Significant progress of neural networks for computer vision has been given to the field of Single Image Super-Resolution (SISR). SISR aims to reconstruct a super-resolution image from a single low-resolution image . This task, refered as super-resolution, finds direct applications in numerous areas such as medical image processing greenspan2002mri ; peled2001superresolution , HDTV goto2014supergunturk2003eigenface ; wheeler2007multi , satellite image processing thornton2006sub ; tatem2001super ; tatem2002super and surveillance zhang2010super ; lin2005investigation . Furthermore, the super-resolution task can also be expressed as a one-to-many mapping from low-resolution to high-resolution space for each pixel. Super-resolution is an inference problem and the main solution to this problem relies on the statistical model in recent researches wang2019deep .
Recently, deep learning based SISR has attracted wide attention. Hedong2015image introduced the first deep learning method for single image super-resolution called Super-Resolution Convolutional Neural Network (SRCNN). Then, Fast Super-Resolution Convolutional Neural Network (FSRCNN) dong2016accelerating built a lightweight framework to solve real-time problems of super-resolution. Super-resolution Generative Adversarial Networks (SRGAN) ledig2017photo was the first Generative Adversarial Networks (GAN) goodfellow2014generative for super-resolution task and considered the human subjective evaluation of reconstructed images. Enhanced Deep Residual Networks for Single Image Super-Resolution (EDSR) lim2017enhanced was the winner of the NTIRE2017 Super-Resolution Challenge Competition and achieved an outstanding reconstruction performance. Deep Back-Projection Networks (DBPN) haris2018deep exploited iterative up-sampling and down-sampling and providing an error feedback mechanism.
One of the main disadvantages of previous works was that it is difficult to reconstruct clear boundaries and high gradient components. The other was that the architecture of the previous network lacked of skip connection between the convolution layers at the same depth, which caused the information loss. To solve the problem, an improved U-net with a mixed gradient loss is proposed for SISR. The contribution of the new network can be summarized as follows:
The improved U-net network architecture is proposed for super-resolution on a single image. The U-net, which has been approved effective for image segmentation, is modified for SISR task by removing all batch normalization layers and one convolution layer in each block. The operation reduces the computation cost and meanwhile keeps the reconstruction performance. The input image is up-scaled for the larger size and build a new convolution block on the large scale, which has a skip-connection with the output block on the same scale. The direct up-scaled images avoid the errors caused by redundant calculations.
A mixed gradient error (MixGE) is proposed and applied to SISR loss function. As a combination of mean square error (MSE) ephraim1984speech and mean gradient error (MGE), not only pixel error but also gradient error is considered and the improved loss is called MixGE. In the paper, we use the classic gradient calculation method which was proposed by Sobelkanopoulos1988design . The method for MGE computation are presented and analyzed.
The modified U-net for common scenes task super-resolution yields the outstanding performance over existing methods on SET14 and BSD300 dataset. Moreover, the proposed network successfully outperforms other state-of-art methods on texture tasks such as ICDAR2003 dataset.
2 Related Work
The goal of super-resolution methods is to recover a high-resolution image from a low-resolution image irani2009super . Recently most popular SISR methods were implemented by deep learning network instead of traditional mathematical models. This section will analyze and summarize most effective existing super-resolution reconstruction methods which realized by deep learning methods.
2.1 Super-resoution network
For super resolution, the methods can be divided into video super-reslution reconstruction, such as VESPCN caballero2017real , VSRCNN kappeler2016video , and single image super-resolution, which includes SRCNN dong2015image , FSRCNN dong2016accelerating , VDSR kim2016accurate , DRCN kim2016deeply , SRGAN ledig2017photo , ESPCN shi2016real , EDSR lim2017enhanced and DBPN haris2018deep .
To better solve the distortion problem of high-resolution image reconstruction, He dong2015image presented a network architecture named SRCNN which was the earliest proposal to solve super-resolution problem through deep learning network. He demonstrated that a convolution network can be used to learn an efficacious mapping from low-resolution to high-resolution in an end-to-end architecture.
