In recent years, super-resolution (SR), a low-level vision task, became a research focus due to the high demand for better-resolution image quality. Super-resolution addresses the problem of reconstructing a high-resolution (HR) input from a low-resolution (LR) counterpart. We aim to super-resolve a single low-resolution image, a technique, commonly, known as single image super-resolution (SISR). Image SR is a challenging task to achieve as the process is ill-posed, which means that mapping between the output HR image to the input LR image is many-to-one. However, despite being a difficult problem, it is useful in many computer vision applications such as surveillance imaging, medical imaging , forensics , object classification  etc.
|Ground-truth||Bicubic||EDSR ||MSLapSRN ||RCAN ||CARN ||Ours|
|Ground-truth||Bicubic||VDSR ||LapSRN ||MSLapSRN ||RCAN ||Ours|
Deep convolutional neural network (CNN) super-resolution methods [11, 7, 12] have shown improvement over traditional super-resolution methods in SISR. The performance and depth of convolutional neural super-resolution networks have evolved dramatically in recent times. As an example, SRCNN  has three convolutional layers while RCAN  has more than 400. However, using deep networks may be unsuitable for many applications. In this regard, it is essential to design efficient networks. The most straightforward way to reduce the size of the network is simply to reduce the depth, but this will decrease the quality. Therefore, it is essential to design an efficient network that focuses on reusability of the computed features.
An effective alternative to depth reduction is to employ recursive architectures, and such attempts are formulated in the form of DRCN  and DRRN . DRCN  avoids redundant parameters via recursive connections while DRRN  share’s parameters through residual recursive connections. The recursive nets achieved a decrease in the number of parameters, and an increase in performance compared to standard CNN’s; however, these models have some limitations, which are: 1) the upsampled input, 2) increased depth and 3) increased width. Although these enable the model to reconstruct the structural features from the low-resolution image, it is at the cost of a large number of operations and high inference time. Another approach to forming a compact model is to utilize the dense connections between convolutional layers e.g. SRDenseNet  and RDN .
To optimize speed and the number of parameters CARN  employed group convolutions. The network is primarily based on a variant of residual blocks. Although it can achieve good speed and fewer parameters, it failed to reach the PSNR standard set by RCAN . On the other hand, most of the CNN models [5, 16, 9, 17] treat features equally or only at one scale, and therefore, lack adaptability to deal with various frequency levels, e.g. low, mid and high. Super-resolution algorithms aim to restore mid-level and high-level frequencies as the low-level frequencies can be obtained from the input low-resolution image without substantial computations. The state-of-the-art methods [7, 15, 18], models the features equally or on a limited scale, ignoring the abundant rich frequency representation at other scales; hence these lack discriminative learning capability and capacity across channels, and eventually, this limits the ability of convolutional neural networks. To address these issues, we propose the densely residual Laplacian attention Network (DRLN) to reconstruct SR images. DRLN utilizes the dense connection between the residual blocks to use the previously computed features. Similarly, we employ Laplacian pyramid attention to weight the features at multiple scales and according to their importance.
In summary, our main contributions are four-fold:
We propose densely connected residual blocks and a Laplacian attention network for accurate image super-resolution. Our network achieves much better performance through multi-shortcut connections and multi-level representation.
Our novel design employs cascading over residual on the residual architecture, which can assist in training deep networks. Diverse connection types and cascading over residual on the residual in our DRLN help in bypassing enough low-frequency information to learn more accurate representations.
We introduce Laplacian attention, which has a two-fold purpose: 1) To learn the features at multiple sub-band frequencies and 2) to adaptively rescale features and model feature dependencies. Laplacian attention further improves the feature capturing capability of our network.
Through extensive experiments, we show DRLN is efficient and achieves better performance.
2 Related Works
In this section of the paper, we provide chronological advancement in the deep super-resolution. Dong et al. 
proposed pioneering works in super-resolution by introducing a fully convolutional network composed of three convolutional layers followed by ReLU and termed it as SRCNN . The input to the SRCNN 
is a bicubic interpolated image which diminishes high-frequencies and requires additional computation. To reduce the burden on the network, FSRCNN inputs the original low-resolution image and employ deconvolution to upsample the features to the desired dimensions before the final objective function. The authors of  also uses the shrinking and expansion of channels to make the model near real-time on a CPU.
Initially, the focus was on linear networks, bearing a simple architecture with no skip-connections i.e. only one path for the signal flow with the layers stacked consecutively. SRCNN  and FSRCNN  are examples of linear networks. Similarly, Image Restoration CNN abbreviated as IRCNN 
, another straight model, can restore several low-level vision tasks jointly. The aim here is to employ dilation in convolutional layers to capture a larger receptive field for better learning coupled with batch normalization and non-linear activation (ReLU) to reduce the depth of the network. Furthermore, SRMD, an extended super-resolution network, can handle different degradations. SRMD  inputs low-resolution images and their computed degradation maps. The model structure is similar to [11, 21].
