The learning rate is
initially set to $10^{-4}$ and then multiplies by $0.5$ after 5K, 10K, 20K,
and 30K iterations. Our all experiments are performed with a scaling factor of
$\times 4$ for the LR and HR images.

TABLE I: $\times 4$ SR quantitative results comparison of our method with
others over the DIV2K (100 images of validation-set) and RealSR (93 images of
testset) that are total 393 images of the testset with the four LR
degradation. The arrows indicate if high $\uparrow$ or low $\downarrow$ values
are desired. The best performance is shown in  red and the second best
performance is shown in  blue.

SR methods | #Params | Bicubic | Bilinear | Nearest | Real | Average
---|---|---|---|---|---|---
PSNR$\uparrow$ / SSIM$\uparrow$ / LPIPS$\downarrow$ |  PSNR$\uparrow$ / SSIM$\uparrow$ / LPIPS$\downarrow$ |  PSNR$\uparrow$ / SSIM$\uparrow$ / LPIPS$\downarrow$ |  PSNR$\uparrow$ / SSIM$\uparrow$ / LPIPS$\downarrow$ |  PSNR$\uparrow$ / SSIM$\uparrow$ / LPIPS$\downarrow$
EDSR [5] | $43M$ | 21.33 / 0.66 / 0.3477 |  23.05 / 0.72 / 0.3083 | 19.34 / 0.56 / 0.3653 |  28.06 / 0.82 / 0.4182 | 22.95 / 0.69 / 0.3599
ESRGAN [12] | $16.7M$ | 16.02 / 0.31 / 0.6008 | 17.25 / 0.37 / 0.5186 | 15.29 / 0.26 / 0.6254 |  27.98 / 0.82 / 0.3840 | 19.14 / 0.44 / 0.5322
SRResCGAN [1] | $380K$ |  23.30 / 0.67 / 0.2900 |  24.43 / 0.70 / 0.2720 |  21.10 / 0.60 / 0.3044 |  27.96 / 0.82 / 0.3676 |  24.20 / 0.69 / 0.3085
SRResCycGAN [2] | $380K$ |  24.56 / 0.73 / 0.3380 |  25.58 / 0.75 / 0.3183 |  21.75 / 0.63 / 0.3541 |  28.02 / 0.82 / 0.3827 |  24.98 / 0.73 / 0.3483
SR${}^{2~{}*}$GAN (ours) | $380K$ |  25.52 / 0.75 / 0.4250 |  26.23 / 0.76 / 0.4083 |  22.75 / 0.66 / 0.4415 |  28.02 / 0.82 / 0.4353 |  25.63 / 0.75 / 0.4275

###  IV-D Evaluation metrics

We evaluate the trained model under the Peak Signal-to-Noise Ratio (PSNR),
Structural Similarity (SSIM), and LPIPS [26] metrics. The PSNR and SSIM are
distortion-based measures, while the LPIPS better correlates with human
perception. We measure the LPIPS based on the features of pretrained AlexNet
[26]. The quantitative SR results are evaluated on the $RGB$ color space.

(a) SR results on the LR bicubic

(b) SR results on the LR real

Figure 3: Visual comparison of our method with other state-of-art methods on
$\times 4$ super-resolution.

###  IV-E Comparison with the state-of-art methods

We compare our method with other state-of-art SISR methods including EDSR [5],
ESRGAN [12], SRResCGAN [1], and SRResCycGAN [2]. We compare the SR results
with one deep feed-forward residual network (_i.e._ EDSR) and other three GAN-
based approaches (_i.e._ ESRGAN, SRResCGAN, SRResCycGAN). Although there are
existing SR methods [7], [10], and [17] by handling multiple degradation
settings, but they are the non-blind SR techniques with deep feed-forward
networks, while our proposed method is a blind SR GAN-based approach. So, the
comparison with [7], [10], and [17] methods is not fair. We run all the
original source codes and trained models by the default parameters settings
for the comparison. The competing methods are trained for just one degradation
setting and tested on the different ones. Unlike them, the proposed approach
can be trained with multiple degradations instead of single degradation.

Table I shows the quantitative results comparison of our method with the
others over the DIV2K (100 images of validation-set) and RealSR (93 images of
testset) that are total 393 images of the testset with the four LR
degradation. We have excellent results in terms of PSNR and SSIM compared to
the other methods, while in the case of LPIPS, we lag by the others because
our training objective is to get better PSNR/SSIM. The reason for none of the
competing methods achieved their best performance against the bicubic down-
sampling, is that the other GAN-based approaches focus more on the perceptual
quality, as good perceptual image quality reduces the PSNR/SSIM scores. Our
model is trained with reasonably perceptual quality, while good PSNR/SSIM,
refers to section IV-F.