Although the SRCNN introduced a new way to solve the super-resolution reconstruction problem by deep learning, this method had 2 obvious limitations. First, the observation field was too narrow that can not get enough corresponding information. Second, the training of SRCNN was hard to converge and easy to be overfitted.
To solve these two limitations, FSRCNN dong2016accelerating was proposed, which was different from SRCNN in 3 aspects. First, FSRCNN adopted the original low-resolution image as input instead of the bicubic de1962bicubic interpolate image in SRCNN. Second, The de-convolution layer was added at the end of the network for upsampling. The third and the most efficient part was to adapt smaller filter kernels and a deeper network into super-resolution task.
The VDSR kim2016accurate came up with a much deeper network. To get a large observation field, VDSR chose a convolution kernel of 33 in the deep network. Otherwise, very deep networks converged too slowly because of the big number of parameters. In the VDSR
method, residual learning and gradient clipping were chosen to be the solution to the training problem.
Taking an interpolated image as the input, DRCN kim2016deeply
was composed of three modules, namely embedding network for feature extraction, inference network for nonlinear feature mapping, and reconstruction network for SR image generation. The Inference network was a recursive network, that is, data looped through the layer multiple times. Expanding this loop was equivalent to multiple concatenated convolution layers using the same set of parameters.
Generative adversarial networks (GAN) goodfellow2014generative
, which was proposed by Goodfellow in 2014, was set up for estimating generative models via adversarial process. FirstGAN proposed for super-resolution task was SRGAN ledig2017photo
. The experimental results in this work showed that the generator network trained on MSE loss function could output SR images with high Peak signal-to-noise ratio (PSNR) but over-smoothed. The output images ofSRGAN had a better visual effect than other methods without adversarial process. The work proposed a GAN that apply a deep residual network (ResNet) he2016deep with skip-connection. For improving the visual effect of the super-resolution reconstructed results, they put forward the perceptual loss instead of the MSE loss function.
To solve the high computational complexity of deep network, ESPCN shi2016real was proposed for super-resolution task with a much higher processing speed than previous methods. The core concept of ESPCN was the sub-pixel convolutional layer. The input to the network was the original low-resolution image. After passing through two convolutional layers, the result feature image was the same size as the input image, and the feature channel was where was the magnification scale. Feature images of size were re-arranged into high-resolution images of size . The operation of convolution layer re-arrangement greatly improved the efficiency of de-convolution and the ESPCN had a better performance on super-resolution tasks.
EDSR lim2017enhanced was the winner of the NTIRE2017 Super-Resolution Challenge Competition. As stated in the paper, the most significant performance improvement of EDSR was to remove the batch normalization layers of SRResNet, which can expand the size of the model to improve the quality of the results.
Haris haris2018deep proposed Deep Back-Projection Networks (DBPN), applying iterative up-sampling and down-sampling and exploiting an error feedback mechanism for projection errors in every block. This work constructed mutually-connected up-sampling and down-sampling blocks, which represented different parts of low-resolution and high-resolution components.
2.2 Problem analysis
Previous works on SISR reconstruction task achieved a good performance, but there were still many shortcomings and many parts that lacked reasonable explanations. First, previous studies of SISR had not dealt with the problem of blurred edge, shown as reconstructed results by methods of SRCNN and VDSR in Figure 1, because these researches were limited to MSE loss function. Though the performance of SRCNN on MSE loss function was outstanding, subjective observation of the reconstructed images was blurred. Therefore, gradient components should be considered into the SISR task.
Second, most convolutional layers of SISR deep networks were directly connected which led to a part of data loss in low-dimensional feature layers. High-resolution images which only reconstructed by high-level semantic information lost most basic fine-grained texture details. It is necessary to build a skip-connection between same depth layers to combine high-level semantic information with low-level fine-grained texture details.