With the emergence of skip-connections in CNN networks, its usage became a prominent feature in super-resolution. In this regard, very deep super-resolution (VDSR) 
incorporated a global skip connection to enforce residual learning using gradient clipping to avoid gradient vanishing. VDSR improved upon the previous CNN super-resolution methods. Inspired from VDSR , the same authors next presented DRCN , which shares parameters using a deep recursive structure. This sharing technique reduces the number of parameters significantly; however, the performance is lagging behind VDSR . Subsequently, deep recursive residual network (DRRN)  replicates primary skip-connections across different convolutional blocks to enforce residual learning through multi-path architecture. The aim is to reduce the memory cost and computational complexity via parameter sharing. Further, Tai et al.  introduces a persistent memory network (MemNet), which is composed of memory blocks stacked together recursively. Each block is then connected to a gate unit densely, where each gate unit is a convolutional layer with kernel size 11. The performance of the networks employing recursive connections is comparable to each other.
Lim et al.  proposed the enhanced deep super-resolution (EDSR) network, which employs residual blocks and a long skip-connection. EDSR  rescaled the features by a factor of 0.1 to avoid gradient exploding. EDSR improved upon all previous methods by a significant margin. More recently, Ahn et al.  proposed the cascading residual network (CARN) which also employs a variant of residual blocks i.e. having three convolutional layers as compared to the customarily-used two convolutional layers with cascading connections. CARN  lags behind EDSR  in terms of PSNR.
Driven by the success of the dense-connection architecture proposed in DenseNet  by Huang et al. for image classification, super-resolution networks have focused on the dense-connections to improve performance. As an example, SRDenseNet  utilized dense-connections where every convolutional layer in a block operates on the output of all prior convolutional layers. To upsample the features, SRDenseNet  orders the blocks sequentially followed by deconvolutional layers at the end of the network. Likewise, Zhang et al.  proposed a residual dense network (RDN) to learn local features from the images via dense-connections. Furthermore, to avoid vanishing gradients and for ease of flow of information from low-level to high-level layers, RDN  employed skip-connections. Lately, DDBPN  aims to model a feedback mechanism with a feed-forward procedure; hence, a series of densely connected upsampling and downsampling layers are used as a single block. To predict the final super-resolved image, the outputs of the intermediate blocks are concatenated as well.
To obtain distinct features at multiple scales, multi-branch networks [25, 26, 27] are proposed. Ren et al.  employ SRCNN  at various branches with a different number of layers to learn features uniquely and lastly combine them using a sum-pooling layer. Similarly, Hu et al.  proposed cascaded multi-scale cross-network composed of subnets. Each subnet has merge-and-run units consisting of two parallel branches, each having two convolutional layers. Batch normalization and Leaky-ReLU  follows each convolutional layer in the merge-and-run unit. In contrast to multi-branch, Lai et al.  proposed a multi-stage network where each sub-network progressively predicts the residual output up to an 8 factor.
To enhance the visual quality of the images, Generative Adversarial Networks (GANs) [30, 31] aim to improve the perceptual quality through super-resolution. The first exciting work in this regard is SRResNet , where the generator is comprised of residual blocks similar to  with a skip-connection from the input to the output while the discriminator is fully convolutional. The SRResNet  combined three different losses, which include perceptual, adversarial and . Next, to create the textures faithful to the original image, EnhanceNet 
used an additional texture matching loss with the mentioned losses. This loss aims to match the textures of low-resolution and high-resolution patches as gram matrices computed from deep features via the.
Similar to , to generate more realistic super-resolved images, Park et al.  proposed SRFeat, which utilizes an additional discriminator to help the generator. The results of SRFeat  are perceptually better than . Inspired by  network, ESRGAN  removed the batch normalization and used dense-connections between the convolutional layers in the same segment. A global skip-connection is incorporated for residual learning. Besides, changing the elements of the generator, an enhanced discriminator i.e. Relativistic GAN  is used instead of the traditional one. The performance of the ESRGAN  is the best among the current super-resolution GAN algorithms. Furthermore, the GAN super-resolution models have significantly improved the perceived quality compared to its CNN competitors.
Visual attention  is primarily employed in image classification. This concept was brought to image super-resolution by RCAN , which uses a channel attention mechanism for modeling the inter-channel dependencies coupled with stacking of groups of residual blocks. The PSNR values of RCAN  is the best among all the algorithms as mentioned earlier. In parallel to RCAN , Kim et al.  proposed a dual attention mechanism, namely, the super-resolution residual attention module (SRRAM). The depth of the SRRAM  is comparatively smaller than RCAN  and lag behind RCAN  in PSNR numbers. On the other hand, our method improves upon RCAN  both visually and in numbers by exploiting densely connected residual blocks followed by multi-scale attention using different levels of the skip and the cascading connections.
