超分辨率重建.pdf

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Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network Christian Ledig, Lucas Theis, Ferenc Husz´ar, Jose Caballero, Andrew Cunningham, Alejandro Acosta, Andrew Aitken, Alykhan Tejani, Johannes Totz, Zehan Wang, Wenzhe Shi Twitter {cledig,ltheis,fhuszar,jcaballero,aacostadiaz,aaitken,atejani,jtotz,zehanw,wshi}@twitter.com Abstract 1. Introduction Despite the breakthroughs in accuracy and speed of single image super-resolution using faster and deeper con- volutional neural networks, one central problem remains largely unsolved: how do we recover the ﬁner texture details when we super-resolve at large upscaling factors? The behavior of optimization-based super-resolution methods is principally driven by the choice of the objective function. Recent work has largely focused on minimizing the mean squared reconstruction error. The resulting estimates have high peak signal-to-noise ratios, but they are often lacking high-frequency details and are perceptually unsatisfying in the sense that they fail to match the ﬁdelity expected at the higher resolution. In this paper, we present SRGAN, a generative adversarial network (GAN) for image super- resolution (SR). To our knowledge, it is the ﬁrst framework capable of inferring photo-realistic natural images for 4× upscaling factors. To achieve this, we propose a perceptual loss function which consists of an adversarial loss and a content loss. The adversarial loss pushes our solution to the natural image manifold using a discriminator network that is trained to differentiate between the super-resolved images and original photo-realistic images. In addition, we use a content loss motivated by perceptual similarity instead of similarity in pixel space. Our deep residual network is able to recover photo-realistic textures from heavily downsampled images on public benchmarks. An extensive mean-opinion-score (MOS) test shows hugely signiﬁcant gains in perceptual quality using SRGAN. The MOS scores obtained with SRGAN are closer to those of the original high-resolution images than to those obtained with any state-of-the-art method. The highly challenging task of estimating a high- resolution (HR) image from its low-resolution (LR) counterpart is referred to as super-resolution (SR). SR received substantial attention from within the computer vision research community and has a wide range of applications [62, 70, 42]. 4× SRGAN (proposed) original Figure 1: Super-resolved image (left) is almost indistin- guishable from original (right). [4× upscaling] The ill-posed nature of the underdetermined SR problem is particularly pronounced for high upscaling factors, for which texture detail in the reconstructed SR images is typically absent. The optimization target of supervised SR algorithms is commonly the minimization of the mean squared error (MSE) between the recovered HR image and the ground truth. This is convenient as minimizing MSE also maximizes the peak signal-to-noise ratio (PSNR), which is a common measure used to evaluate and compare SR algorithms [60]. However, the ability of MSE (and PSNR) to capture perceptually relevant differences, such as high texture detail, is very limited as they are deﬁned based on pixel-wise image differences [59, 57, 25]. This is illustrated in Figure 2, where highest PSNR does not necessarily reﬂect the perceptually better SR result. The 4681

bicubic (21.59dB/0.6423) SRResNet (23.53dB/0.7832) SRGAN (21.15dB/0.6868) original Figure 2: From left to right: bicubic interpolation, deep residual network optimized for MSE, deep residual generative adversarial network optimized for a loss more sensitive to human perception, original HR image. Corresponding PSNR and SSIM are shown in brackets. [4× upscaling] perceptual difference between the super-resolved and orig- inal image means that the recovered image is not photo- realistic as deﬁned by Ferwerda [15]. In this work we propose a super-resolution generative adversarial network (SRGAN) for which we employ a deep residual network (ResNet) with skip-connection and diverge from MSE as the sole optimization target. Different from previous works, we deﬁne a novel perceptual loss us- ing high-level feature maps of the VGG network [48, 32, 4] combined with a discriminator that encourages solutions perceptually hard to distinguish from the HR reference images. An example photo-realistic image that was super- resolved with a 4× upscaling factor is shown in Figure 1. 