Third, according to the impressive analysis of VDSR kim2016accurate which concluded that better performance could be achieved with deeper network, the number of parameters of the most SISR network were very large due to very deep networks were used to obtain high performance. The networks suffered from large computation cost which makes it difficult to run in real-time.
The task of the single image super-resolution was to reconstruct a super-resolution image from a low-resolution image . To solve this single image super-resolution problem, network architecture is constructed where input image
is represented as real-valued tensors of sizeand output image represented as a tensor of size .
This work proposes an improved network called modified U-net and a mixed gradient loss function which combines with Mean Square Error and mean gradient error.
3.1 Modified U-net
U-net ronneberger2015u was first proposed by Ronneberger and widely used in the field of semantic segmentation. Ronneberger showed that the U-net
can be trained as a end-to-end system from extremely few images. Meanwhile, this network architecture surpassed the previous state-of-the-art method on the ISBI challenge for semantic segmentation of neuronal structures.
The U-net architecture is illustrated in Figure 2(a). The left side is the contracting path which is used for extracting features and the right side is called expansive path for decoding. The contracting path contains the continuous part of two 32 convolution that halves the number of feature channels, and two 33 convolution kernels, each followed by a ReLU layer.
The most important contribution of U-net is to put forward the skip-connection. The U-net network architecture is proposed after the Fully Convolutional Network (FCN)long2015fully and modified in a creative method that it yields the state-of-the-art segmentation in medical image processing at that time. Compared with FCN, the first main difference is U-net is symmetric and the second one is the skip connections between the down-sampling path and the up-sampling path employ a concatenation operation instead of a direct sum. Skip connections in the network aim to provide the original local information to the global information when up-sampling. Because of the symmetry of U-net network architecture, the U-net has numerous feature maps in up-sampling blocks that allows the efficacious transmission of information.
As illustrated in Figure 2(b), the modified U-net designed in this work for SISR has three differences comparing with the original U-net. First, it removes all batch normalization layers and one of the convolution layers in each block. The reason for this is that super-resolution reconstruction is a pixel-level task because the solution to interpolation problem is mainly consider pixels in a certain area. Directly magnified images avoid the errors caused by redundant calculations, which can get closer to real results.
Second, the input image is up-scaled for the larger size and build a new convolution block on the larger scale, which has a skip-connection with the output block on the same scale. The direct up-scaled images avoid the errors caused by redundant calculations, which can get much closer to ground truth. Each addition of upscale layer means expand the size into twice. In other words, the network should have 3 upscale layers if upscale size is 8 and similarly 2 upscale layers for upscale size is 4.
Third, the depth of the original U-net is fixed to 4, which means there are 4 downscale blocks and corresponding 4 upscale blocks. Previous work ronneberger2015u has shown that the deeper network leads to the better performance and higher computation cost in most situations. In our work, the depth of the modified U-net for SISR is discussed in section 4, showing a trade off between reconstruction accuracy and computation cost.
3.2 Mixed Gradient Error
The aim of SISR is to learn a mapping function for generating an high-resolution image from a low-resolution image that is close to the ground truth image . MSE allen1971mean is widely used as most loss function, which measures the average of the squares of each pixel errors in super-resolution reconstruction. MSE can be shows as follows:
where is the number of horizontal pixels and is the number of vertical pixels.
To solve the gradient error measurement problem, we introduce classic gradients to the SISR loss function. In our work, Sobel operatorkanopoulos1988design is used for gradient calculation, that is,
where is the convolution operation.
The gradient map in direction of the ground truth image shows below:
Then we combine the gradient value of and direction as follows:
Meanwhile, the gradient map can be calculated in the same way. The aim of measure the gradient error is to learn a sharp edge which is close to the groud truth edge. The Mean Gradient Error (MGE) shows as follows:
After achieving the MGE, it should be emphasized in the mixed gradient error. As the main component of mixed gradient error, Mean Square Error forms a Mixed Gradient Error (MixGE) by adding Mean Gradient Error with a weight of .