3 Our Model
3.1 Network Architecture
Our model is constituted of four integral components, i.e., feature extraction, cascading over residual on the residual, upsampling, and reconstruction, as shown in Figure 2. Let’s suppose the low-resolution input image, and the super-resolved output image is represented by and , respectively. To formally illustrate the model implementation, let be a convolutional layer and
where is the convolutional operator applied on the low-resolution image. Next, is passed on to the cascading residual on the residual component, termed as ,
are the estimated features andis the main cascading residual on the residual component which is composed of dense residual Laplacian modules cascaded together. The output features of the are novel to the best of our knowledge in image super-resolution. Our method’s depth is not significant compared to RCAN ; however, it provides a wide receptive field and the best results. Following this, the extracted deep features from the cascaded residual on the residual component are upscaled through the upsampling component, as:
where and denote an upsampling operator and upscaled features, respectively. Although several choices are available for such as a deconvolutional layer , or nearest-neighbor upsampling with convolution ; we opt for ESPCN  following the footsteps of [7, 5]. Next, the features are passed through the reconstruction component which is composed of one convolutional layer to predict the super-resolved RGB color channels as an output, expressed as:
where is the estimated super-resolved image while denotes the reconstruction operator.
To optimize our model, several choices are available for the loss function, including[11, 9], [5, 7], perceptual , total variation  and adversarial [35, 16]. To be fair with the competing state-of-the-art methods [5, 15, 7], we also choose loss function for our network optimization. Now, for a batch of training pairs, i.e. , the aim is to minimize the loss function as
where DRLN() is our network and denotes the set of all the network parameters learned. The feature extraction and reconstruction are similar to previous algorithms [9, 20]. In the next section, we focus on the .
3.2 Cascading Residual on the Residual
In this section, we provide more details on the cascading residual on the residual structure, which has a hierarchical architecture and composed of cascading blocks. Each cascading block has a medium skip-connection (MSC), cascading features concatenation and is made up of dense residual Laplacian modules (DRLM) each of which consists of a densely connected residual unit, compression unit and Laplacian pyramid attention unit. The lower part of Figure 2 shows DRLM, which will be explained further in Section 3.3.
Recently, in image recognition  and super-resolution , residual blocks are stacked together to construct a network of more than 1000 layers and 400 layers, respectively, via skip-connections, although the performance has increased; however, the computational overhead has also increased. We aim here to construct a compact and efficient model with a much lower number of the convolutional layers amidst improved performance and computation time. Therefore, we introduce cascading of the blocks employing medium and long skip connections. Let’s suppose that the -th dense residual Laplacian module (DRLM) of the -th cascaded block is given as:
where are the features from the -th dense residual Laplacian module (DRLM) of the -th cascaded block. Each cascaded block is composed of DRLMs, and hence the input to the cascaded block is summed with the output of the DRLM as , i.e. medium skip-connection (MSC) as:
where are the weights and biases learned in the cascaded block. The addition of medium skip-connection eases the flow of information across group of DRLM while the addition of long-skip connection (LSC) helps the flow of information through cascaded blocks. The group features are passed to the reconstruction layer to output the same number of channels as the input to the network. Next, we provide information about the dense residual Laplacian modules and its subcomponents.
3.3 Dense Residual Laplacian Module
As briefly mentioned earlier, DRLM is composed of three subcomponents i.e. densely connected residual blocks unit, compression unit, and Laplacian pyramid attention.
The residual blocks we employ, have the traditional two convolutional layers and two ReLUs structure followed by an addition from the input of the residual block, as:
where is the output of the previous convolutional layer or residual block while are the weights of the convolutional layer and are the biases (). Each densely connected residual unit has three residual blocks with dense connection as
where is the concatenation of the previous residual blocks and is the final output of the densely connected residual unit. The features are then passed through a compression unit which compresses the high number of parameters resulted from dense concatenation. The compression unit is comprised of a single convolutional layer with a kernel of 11. The compressed features are then forwarded to the Laplacian attention unit which is described next.
Laplacian Attention: Image Attention has been employed in image classification , image captioning  etc. to converge on essential image regions. In super-resolution, the same concept with a little variation can be applied that features should be weighted according to their relative importance. Here, we propose Laplacian attention to boost and exploit the relationship between the features that are essential for super-resolving the images.
To produce attention differently at the Laplacian pyramids in the DRLM, we use a global descriptor to capture the statistics expressing the entire image. The proposed Laplacian pyramid weights the sub-band features of high importance progressively in each DRLM. The global descriptor takes the output from the compression unit i.e. which has size with feature maps. After processing, the global descriptor reduces the size from to as:
where is the value at position in the feature maps.