1.1. Related work 1.1.1 Image super-resolution Recent overview articles on image SR include Nasrollahi and Moeslund [42] or Yang et al. [60]. Here we will focus on single image super-resolution (SISR) and will not further discuss approaches that recover HR images from multiple images [3, 14]. Prediction-based methods were among the ﬁrst methods to tackle SISR. While these ﬁltering approaches, e.g. linear, bicubic or Lanczos [13] ﬁltering, can be very fast, they oversimplify the SISR problem and usually yield solutions with overly smooth textures. Methods that put particularly focus on edge-preservation have been proposed [1, 38]. More powerful approaches aim to establish a complex mapping between low- and high-resolution image informa- tion and usually rely on training data. Many methods that are based on example-pairs rely on LR training patches for which the corresponding HR counterparts are known. Early work was presented by Freeman et al. [17, 16]. Related ap- proaches to the SR problem originate in compressed sensing [61, 11, 68]. In Glasner et al. [20] the authors exploit patch redundancies across scales within the image to drive the SR. This paradigm of self-similarity is also employed in Huang et al. [30], where self dictionaries are extended by further allowing for small transformations and shape variations. Gu et al. [24] proposed a convolutional sparse coding approach that improves consistency by processing the whole image rather than overlapping patches. To reconstruct realistic texture detail while avoiding edge artifacts, Tai et al. [51] combine an edge-directed SR algorithm based on a gradient proﬁle prior [49] with the beneﬁts of learning-based detail synthesis. Zhang et al. [69] propose a multi-scale dictionary to capture redundancies of similar image patches at different scales. To super-resolve landmark images, Yue et al. [66] retrieve correlating HR images with similar content from the web and propose a structure-aware matching criterion for alignment. Neighborhood embedding approaches upsample a LR image patch by ﬁnding similar LR training patches in a low dimensional manifold and combining their corresponding HR patches for reconstruction [53, 54]. In Kim and Kwon [34] the authors emphasize the tendency of neighborhood approaches to overﬁt and formulate a more general map of example pairs using kernel ridge regression. The regression problem can also be solved with Gaussian process regres- sion [26], trees [45] or Random Forests [46]. In Dai et al. [5] a multitude of patch-speciﬁc regressors is learned and the most appropriate regressors selected during testing. Recently convolutional neural network (CNN) based SR 4682

In Wang algorithms have shown excellent performance. [58] the authors encode a sparse representation et al. prior into their feed-forward network architecture based on the learned iterative shrinkage and thresholding algorithm (LISTA) [22]. Dong et al. [8, 9] used bicubic interpolation to upscale an input image and trained a three layer deep fully convolutional network end-to-end to achieve state- of-the-art SR performance. Subsequently, it was shown that enabling the network to learn the upscaling ﬁlters directly can further increase performance both in terms of accuracy and speed [10, 47, 56]. With their deeply-recursive convolutional network (DRCN), Kim et al. [33] presented a highly performant architecture that allows for long-range pixel dependencies while keeping the number of model parameters small. Of particular relevance for our paper are [4], the works by Johnson et al. who rely on a loss function closer to perceptual similarity to recover visually more convincing HR images. [32] and Bruna et al. 1.1.2 Design of convolutional neural networks The state of the art for many computer vision problems is meanwhile set by speciﬁcally designed CNN architectures following the success of the work by Krizhevsky et al. [36]. It was shown that deeper network architectures can be difﬁcult to train but have the potential to substantially increase the network’s accuracy as they allow modeling mappings of very high complexity [48, 50]. To efﬁ- ciently train these deeper network architectures, batch- normalization [31] is often used to counteract the internal co-variate shift. Deeper network architectures have also been shown to increase performance for SISR, e.g. Kim et al. [33] formulate a recursive CNN and present state-of-the- art results. Another powerful design choice that eases the training of deep CNNs is the recently introduced