ICDAR2003 karatzas2013icdar is a dataset of the ICDAR Robust Reading Competition for text detection and recognition tasks. For the single image super-resolution task, there is not a commonly used dataset. The ICDAR2003 dataset consists of 258 training images and 249 testing images, which contains texts in most of the complex circumstances in common life. Because of the resolution of images varies from 422102 to 640480, we resize them into 224224 with bicubic interpolation. This network is also compared with other existing methods on standard benchmark dataset: SET14 bevilacqua2012low , BSD300 martin2001database .
4.2 Evaluation method
Two commonly used performance metric are employed for evaluation and comparsion: PSNR huynh2008scope and Structural Similarity Index (SSIM) hore2010image . The super-resolution results are evaluated with the criteria of PSNR huynh2008scope and SSIM hore2010image on three channels in RGB colour space. The criterion of PSNR is based on the error between each corresponding pixels. Because this criterion only consider the numerical error, most high PSNR results do not have good visual performance. Therefore, the criterion of SSIM hore2010image observes the distortion of the image by comparing the changes in the image structure information, thereby obtaining an objective quality evaluation. The criteria of PSNR and SSIM are all based on luminance. The higher the value of these criteria, the better the performance of image reconstruction.
Two criteria are described as follows. Let donate the ground truth and donate the reconstructed high-resolution images respectively.
The criterion of SSIM between patches and at the same location on ground truth images and reconstructed high-resolution image is defined as
where and are the mean of patch and respectively. Meanwhile, and are the deviation of patch and . and are small constants. Then, The criterion of is the average of patch-based SSIM over the image.
4.3 Implement Details
These existed SISR methods are evaluated on 3 common used dataset: SET14, BSD300, ICDAR2003. SET14 and BSD300 consist of natural scenes and ICDAR2003 contain various types of texts in a robust common scene. The ground truth high-resolution images are downscaled by bicubic interpolation to generate low-resolution and high-resolution image pairs for training and testing on Table.1. We convert all images into RGB colour space and processing the data into three channels.
4.4.1 Network analysis
Before comparison with other state-of-the-art methods, some parameters of the modified U-net and MixGE loss function need to be determined. The first part is the depth of modified U-net, which influences the performance of super-resolution results and computational complexity. The second one is the MGE weight for MixGE loss function. 50 randomly selected images from training set are taken as validation data for parameter determination..
Depth analysis. Figure 3 shows the PSNR with increasing depth of U-net, in which the numbers of the networks parameter are shown above each bar. It can be seen from the figure that the performance has a significant improvement from the depth of 2 to 5, while has a slight improvement from the depth of 5 to 8 with large increase in model complexity. Therefore, the depth of 5 is a proper choice that keep a trade-off between reconstruction accuracy and computation cost.
Loss analysis. For the comparison of MixGE and MSE loss, Figure 4 shows that the results have a great improvement on each dataset if considering the Mean Gradient Error. The method with MixGE loss performs better than that with MSE loss.
In this experiment, the independent variable, , was set as , , , and . It can be clearly seen from the Figure 4 that the performance is getting better with the increasing value of from to and achieves the peak of performance on . This shows that it will greatly improve the performance when choosing the MSE as main component and the MGE as an important auxiliary component. The best performance reaches the PSNR of 29.4dB when the weight equals .
It can be seen that MSE loss function is still an irreplaceable loss component in MixGE. MGE becomes an auxiliary component in MixGE to support deep networks to build sharp-edged, gradient-accurate reconstructed images.
4.4.2 Comparison with the state-of-the-arts
To assess the performance of our method, we compare the modified U-net architecture with existing super-resolution deep learning network, including SRCNN dong2015image , FSRCNN dong2016accelerating , VDSR kim2016accurate , DRCN kim2016deeply , SRGAN ledig2017photo , ESPCN shi2016real , EDSR lim2017enhanced and DBPN haris2018deep . In this experiment, the performance of bicubic de1962bicubic interpolation is chosen to be the baseline method for evaluating performance of deep learning method.