To capture the channel dependencies from the retrieved global descriptor, we utilize a gating approach. As studied in 
, the system must be able to learn the nonlinear synergies between feature maps and mutually-exclusive associations via gating. To implement the gating mechanism formally, we utilize ReLU and sigmoid functions, denoted by, and , respectively. The features are passed through the Laplacian pyramid to learn the critical features at different scales as:
is the feature reduction operator while theand are the convolutional layers with kernel dilation specified by the subscripts. The multi-level representations and obtained from the the global descriptor are concatenated as:
Furthermore, as shown in Eq 11, the output of the Laplacian pyramid is convolved with a downsampling operator. Therefore, to upsample and differentiate between the features maps, the output is then fed into the upsampling operator followed by sigmoid activation as:
As a final step, the learned statistics are utilized by adaptively rescaling the output of sigmoid function i.e. by the input of the Laplacian attention unit as:
|Dense Connections (DC)||✓||✓||✓||✓||✓||✓|
|Medium Skip Connections (MSC)||✓||✓||✓||✓||✓||✓|
|Long Skip Connection (LSC)||✓||✓||✓||✓||✓||✓|
|Laplacian Attention (LA)||✓||✓||✓|
|PSNR (in dB)||31.92||32.30||32.06||32.06||32.07||31.85||32.12||31.97||32.10||32.37|
|Original||Bicubic||SRCNN ||VDSR ||MSLapSRN |
|Urban100 (4)||DRRN ||EDSR ||RCAN ||CARN ||Ours|
|Original||Bicubic||SRCNN ||VDSR ||MSLapSRN |
|Urban100 (4)||DRRN ||EDSR ||RCAN ||CARN ||Ours|
|Original||Bicubic||SRCNN ||FSRCNN ||LapSRN |
|MANGA109 (4)||VDSR ||DRRN ||RCAN ||CARN ||Ours|
In this section of the paper, we present the implementation details of our system. In each cascading residual on the residual block, we have three (=3) DRLMs, and in each DRLM, we have three RBs densely connected, one compression unit and one Laplacian attention. The filter size in all the layers is set to 33 with dilation of 1
1 except in the Laplacian pyramid where it is three, five and seven. Likewise, the number of feature maps in all the convolutional layers are fixed to 64, except the last reconstruction layer where the output is either one for grayscale or three for color images. To keep the size of the feature maps the same, zeros are padded accordingly. In pyramid attention, the feature maps are reduced by a factor of four. We also use a post-upscaling procedure instead of pre-scaling for more efficient processing and to avoid the pre-scaling artifacts.
In this section, we first examine the contributions of various elements of our proposed network. Then we test the model on five publicly available super-resolution dataset, namely, SET5 , SET14 , URBAN100 , B100 , and MANGA109 . The metrics employed for evaluation are PSNR and SSIM on the luminance channel obtained through YCbCr color space. We also give a comparison on object recognition performance against the competing super-resolution methods.
4.1 Training settings
To make fair comparisons with the current state-of-the-art use CNN methods [35, 7, 5], we use the same settings which are specified in their particular papers. Similar to , we train our network on DIV2K and Flicker2K datasets . Furthermore, we diversify the training images through data augmentation, which is accomplished by random rotations using multiples of 90 supplemented via horizontal and vertical flipping. The batch size is 16 while the size of the low-resolution input is . To optimize the system, ADAM  is utilized with the default parameters of =0.9, =0.999, and . The learning rate is fixed to originally and then decreased to half after every
iterations. The network is designed utilizing the PyTorch framework on a Tesla P100 GPU.
4.2 Ablation Studies
4.2.1 Influence of the skip connections
Skip connections are the backbone of the current state of the art network [9, 8, 15, 7]. Here, we demonstrate the effectiveness of the skip-connections i.e. Long skip connection (LSC), Medium skip connection (MSC), and dense local connections (DLC), in our model. The connections are categorized based on their length. Table I shows the average PSNR on SET5 for 2 for the different settings of connections. The PSNR is higher when all the connections are present while the performance relatively downgrades when some of the connections are absent. In the absence of all connections, the depth of the network does not yield benefit. This experiment illustrates the significance of the different connection types for our deep network.
|Original||Bicubic||SRCNN ||FSRCNN ||VDSR |
|Urban100 (8)||DRCN ||DRRN ||MSLapSRN ||RCAN ||Ours|
|Original||Bicubic||SRCNN ||FSRCNN ||VDSR |
|MANGA109  (8)||DRCN ||DRRN ||MSLapSRN ||RCAN ||Ours|
4.2.2 Laplacian attention
The second essential component of our model is Laplacian attention. We provide a comparison of the network with and without the use of Laplacian attention in Table I. The results shown support our claim that the selection of essential features through multiple frequency bands assist enhancement of the image and improve the overall accuracy. It should be considered that super-resolution techniques [5, 18] have matured greatly since SRCNN  and further improvement requires sophisticated network design and the weighting of features through appropriate selection criteria. Both of the mentioned provisions are achieved in our model through Laplacian pyramid attention, and cascading with residual on the residual architecture.
4.2.3 Parameters, runtime, and depth analysis
The number of parameters is a crucial factor in determining the potential of the CNN networks. More parameters usually lead to better performance, however, computing more parameters requires deeper networks, which increases the computational load. Our aim here is to utilize previously computed features; hence, concatenating the earlier computed features maps strike a balance between performance, depth, and run time. Furthermore, our network achieves state-of-the-art performance with a mere 160 convolutional layers as compared to RCAN  i.e. 400+. In Figure 4, we provide a comparison of the parameters and the performance. Our model has fewer parameters as compared to EDSR  and the runtime is less as compared to RCAN  i.e. the time taken by RCAN for an image of size 8241168 on average is 1.14s opposed to our method 0.045s on MANGA109  for 4. This efficiency is due to the fact that our method mainly uses concatenations instead of expensive addition operations. In Figure 5, the runtime comparisons are provided against state-of-the-art methods. The PSNR and efficiency are higher for our model, which essentially demonstrates that compact models can push the boundaries with non-conventional architectures.