concept of residual blocks [28] and skip-connections [29, 33]. Skip- connections relieve the network architecture of modeling the identity mapping that is trivial in nature, however, po- tentially non-trivial to represent with convolutional kernels. In the context of SISR it was also shown that learning upscaling ﬁlters is beneﬁcial in terms of accuracy and speed [10, 47, 56]. This is an improvement over Dong et al. [9] where bicubic interpolation is employed to upscale the LR observation before feeding the image to the CNN. 1.1.3 Loss functions Pixel-wise loss functions such as MSE struggle to handle the uncertainty inherent in recovering lost high-frequency details such as texture: minimizing MSE encourages ﬁnd- ing pixel-wise averages of plausible solutions which are typically overly-smooth and thus have poor perceptual qual- ity [41, 32, 12, 4]. Reconstructions of varying perceptual Figure 3: Illustration of patches from the natural image manifold (red) and super-resolved patches obtained with MSE (blue) and GAN (orange). The MSE-based solution appears overly smooth due to the pixel-wise average of possible solutions in the pixel space, while GAN drives the reconstruction towards the natural image manifold produc- ing perceptually more convincing solutions. quality are exempliﬁed with corresponding PSNR in Fig- ure 2. We illustrate the problem of minimizing MSE in Fig- ure 3 where multiple potential solutions with high texture details are averaged to create a smooth reconstruction. In Mathieu et al. [41] and Denton et al. [6] the authors tackled this problem by employing generative adversarial networks (GANs) [21] for the application of image genera- tion. Yu and Porikli [65] augment pixel-wise MSE loss with a discriminator loss to train a network that super-resolves face images with large upscaling factors (8×). GANs were also used for unsupervised representation learning in Radford et al. [43]. The idea of using GANs to learn a mapping from one manifold to another is described by Li and Wand [37] for style transfer and Yeh et al. [63] for inpainting. Bruna et al. [4] minimize the squared error in the feature spaces of VGG19 [48] and scattering networks. Dosovitskiy and Brox [12] use loss functions based on Euclidean distances computed in the feature space of neural networks in combination with adversarial training. It is shown that the proposed loss allows visually superior image generation and can be used to solve the ill-posed inverse problem of decoding nonlinear feature representa- tions. Similar to this work, Johnson et al. [32] and Bruna et al. [4] propose the use of features extracted from a pretrained VGG network instead of low-level pixel-wise error measures. Speciﬁcally the authors formulate a loss function based on the euclidean distance between feature maps extracted from the VGG19 [48] network. Perceptually more convincing results were obtained for both super- resolution and artistic style-transfer [18, 19]. Recently, Li and Wand [37] also investigated the effect of comparing and 4683

blending patches in pixel or VGG feature space. 1.2. Contribution GANs provide a powerful framework for generating plausible-looking natural images with high perceptual qual- ity. The GAN procedure encourages the reconstructions to move towards regions of the search space with high probability of containing photo-realistic images and thus closer to the natural image manifold as shown in Figure 3. In this paper we describe the ﬁrst very deep ResNet [28, 29] architecture using the concept of GANs to form a perceptual loss function for photo-realistic SISR. Our main contributions are: • We set a new state of the art for image SR with high upscaling factors (4×) as measured by PSNR and structural similarity (SSIM) with our 16 blocks deep ResNet (SRResNet) optimized for MSE. • We propose SRGAN which is a GAN-based network optimized for a new perceptual loss. Here we replace the MSE-based content loss with a loss calculated on feature maps of the VGG network [48], which are more invariant to changes in pixel space [37]. • We conﬁrm with an extensive mean opinion score (MOS) test on images from three public benchmark datasets that SRGAN is the new state of the art, by a large margin, for the estimation of photo-realistic SR images with high upscaling factors (4×). We describe the network architecture and the perceptual loss in Section 2. A quantitative evaluation on public bench- mark datasets as well as visual illustrations are provided in Section 3. The paper concludes with a discussion in Section 4 and concluding remarks in Section 5. 