Table.2 shows the super-resolution performance of different methods on SET14, BSD300, ICDAR2003 dataset, where UnetSR denotes the modified U-net with MSE and UnetSR+ denotes the modified U-net with MixGE. In the Table.2, the best performance is marked in red and the second best performance is marked in blue in each row. It can seen clearly from the table that UnetSR+ has the highest PSNR, which means the best performance, at upscale size 2 and 8 on ICDAR2003 dataset. Meanwhile, UnetSR+ has the second best performance when upscale size is 4.
We average values of PSNR and SSIM of different datasets and upscale sizes for each method. The results are shown in Table 3, together with parameter numbers of each network. It is apparent from the Table.3 that the proposed UnetSR+ achieves the best reconstruction accuracy on average. Commonly, the ISIR performance improves with more network size, while the UnetSR+ only has parameter numbers of DBPN, but the experimental performance exceeds DBPN on PSNR and on SSIM. In addition, it can be seen from the table that the proposed UnetSR+ shows a distinguished trade-off between reconstruction accuracy and model complexity. For example, comparing with SRGAN, DBPN increased model size by more than 2 times with PSNR increased and SSIM increased , while the UnetSR+ improves on PSNR and on SSIM with parameters increased only .
|Method||Number of parameters||PSNR||SSIM|
For subjective visual evaluation, we compare reconstruction examples with different deep learning methods of SISR for common scenes task on SET14 and BSD300 dataset in Figures 5 and 6 and examples for texture task on ICDAR2003 dataset in Figures 7 and 8. In Figure 5, super-resolution results on BSD300 dataset for common scenes tasks with the scale of 2 are shown with up-scaled details on the right. As illustrated in the figure, the iron pin can be figured out in four methods, which is ESPCN, DBPN, UnetSR and UnetSR+. However, the pip strap, a much smaller detail, only reconstructed perfectly by the method of UnetSR+. It is also clear from the Figure 6 that though methods of ESPCN, DBPN, UnetSR and UnetSR+ reconstruct four distinguishable pendants, only the method of UnetSR+ provides clear and proper edges for pedants.
For texture task, super-resolution results on ICDAR2003 dataset on the scale of 4 are shown in Figure 7. The left original image has clear convex white characters on a uniform dark brown background. Under this classic super-resolution scene, the reconstructed images of Bicubic, SRCNN, ESPCN, DRCN and VDSR produced a serious overlap phenomenon. Contrary to these results, each image reconstructed by methods of DBPN, UnetSR and UnetSR+ produced a visible border. The method of UnetSR+ not only restores the sharp border, but also even restores the convexity of the original character. In Figure 8, it shows super-resolution results on ICDAR2003 dataset with the scale of 8 under a more complex scene. The methods of ESPCN, DBPN and UnetSR+ are still able to provide distinguishable reconstruction results, in which the UnetSR+ restores almost all the details and boundaries with sharper edges.
U-net for image segmentation is modified in the paper and applied to SISR. First, we remove the superfluous part which includes batch normalization layers and one of the convolution layers. Second, the input image is up-scaled for the larger size and the direct up-scaled images avoid the errors caused by redundant calculations. The modified U-net network achieve a high value of PNSR with the trade-off the depth of 5. Furthermore, a Mixed Gradient Loss, which is combined with Mean Square Error and Mean Gradient Error, is proposed for sharp edge reconstruction. Experiments show that the proposed network successfully outperforms other state-of-art methods on SET14, BSD300 and ICDAR2003 datasets. In view of the outstanding performance of the work on texture reconstruction task, it is readily applicable to low-resolution texture detection and recognition in future work.
This work was supported by the National Natural Science Foundation of China (61573168).
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