We present the comparison of our model with the state-of-the-art CNN models which include SRCNN , FSRCNN , VDSR , SCN , SPMSR , LapSRN , MSLapSRN , MemNet , EDSR , SRMDNF , D-DBPN , IRCNN , RDN , RCAN  and CARN . Similar to , we employ self-ensemble to boost the performance of our model and denote it with a ’+’ to differentiate it from the single model.
Similar to contemporary state-of-the-art models, we experiment on two types of image degradations; bicubic-downsample and blur-downsample . For evaluation of the models, the bicubic downsampling scales of 2, 3, 4, and 8 are adopted, while blur-downsampling is achieved through a Gaussian kernel having 1.6 for a scale of 3.
|Method||Scale||SET5 ||SET14 ||BSD100 ||URBAN100 ||MANGA109 |
4.3.1 Bicubic degradations
4 Visual Comparisons: To be fair in comparison, the images furnished for qualitative comparison in Figure 6 are from the same dataset images as RCAN . The first two images are from URBAN100 , and the last picture is from MANGA109  for upscaling of 4. As shown in Figure 6, all competing methods, in general, fail to recover edges and introduce blurring artifacts. In “img_076”, the competing CNN algorithms are unable to retrieve the rectangular shapes and blur out the edges and boundaries representing the outlines of the windows. Our method is faithful to the original image, providing results with proper rectangular structures and straight lines.
Similarly, in the second example, i.e. “img_044” in Figure 6, most of the methods distort the horizontal lines and blur out the background. Furthermore, the orientation of the lines on the cropped parts is in the opposite direction and forms a checkerboard pattern for [11, 9]. Moreover, a close inspection reveals that RCAN  and CARN  fused the background with the horizontal lines, removing the sharpness from the images shown while in our case, the lines are clearly visible and separated from the background, recovering sharp details.
The last image in Figure 6 is from MANGA109  for 4 scale. The textures in the cropped regions are blemished and mixed by together most of the state-of-the-art methods and are unable to recover the shape of the green colored strokes except for RCAN . However, RCAN  is also unequipped to super-resolve the lines correctly as it can be witnessed that the lines are blended in the right side of the cropped image. Furthermore, the super-resolved green lines are blurry in the case of RCAN . Our network can super-resolve most of the details and textures without producing visible artifacts from the shown low-resolution image. The green lines are sharp and closer in structure to the original.
|Original||Bicubic||SRCNN ||FSRCNN ||VDSR |
|URBAN100 (3)||IRCNN ||SRMDNF ||RDN ||RCAN ||Ours|
|Original||Bicubic||FSRCNN ||VDSR ||IRCNN |
|URBAN100 (3)||EDSR ||SRMDNF ||RCAN ||CARN ||Ours|
|SET5 ||SET14 ||BSD100 ||URBAN100 ||MANGA109 |
8 Visual Comparisons: To show the powerful reconstruction ability of our network, we present extreme examples of 8 super-resolution in Figure 7 from URBAN100  and MANGA109 . Because of the significant scaling factor in image “img_045”, the models [28, 9, 13] using bicubic upsampled input creates artificial checkerboard artifacts and structures in the images due to the incorrect initial input. While, on the other hand, the recent state-of-the-art method  which takes the low-resolution photographs as input, is unable to recover the high frequencies reliably due to the notable upscaling and also produces new structures instead of recovering the original lines. MSLapSRN  is able to super-resolve the lines correctly in the lower half of the image, and this may be due to the progressive reconstruction i.e. employing loss after every 2 resolution to achieve 8 output. In our case, the lines are super-resolved correctly without employing multiple losses. This shows the super-resolution capability of our CNN model.
|IRCNN  (28.73/0.6762)||RCAN  (28.44/0.6607)||Ours (32.46/0.8760)|
|Noisy||GT||BM3D-SR ||BM3D-SRNI ||Ours|
The second low-resolution image, in Figure 7 for 8 is from MANGA109 , titled, “TaiyouNiSmash”, contains minimal high-frequencies and hence is challenging to super-resolve to the desired outcome. Nevertheless, our method still can reproduce better results and avoids producing blurring and artificial structures as compared to competitive techniques. The algorithms of VDSR , MSLapSRN , etc. creates blurry outputs and unsharp images. Similarly, RCAN  can produce slightly sharp edges than its predecessor; however, it connected the gaps in different letters. Our model is more faithful to the original image and better captures the small gaps present in the letters.
Quantitative Comparisons: Table II shows the quantitative results for all the competing methods. These results are borrowed from their corresponding published papers. Our scheme outperforms all other approaches on all datasets for all scales which complements the visual sequences presented earlier in Figures 6 and 7. Our model quantitative results outperform even without employing the self-ensemble technique.
The improvement of our method on SET5  and SET14  is marginal due to a small number of images (the number with the dataset shows the images present i.e. SET5 has only five photographs, and SET14 has only 14 images) in these mentioned datasets; however, a clear trend emerges when the number of images increases. For example, on MANGA109 , the average PSNR increment across all scales for our model is 0.34dB and 3.98dB compared to second leading method i.e. RCAN  and the pioneering SRCNN , respectively.