2. Method In SISR the aim is to estimate a high-resolution, super- resolved image I SR from a low-resolution input image I LR. Here I LR is the low-resolution version of its high- resolution counterpart I HR. The high-resolution images In training, I LR is are only available during training. obtained by applying a Gaussian ﬁlter to I HR followed by a downsampling operation with downsampling factor r. For an image with C color channels, we describe I LR by a real-valued tensor of size W × H × C and I HR, I SR by rW × rH × C respectively. Our ultimate goal is to train a generating function G that estimates for a given LR input image its corresponding HR counterpart. To achieve this, we train a generator network as a feed-forward CNN GθG parametrized by θG. Here θG = {W1:L; b1:L} denotes the weights and biases of a L-layer deep network and is obtained by optimizing a SR-speciﬁc loss function lSR. For training images I HR with corresponding I LR , n = 1, . . . , N , we solve: n , n = 1, . . . , N n ˆθG = arg min θG 1 N N X n=1 lSR(GθG (I LR n ), I HR n ) (1) In this work we will speciﬁcally design a perceptual loss lSR as a weighted combination of several loss components that model distinct desirable characteristics of the recovered SR image. The individual loss functions are described in more detail in Section 2.2. 2.1. Adversarial network architecture Following Goodfellow et al. [21] we further deﬁne a discriminator network DθD which we optimize in an alternating manner along with GθG to solve the adversarial min-max problem: min θG max θD E IHR∼ptrain(IHR)[log DθD (I HR)]+ E I LR∼pG(I LR)[log(1 − DθD (GθG(I LR))] (2) The general idea behind this formulation is that it allows one to train a generative model G with the goal of fooling a differentiable discriminator D that is trained to distinguish super-resolved images from real images. With this approach our generator can learn to create solutions that are highly similar to real images and thus difﬁcult to classify by D. This encourages perceptually superior solutions residing in the subspace, the manifold, of natural images. This is in contrast to SR solutions obtained by minimizing pixel-wise error measurements, such as the MSE. At the core of our very deep generator network G, which is illustrated in Figure 4 are B residual blocks with identical layout. Inspired by Johnson et al. [32] we employ the block layout proposed by Gross and Wilber [23]. Speciﬁcally, we use two convolutional layers with small 3×3 kernels and 64 feature maps followed by batch-normalization layers [31] and ParametricReLU [27] as the activation function. We increase the resolution of the input image with two trained sub-pixel convolution layers as proposed by Shi et al. [47]. To discriminate real HR images from generated SR samples we train a discriminator network. The architecture is shown in Figure 4. We follow the architectural guidelines [43] and use LeakyReLU summarized by Radford et al. activation (α = 0.2) and avoid max-pooling throughout the network. The discriminator network is trained to solve the maximization problem in Equation 2. It contains eight convolutional layers with an increasing number of 3 × 3 ﬁlter kernels, increasing by a factor of 2 from 64 to 512 ker- nels as in the VGG network [48]. Strided convolutions are used to reduce the image resolution each time the number of features is doubled. The resulting 512 feature maps are followed by two dense layers and a ﬁnal sigmoid activation 4684

Figure 4: Architecture of Generator and Discriminator Network with corresponding kernel size (k), number of feature maps (n) and stride (s) indicated for each convolutional layer. function to obtain a probability for sample classiﬁcation. 2.2. Perceptual loss function The deﬁnition of our perceptual loss function lSR is crit- ical for the performance of our generator network. While lSR is commonly modeled based on the MSE [9, 47], we improve on Johnson et al. [32] and Bruna et al. [4] and design a loss function that assesses a solution with respect to perceptually relevant characteristics. We formulate the perceptual loss as the weighted sum of a content loss (lSR X ) and an adversarial loss component as: lSR = lSR X |{z} | content loss adversarial loss + 10−3lSR Gen } } | {z {z perceptual loss (for VGG based content losses) (3) In the following we describe possible choices for the con- tent loss lSR X and the adversarial loss lSR Gen. 2.2.1 