Regarding the visual quality, Fig. 3 shows the visual comparison of our method
with other SR methods at the $\times 4$ upscaling factor on the test-set. We
have comparable visual SR results with others.

TABLE II: This table reports the quantitative SR results of our method over
the DIV2K and RealSR validation-set (20 images, not used during the training
phase) with the four LR domains (_i.e._ Bicubic, Bilinear, Nearest, Real) for
our ablation study. The arrows indicate if high $\uparrow$ or low $\downarrow$
values are desired.

SR method | Domain label Conditioning ($\ell$) | PSNR$\uparrow$ | SSIM$\uparrow$ | LPIPS$\downarrow$
---|---|---|---|---
SR${}^{2~{}*}$GAN (v1) |  |  $\mathbf{G}$ Conditioned on only HR target domain
---
& used two separate Disc. ($\mathbf{D}_{trg}$, $\mathbf{D}_{src}$)
26.95 | 0.75 | 0.3423
SR${}^{2~{}*}$GAN (v2) |  |  $\mathbf{G}$ Conditioned on only HR target domain
---
& used one Disc. ($\mathbf{D}_{trg}$)
27.20 | 0.76 | 0.3176
SR${}^{2~{}*}$GAN (v3) |  |  $\mathbf{G}$ Conditioned on random target domains
---
& used one Disc. ($\mathbf{D}_{trg}$)
28.09 | 0.78 | 0.3891

###  IV-F Ablation Study

For our ablation study, we train three variants of the proposed
SR${}^{2~{}*}$GAN network structure with conditioning of the domain labels. By
referencing to the Fig. 2, the first network variant v1 is trained by
conditioning the first branch generator $\mathbf{G}$ on only HR target domain
labels, while, the other branch generator $\mathbf{G}$ (shared weights) is
conditioned on the multiple LR source domain labels. We use two separate
discriminators _i.e._ $\mathbf{D}_{trg}$ for the target domain supervision,
$\mathbf{D}_{src}$ for the source domain supervision in the SR${}^{2~{}*}$GAN
(v1). Similarly, the second network variant v2 is trained as the v1, but only
uses one discriminator _i.e._ $\mathbf{D}_{trg}$ for the target domain
supervision. Finally, the third network variant v3 is trained by conditioning
both generators $\mathbf{G}$ on random domain labels and use only one
discriminator $\mathbf{D}_{trg}$ for the real target domain supervision by
minimizing the the total loss functions in the Eqs. (2) and (3). Table II
shows the quantitative SR results of SR${}^{2~{}*}$GAN (v1, v2, v3) over the
DIV2K and RealSR validation-sets (20 images, not used during the training
phase) with the four LR domains _i.e._ Bicubic, Bilinear, Nearest, Real. The
third network variant v3 performs better in terms of PSNR/SSIM among others.
This shows the effectiveness of random target domain labeling and real target
domain images supervision by the discriminator. Therefore, we opt for the
third version v3 and used it for the evaluation in the section-IV-E.

##  V Conclusion

We proposed a unified deep SR${}^{2~{}*}$GAN for the multi-domain image super-
resolution task. The proposed scheme learns the multiple degradation of
different domains within a single model. The proposed method trains the single
generator and discriminator networks to efficiently learn mappings among
multiple domains using StarGAN like network topology. Our method achieves
excellent SR results in terms of the PSNR/SSIM values compared to the existing
SR methods.

## Acknowledgement

This work was supported by EU H2020 MSCA through Project ACHIEVE-ITN (Grant No
765866).