4.3.2 Blur-Downscale (BD) degradations
More recently, blur-down (BD) degraded images  are super-resolved to showcase the potential of super-resolution architectures. We also utilize blur-downsampled photographs to compare against the state-of-the-art.
3 Visual Comparisons: We first present three examples; two from URBAN100  and one from MANGA109  in Fig. 8. The images from URBAN100  super-resolved by the competing methods contain blur effects near the upper end of the buildings as can be seen in the cropped versions. The only methods which perform comparatively better are RDN  and RCAN ; however, our approach is not only able to remove the blur but also restore the high-frequency details. This may be due to the Laplacian-attention used at the end of each DRLM, which captures the important discriminative features that are useful for high-frequency restoration.
Next, we evaluate our algorithm on an image from the classical SET14  shown in Figure 8. In the crop sections, our method produces relatively sharp edges and crisper text than state-of-the-art algorithms which mostly exhibit blurry and distorted text. IRCNN , SRMD , and RCAN  are specifically designed to handle blur-downscale super-resolution; however, our method produces best qualitative results having more than 1dB PSNR for this particular image.
Quantitative Comparisons: Next, Table III provides the comparison against nine competitive methods. Here, again RDN  and RCAN  shows good results compared to [28, 21, 9]; however, our single and self-ensemble models achieve a notable performance gain over all methods in general, and RDN  and RCAN  particular. The average PSNR gain over both the mentioned methods for 3 super-resolution of blur-down degraded images is 0.55dB and 0.33dB for all the datasets. Our architecture better generalizes the task at hand, and our Laplacian attention can select the relevant features more reliably in contrast to RCAN’s  channel attention.
|Evaluation||Bicubic||DRCN ||FSRCNN ||PSyCo ||ENet-E ||RCAN ||Ours||Baseline|
4.3.3 Noisy downscale (ND) degradations
2 Visual Comparisons: We present two images for super-resolving the noisy images. Figure 10 shows the comparison of our method with CNN methods on the Birds image from BSD100  for a low-level noise (). It can be observed that our method significantly recovered more texture and removed the noise close to the ground truth image. IRCNN  and RCAN  fail to remove the noise, rather they amplify it. The other noisy image, “Llama”, shown in Figure 10 is taken from Singh et al.  for a fair comparison against traditional algorithms. The difference in texture details on the fur and the background can be observed in our case and the conventional methods. Our method can super-resolve the fur more appropriately as compared to the other methods.
Quantitative Comparisons: To compare quantitatively, we follow the footsteps of Singh et al.  which uses the first 50 images from the BSD100 . We compare against super-resolving noisy image algorithms, which include (SRNI) , BM3D-SR  and NLM-SR  as well as the image restoration algorithm IRCNN . Moreover, BM3D-SR or NLM-SR indicates applying the traditional denoising approach first i.e. (BM3D or NLM), followed by image super-resolution (SR).
Currently, RCAN  is state-of-the-art in single image super-resolution; however, we show that it is unable to handle noisy images. In Figure 11, we present the quantitative results with the competing algorithms for four noise levels i.e. and . Our algorithm constantly outperforms CNN-based algorithms and specifically designed methods at all noise levels. Furthermore, the CNN methods [21, 7] performance is relative to the traditional algorithms when the noise levels are low i.e. and ; however, it degrades significantly as increases while, on the other hand, the performance of our algorithm is better at high-noise levels as well.
|LR input||DRCN ||Ours|
|FSRCNN ||VDSR |
|LR input||MSLapSRN ||Ours|
4.3.4 Real-World historic super-resolution
In this section, we illustrate the application of our algorithm on real-world historic  images suffering from JPEG compression artifacts. The information about the downsampling operators and ground-truth images are unavailable. The results of our reconstruction against state-of-the-art algorithms are shown in Figure 12. The output of our algorithm is clear and sharper as shown in both Figures.
4.4 Performance on Object Recognition
As discussed earlier, image restoration tasks assist in high-level computer vision tasks; therefore, we demonstrate and analyze the effectiveness of our method on object recognition current state-of-the-art super-resolution techniques. We use the same settings as 
, which evaluates the performance on the initial 1k images from ImageNet. The image of size 224224 is downscaled by 4 to achieve the image size of 5656. The downscaled versions are then upscaled to the original size images via the super-resolution algorithms and subsequently fed through ResNet50  for classifications. The accuracy of the classification network is used to determine the potential of the super-resolution algorithms.