Content loss The pixel-wise MSE loss is calculated as: This is the most widely used optimization target for im- age SR on which many state-of-the-art approaches rely [9, 47]. However, while achieving particularly high PSNR, solutions of MSE optimization problems often lack high- frequency content which results in perceptually unsatisfy- ing solutions with overly smooth textures (c.f . Figure 2). Instead of relying on pixel-wise losses we build on the ideas of Gatys et al. [18], Bruna et al. [4] and Johnson et al. [32] and use a loss function that is closer to perceptual similarity. We deﬁne the VGG loss based on the ReLU activation layers of the pre-trained 19 layer VGG network described in Simonyan and Zisserman [48]. With φi,j we indicate the feature map obtained by the j-th convolution (after activation) before the i-th maxpooling layer within the VGG19 network, which we consider given. We then deﬁne the VGG loss as the euclidean distance between the feature representations of a reconstructed image GθG (I LR) and the reference image I HR: lSR V GG/i.j = 1 Wi,jHi,j Wi,j X Hi,j X (φi,j(I HR)x,y y=1 x=1 − φi,j(GθG (I LR))x,y)2 (5) lSR M SE = 1 r2W H rW X rH X x=1 y=1 (I HR x,y − GθG (I LR)x,y)2 (4) Here Wi,j and Hi,j describe the dimensions of the respective feature maps within the VGG network. 4685

2.2.2 Adversarial loss In addition to the content losses described so far, we also add the generative component of our GAN to the perceptual loss. This encourages our network to favor solutions that reside on the manifold of natural images, by trying to fool the discriminator network. The generative loss lSR Gen is deﬁned based on the probabilities of the discriminator DθD (GθG (I LR)) over all training samples as: lSR Gen = N X n=1 − log DθD (GθG(I LR)) (6) Here, DθD (GθG (I LR)) is the probability that the recon- structed image GθG (I LR) is a natural HR image. For better gradient behavior we minimize − log DθD (GθG (I LR)) in- stead of log[1 − DθD (GθG(I LR))] [21]. 3. Experiments 3.1. Data and similarity measures We perform experiments on three widely used bench- mark datasets Set5 [2], Set14 [68] and BSD100, the testing set of BSD300 [40]. All experiments are performed with a scale factor of 4× between low- and high-resolution images. This corresponds to a 16× reduction in image pixels. For fair comparison, all reported PSNR [dB] and SSIM [57] measures were calculated on the y-channel of center-cropped, removal of a 4-pixel wide strip from each border, images using the daala package1. Super-resolved images for the reference methods, including nearest neigh- bor, bicubic, SRCNN [8] and SelfExSR [30], were obtained from online material supplementary to Huang et al.2 [30] and for DRCN from Kim et al.3 [33]. Results obtained with SRResNet (for losses: lSR V GG/2.2) and the SRGAN variants are available online4. Statistical tests were performed as paired two-sided Wilcoxon signed-rank tests and signiﬁcance determined at p < 0.05. M SE and lSR The reader may also be interested in an independently developed GAN-based solution on GitHub5. However it only provides experimental results on a limited set of faces, which is a more constrained and easier task. 3.2. Training details and parameters We trained all networks on a NVIDIA Tesla M40 GPU using a random sample of 350 thousand images from the ImageNet database [44]. These images are distinct from the 1https://github.com/xiph/daala (commit: 8d03668) 2https://github.com/jbhuang0604/SelfExSR 3http://cv.snu.ac.kr/research/DRCN/ 4https://twitter.box.com/s/ lcue6vlrd01ljkdtdkhmfvk7vtjhetog 5https://github.com/david-gpu/srez testing images. We obtained the LR images by downsam- pling the HR images (BGR, C = 3) using bicubic kernel with downsampling factor r = 4. For each mini-batch we crop 16 random 96 × 96 HR sub images of distinct training images. Note that we can apply the generator model to images of arbitrary size as it is fully convolutional. For optimization we use Adam [35] with β1 = 0.9. The SRRes- Net networks were trained with a learning rate of 10−4 and 106 update iterations. We employed the trained MSE-based SRResNet network as initialization for the generator when training the actual GAN to avoid undesired local optima. All SRGAN variants were trained with 105 update iterations at a learning rate of 10−4 and another 105 iterations at a lower rate of 10−5. We alternate updates to the generator and discriminator network, which is equivalent to k = 1 as used in Goodfellow et al. [21]. Our generator network has 16 identical (B = 16) residual blocks. During test time we turn batch-normalization update off to obtain an output that deterministically depends only on the input [31]. Our implementation is based on Theano [52] and Lasagne [7]. 