## References

  * [1] R. Muhammad Umer, G. Luca Foresti, and C. Micheloni, “Deep generative adversarial residual convolutional networks for real-world super-resolution,” in _CVPRW_ , 2020, pp. 438–439.
  * [2] R. Muhammad Umer and C. Micheloni, “Deep cyclic generative adversarial residual convolutional networks for real image super-resolution,” in _ECCVW_ , August 2020.
  * [3] R. Muhammad Umer, G. Luca Foresti, and C. Micheloni, “Deep iterative residual convolutional network for single image super-resolution,” in _ICPR_ , January 2021.
  * [4] J. Kim, J. K. Lee, and K. M. Lee, “Accurate image super-resolution using very deep convolutional networks,” _CVPR_ , pp. 1646–1654, 2016.
  * [5] B. Lim, S. Son, H. Kim, S. Nah, and K. M. Lee, “Enhanced deep residual networks for single image super-resolution,” _CVPRW_ , pp. 1132–1140, 2017\.
  * [6] K. Zhang, W. Zuo, S. Gu, and L. Zhang, “Learning deep cnn denoiser prior for image restoration,” _CVPR_ , pp. 2808–2817, 2017.
  * [7] K. Zhang, W. Zuo, and L. Zhang, “Learning a single convolutional super-resolution network for multiple degradations,” _CVPR_ , pp. 3262–3271, 2018.
  * [8] Y. Yuan, S. Liu, J. Zhang, Y. Zhang, C. Dong, and L. Lin, “Unsupervised image super-resolution using cycle-in-cycle generative adversarial networks,” in _CVPRW_ , 2018, pp. 701–710.
  * [9] Y. Li, J. Yang, Z. Liu, X. Yang, G. Jeon, and W. Wu, “Feedback network for image super-resolution,” _CVPR_ , 2019.
  * [10] K. Zhang, W. Zuo, and L. Zhang, “Deep plug-and-play super-resolution for arbitrary blur kernels,” in _CVPR_ , 2019, pp. 1671–1681.
  * [11] C. Ledig _et al._ , “Photo-realistic single image super-resolution using a generative adversarial network,” in _CVPR_ , 2017, pp. 4681–4690.
  * [12] X. Wang, K. Yu, S. Wu, J. Gu, Y. Liu, C. Dong, Y. Qiao, and C. Change Loy, “ESRGAN: Enhanced super-resolution generative adversarial networks,” in _ECCV_ , 2018.
  * [13] A. Lugmayr, M. Danelljan, and R. Timofte, “Unsupervised learning for real-world super-resolution,” _ICCVW_ , 2019.
  * [14] M. Fritsche, S. Gu, and R. Timofte, “Frequency separation for real-world super-resolution,” _ICCVW_ , 2019.
  * [15] Y. Choi, M. Choi, M. Kim, J.-W. Ha, S. Kim, and J. Choo, “StarGAN: Unified generative adversarial networks for multi-domain image-to-image translation,” in _CVPR_ , 2018, pp. 8789–8797.
  * [16] C. Dong, C. C. Loy, K. He, and X. Tang, “Learning a deep convolutional network for image super-resolution,” _ECCV_ , pp. 184–199, 2014.
  * [17] R. M. Umer, G. L. Foresti, and C. Micheloni, “Deep super-resolution network for single image super-resolution with realistic degradations,” in _ICDSC_ , September 2019, pp. 21:1–21:7.
  * [18] A. Lugmayr, M. Danelljan, R. Timofte _et al._ , “AIM 2019 challenge on real-world image super-resolution: Methods and results,” in _ICCVW_ , 2019\.
  * [19] A. Lugmayr, M. Danelljan, and R. Timofte, “NTIRE 2020 challenge on real-world image super-resolution: Methods and results,” in _CVPRW_ , June 2020.
  * [20] P. Wei, H. Lu, R. Timofte _et al._ , “AIM 2020 challenge on real image super-resolution: Methods and results,” in _ECCVW_ , August 2020.
  * [21] S. Lefkimmiatis, “Universal denoising networks: A novel cnn architecture for image denoising,” _CVPR_ , pp. 3204–3213, 2018.
  * [22] E. Agustsson and R. Timofte, “Ntire 2017 challenge on single image super-resolution: Dataset and study,” in _CVPRW_ , 2017, pp. 126–135.
  * [23] R. Timofte, E. Agustsson, L. Van Gool, M.-H. Yang, and L. Zhang, “Ntire 2017 challenge on single image super-resolution: Methods and results,” in _CVPRW_ , 2017, pp. 114–125.
  * [24] P. Wei, H. Lu, R. Timofte, L. Lin, W. Zuo _et al._ , “AIM 2020 challenge on real image super-resolution: Methods and results,” in _ECCVW_ , August 2020.
  * [25] J. Yoo, N. Ahn, and K.-A. Sohn, “Rethinking data augmentation for image super-resolution: A comprehensive analysis and a new strategy,” in _CVPR_ , 2020, pp. 8375–8384.
  * [26] R. Zhang, P. Isola, A. A. Efros, E. Shechtman, and O. Wang, “The unreasonable effectiveness of deep features as a perceptual metric,” in _CVPR_ , 2018, pp. 586–595.