We compare with six methods i.e. Bicubic, DRCN , FSRCNN , PSyCo , ENet-E  and RCAN . The top-1 and top-5 errors for object recognition are recorded in Table IV. Our method is more accurate as it provides the lowest error; hence, this illustrates the ability of our network to reconstruct appropriate frequencies more reliably.
|FSRCNN ||SelfExSR ||DRCN |
|Ground-truth||VDSR ||LapSRN ||Ours|
Our model has shown the ability to render sharp and clean images for all upsampling scales; however, it struggles to “hallucinate” finer details. For example, an image with 8 is shown in Figure 13, the top of the building is very challenging as due to the large downsampling operator i.e. 8. All the algorithms fail to recover the fine details at this level. The traditional methods, e.g. SelfExSR , which exploit the self-similarity and 3D scene geometry, also fail to recover fine details. Similarly, MS-LapSRN  progressively upsamples to produce the 8 results as opposed to ours where the 8 upsampling is achieved directly; however,  is unable to give the desired outcome. Furthermore, this limitation is common to all the super-resolution methods [6, 7, 11, 9].
In this exposition, we propose a modular convolution neural network for highly accurate image super-resolution. We also employ various components to boost the performance of super-resolution. We thoroughly analyze and present a comprehensive evaluation of the choice of our network design.
We employ cascading residual on the residual structure to design a large depth network using long skip connection, short skip connection, and local connections. The cascading residual on the residual architecture helps in the flow of low-frequency information to make network learn high and mid-level frequency information. We use densely connected residual blocks, which re-use the previously computed features. This type of setting has multiple advantages such as implicit “deep supervision” and learning from high-level complex features. We also introduce Laplacian attention, which models the essential features on multiple scales and learns the inter and intra-level dependencies between the feature maps.
Furthermore, we perform an extensive evaluation of super-resolution datasets, low-resolution noisy images and real-world images (unknown blur downsampling). We also have shown the results on Bicubic and blur-down kernels to demonstrate the effectiveness of our proposed methods. Further, we present the performance of object recognition on the super-resolved images by different methods. We have illustrated the potential of our network for image super-resolution; however, our network is general and can be applied to other low-level vision tasks such as image restoration, synthesis, and transformation problems.
S. P. Mudunuri and S. Biswas, “Low resolution face recognition across variations in pose and illumination,”TPAMI, 2016.
-  H. Greenspan, “Super-resolution in medical imaging,” CJ, 2008.
-  A. Swaminathan, M. Wu, and K. R. Liu, “Digital image forensics via intrinsic fingerprints,” TIFS, 2008.
-  K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in CVPR, 2016.
-  B. Lim, S. Son, H. Kim, S. Nah, and K. M. Lee, “Enhanced deep residual networks for single image super-resolution,” in CVPRW, 2017.
-  W.-S. Lai, J.-B. Huang, N. Ahuja, and M.-H. Yang, “Fast and accurate image super-resolution with deep laplacian pyramid networks,” TPAMI, 2018.
-  Y. Zhang, K. Li, K. Li, L. Wang, B. Zhong, and Y. Fu, “Image super-resolution using very deep residual channel attention networks,” ECCV, 2018.
-  N. Ahn, B. Kang, and K.-A. Sohn, “Fast, accurate, and, lightweight super-resolution with cascading residual network,” ECCV, 2018.
-  J. Kim, J. Kwon Lee, and K. Mu Lee, “Accurate image super-resolution using very deep convolutional networks,” in CVPR, 2016.
-  W.-S. Lai, J.-B. Huang, N. Ahuja, and M.-H. Yang, “Deep laplacian pyramid networks for fast and accurate superresolution,” in CVPR, 2017.
-  C. Dong, C. C. Loy, K. He, and X. Tang, “Image super-resolution using deep convolutional networks,” TPAMI, 2016.
-  Y. Tai, J. Yang, and X. Liu, “Image super-resolution via deep recursive residual network,” in CVPR, 2017.
-  J. Kim, J. Kwon Lee, and K. Mu Lee, “Deeply-recursive convolutional network for image super-resolution,” in CVPR, 2016.
-  T. Tong, G. Li, X. Liu, and Q. Gao, “Image super-resolution using dense skip connections,” in ICCV, 2017.
-  Y. Zhang, Y. Tian, Y. Kong, B. Zhong, and Y. Fu, “Residual dense network for image super-resolution,” in CVPR, 2018.
-  C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. P. Aitken, A. Tejani, J. Totz, Z. Wang et al., “Photo-realistic single image super-resolution using a generative adversarial network.”
-  J.-H. Kim, J.-H. Choi, M. Cheon, and J.-S. Lee, “Ram: Residual attention module for single image super-resolution,” arXiv, 2018.
-  M. Haris, G. Shakhnarovich, and N. Ukita, “Deep backprojection networks for super-resolution,” in CVPR, 2018.
-  K. He, X. Zhang, S. Ren, and J. Sun, “Delving deep into rectifiers: Surpassing human-level performance on imagenet classification,” in ICCV, 2015.
-  C. Dong, C. C. Loy, and X. Tang, “Accelerating the super-resolution convolutional neural network,” in ECCV, 2016.
-  K. Zhang, W. Zuo, S. Gu, and L. Zhang, “Learning deep cnn denoiser prior for image restoration,” in CVPR, 2017.
-  K. Zhang, W. Zuo, and L. Zhang, “Learning a single convolutional super-resolution network for multiple degradations,” in CVPR, 2018.