3.3. Mean opinion score (MOS) testing We have performed a MOS test to quantify the ability of different approaches to reconstruct perceptually convincing images. Speciﬁcally, we asked 26 raters to assign an inte- gral score from 1 (bad quality) to 5 (excellent quality) to the super-resolved images. The raters rated 12 versions of each image on Set5, Set14 and BSD100: nearest neighbor (NN), bicubic, SRCNN [8], SelfExSR [30], DRCN [33], ESPCN [47], SRResNet-MSE, SRResNet-VGG22∗ (∗not rated on BSD100), SRGAN-MSE∗, SRGAN-VGG22∗, SRGAN- VGG54 and the original HR image. Each rater thus rated 1128 instances (12 versions of 19 images plus 9 versions of 100 images) that were presented in a randomized fashion. The raters were calibrated on the NN (score 1) and HR (5) versions of 20 images from the BSD300 training set. In a pilot study we assessed the calibration procedure and the test-retest reliability of 26 raters on a subset of 10 images from BSD100 by adding a method’s images twice to a larger test set. We found good reliability and no signiﬁcant differences between the ratings of the identical images. Raters very consistently rated NN interpolated test images as 1 and the original HR images as 5 (c.f . Figure 5). The experimental results of the conducted MOS tests are summarized in Table 1, Table 2 and Figure 5. 3.4. Investigation of content loss We investigated the effect of different content loss choices in the perceptual loss for the GAN-based networks. Speciﬁcally we investigate lSR = lSR Gen for the following content losses lSR X : X + 10−3lSR • SRGAN-MSE: lSR M SE, to investigate the adversarial network with the standard MSE as content loss. 4686

Table 1: Performance of different loss functions for SR- ResNet and the adversarial networks on Set5 and Set14 benchmark data. MOS score signiﬁcantly higher (p < 0.05) than with other losses in that category∗. [4× upscaling] SRResNet- Set5 MSE PSNR 32.05 SSIM 0.9019 MOS 3.37 VGG22 MSE 30.64 30.51 0.8701 0.8803 3.46 3.77 SRGAN- VGG22 VGG54 29.84 0.8468 3.78 29.40 0.8472 3.58 Set14 PSNR 28.49 SSIM 0.8184 MOS 2.98 27.19 0.7807 3.15∗ 26.92 0.7611 3.43 26.44 0.7518 3.57 26.02 0.7397 3.72∗ • SRGAN-VGG22: lSR V GG/2.2 with φ2,2, a loss deﬁned on feature maps representing lower-level features [67]. • SRGAN-VGG54: lSR V GG/5.4 with φ5,4, a loss deﬁned on feature maps of higher level features from deeper network layers with more potential to focus on the content of the images [67, 64, 39]. We refer to this network as SRGAN in the following. We also evaluate the performance of the generator network without adversarial component for the two losses lSR M SE (SRResNet-MSE) and lSR V GG/2.2 (SRResNet-VGG22). We refer to SRResNet-MSE as SRResNet. Quantitative results are summarized in Table 1 and visual examples provided in Figure 6. Even combined with the adversarial loss, MSE provides solutions with the highest PSNR values that are, however, perceptually rather smooth and less convincing than results achieved with a loss component more sensitive to visual perception. This is caused by competition be- tween the MSE-based content loss and the adversarial loss. We further attribute minor reconstruction artifacts, which we observed in a minority of SRGAN-MSE-based recon- structions, to those competing objectives. We could not determine a signiﬁcantly best loss function for SRResNet or SRGAN with respect to MOS score on Set5. However, SRGAN-VGG54 signiﬁcantly outperformed other SRGAN and SRResNet variants on Set14 in terms of MOS. We observed a trend that using the higher level VGG feature maps φ5,4 yields better texture detail when compared to φ2,2 (c.f . Figure 6). 3.5. Performance of the ﬁnal networks We compare the performance of SRResNet and SR- GAN to NN, bicubic interpolation, and four state-of-the- art methods. Quantitative results are summarized in Table 2 and conﬁrm that SRResNet (in terms of PSNR/SSIM) sets a new state of the art on three benchmark datasets. Please note that we used a publicly available framework Figure 5: Color-coded distribution of MOS scores on BSD100. For each method 2600 samples (100 images × 26 raters) were assessed. Mean shown as red marker, where the bins are centered around value i. [4× upscaling] for evaluation (c.f . Section 3.1), reported values might thus slightly deviate from those reported in the original papers. We further obtained MOS ratings for SRGAN and all reference methods on BSD100. The results shown in Table 2 conﬁrm that SRGAN outperforms all reference methods by a large margin and sets a new state of the art for photo- realistic image SR. All differences in MOS (c.f . Table 2) are highly signiﬁcant on BSD100, except SRCNN vs. SelfExSR. The distribution of all collected MOS ratings is summarized in Figure 5. 