-  Y. Tai, J. Yang, X. Liu, and C. Xu, “Memnet: A persistent memory network for image restoration,” in CVPR, 2017.
-  G. Huang, Z. Liu, L. van der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” in CVPR, 2017.
-  H. Ren, M. El-Khamy, and J. Lee, “Image super resolution based on fusing multiple convolution neural networks,” in CVPRW, 2017.
-  Y. Hu, X. Gao, J. Li, Y. Huang, and H. Wang, “Single image super-resolution via cascaded multi-scale cross network,” arXiv, 2018.
-  Z. Hui, X. Wang, and X. Gao, “Fast and accurate single image super-resolution via information distillation network,” in CVPR, 2018.
-  C. Dong, C. Loy, K. He, and X. Tang, “Learning a deep convolutional network for image super-resolution,” in ECCV, 2014.
-  A. L. Maas, A. Y. Hannun, and A. Y. Ng, “Rectifier nonlinearities improve neural network acoustic models,” in ICML, 2013.
-  A. Radford, L. Metz, and S. Chintala, “Unsupervised representation learning with deep convolutional generative adversarial networks,” arXiv, 2015.
-  I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative adversarial nets,” in NIPS, 2014.
-  K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in CVPR, 2016.
-  M. S. Sajjadi, B. Schölkopf, and M. Hirsch, “Enhancenet: Single image super-resolution through automated texture synthesis,” in ICCV, 2017.
-  S.-J. Park, H. Son, S. Cho, K.-S. Hong, and S. Lee, “Srfeat: Single image super-resolution with feature discrimination,” in ECCV, 2018.
-  X. Wang, K. Yu, S. Wu, J. Gu, Y. Liu, C. Dong, C. C. Loy, Y. Qiao, and X. Tang, “Esrgan: Enhanced super-resolution generative adversarial networks,” ECCV, 2018.
-  A. Jolicoeur-Martineau, “The relativistic discriminator: a key element missing from standard gan,” arXiv, 2018.
-  V. Mnih, N. Heess, A. Graves et al., “Recurrent models of visual attention,” in NIPS, 2014.
-  V. Dumoulin, J. Shlens, and M. Kudlur, “A learned representation for artistic style,” ICLR, 2017.
-  W. Shi, J. Caballero, F. Huszár, J. Totz, A. P. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-time single image and video super-resolution using an efficient sub-pixel convolutional neural network,” in CVPR, 2016.
-  J. Jiao, W.-C. Tu, S. He, and R. W. Lau, “Formresnet: formatted residual learning for image restoration,” in CVPRW, 2017.
-  F. Wang, M. Jiang, C. Qian, S. Yang, C. Li, H. Zhang, X. Wang, and X. Tang, “Residual attention network for image classification,” in CVPR, 2017.
-  O. Vinyals, A. Toshev, S. Bengio, and D. Erhan, “Show and tell: A neural image caption generator,” in CVPR, 2015.
-  A. Fujimoto, T. Ogawa, K. Yamamoto, Y. Matsui, T. Yamasaki, and K. Aizawa, “Manga109 dataset and creation of metadata,” in MANPU, 2016.
-  J. Hu, L. Shen, and G. Sun, “Squeeze-and-excitation networks,” in CVPR, 2018.
-  J.-B. Huang, A. Singh, and N. Ahuja, “Single image super-resolution from transformed self-exemplars,” in CVPR, 2015.
-  M. Bevilacqua, A. Roumy, C. Guillemot, and M. L. Alberi-Morel, “Low-complexity single-image super-resolution based on nonnegative neighbor embedding,” 2012.
-  R. Zeyde, M. Elad, and M. Protter, “On single image scale-up using sparse-representations,” in ICCS, 2010.
-  D. Martin, C. Fowlkes, D. Tal, and J. Malik, “A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics,” in ICCV, 2001.
-  R. Timofte, E. Agustsson, L. Van Gool, M.-H. Yang, L. Zhang, B. Lim, S. Son, H. Kim, S. Nah, K. M. Lee et al., “Ntire 2017 challenge on single image super-resolution: Methods and results,” in CVPRW, 2017.
-  D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv, 2014.
-  A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in pytorch,” 2017.
-  Z. Wang, D. Liu, J. Yang, W. Han, and T. Huang, “Deep networks for image super-resolution with sparse prior,” in ICCV, 2015.
-  T. Peleg and M. Elad, “A statistical prediction model based on sparse representations for single image super-resolution,” TIP, 2014.
-  K. Dabov, A. F., V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” 2007.
-  A. Singh, F. Porikli, and N. Ahuja, “Super-resolving noisy images,” in CVPR, 2014.
-  A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” in CVPR, 2005.
-  E. Pérez-Pellitero, J. Salvador, J. Ruiz-Hidalgo, and B. Rosenhahn, “Psyco: Manifold span reduction for super resolution,” in CVPR, 2016.
-  J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li, and L. Fei-Fei, “Imagenet: A large-scale hierarchical image database,” 2009.
-  J.-B. Huang, A. Singh, and N. Ahuja, “Single image super-resolution from transformed self-exemplars,” in CVPR, 2015.