4. Discussion and future work We conﬁrmed the superior perceptual performance of SRGAN using MOS testing. We have further shown that standard quantitative measures such as PSNR and SSIM fail to capture and accurately assess image quality with respect to the human visual system [55]. The focus of this work was the perceptual quality of super-resolved images rather than computational efﬁciency. The presented model [47], not optimized for video is, in contrast to Shi et al. SR in real-time. However, preliminary experiments on the network architecture suggest that shallower networks have the potential to provide very efﬁcient alternatives at a small reduction of qualitative performance. In contrast to Dong et al. [9], we found deeper network architectures to be beneﬁ- cial. We speculate that the ResNet design has a substantial impact on the performance of deeper networks. We found that even deeper networks (B > 16) can further increase the performance of SRResNet, however, come at the cost of longer training and testing times. We found SRGAN variants of deeper networks are increasingly difﬁcult to train due to the appearance of high-frequency artifacts. Of particular importance when aiming for photo-realistic solutions to the SR problem is the choice of the content loss as illustrated in Figure 6. In this work, we found lSR V GG/5.4 to yield the perceptually most convincing results, which we attribute to the potential of deeper network layers to represent features of higher abstraction [67, 64, 39] away 4687

SRResNet SRGAN-MSE SRGAN-VGG22 SRGAN-VGG54 original HR image (a) (c) (e) (g) (i) (b) (d) (f) (h) (j) Figure 6: SRResNet (left: a,b), SRGAN-MSE (middle left: c,d), SRGAN-VGG2.2 (middle: e,f) and SRGAN-VGG54 (middle right: g,h) reconstruction results and corresponding reference HR image (right: i,j). [4× upscaling] Table 2: Comparison of NN, bicubic, SRCNN [8], SelfExSR [30], DRCN [33], ESPCN [47], SRResNet, SRGAN-VGG54 and the original HR on benchmark data. Highest measures (PSNR [dB], SSIM, MOS) in bold. [4× upscaling] Set5 PSNR SSIM MOS Set14 PSNR SSIM MOS BSD100 PSNR SSIM MOS nearest 26.26 0.7552 1.28 bicubic 28.43 0.8211 1.97 SRCNN SelfExSR DRCN ESPCN SRResNet 30.07 0.8627 2.57 32.05 0.9019 3.37 30.33 0.872 2.65 31.52 0.8938 3.26 30.76 0.8784 2.89 24.64 0.7100 1.20 25.99 0.7486 1.80 27.18 0.7861 2.26 27.45 0.7972 2.34 28.02 0.8074 2.84 27.66 0.8004 2.52 28.49 0.8184 2.98 25.02 0.6606 1.11 25.94 0.6935 1.47 26.68 0.7291 1.87 26.83 0.7387 1.89 27.21 0.7493 2.12 27.02 0.7442 2.01 27.58 0.7620 2.29 SRGAN HR ∞ 29.40 1 0.8472 3.58 4.32 26.02 0.7397 3.72 25.16 0.6688 3.56 ∞ 1 4.32 ∞ 1 4.46 from pixel space. We speculate that feature maps of these deeper layers focus purely on the content while leaving the adversarial loss focusing on texture details which are the main difference between the super-resolved images without the adversarial loss and photo-realistic images. We also note that the ideal loss function depends on the application. For example, approaches that hallucinate ﬁner detail might be less suited for medical applications or surveillance. The perceptually convincing reconstruction of text or structured scenes [30] is challenging and part of future work. The development of content loss functions that describe image spatial content, but more invariant to changes in pixel space will further improve photo-realistic image SR results. 5. Conclusion We have described a deep residual network SRRes- Net that sets a new state of the art on public benchmark datasets when evaluated with the widely used PSNR mea- sure. We have highlighted some limitations of this PSNR- focused image super-resolution and introduced SRGAN, which augments the content loss function with an adversar- ial loss by training a GAN. Using extensive MOS testing, we have conﬁrmed that SRGAN reconstructions for large upscaling factors (4×) are, by a considerable margin, more photo-realistic than reconstructions obtained with state-of- the-art reference methods. 4688

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