Single image super-resolution (SISR) has posed a long-standing challenge in low-level vision with numerous important applications. It is an ill-posed problem that aims to restore a High-Resolution (HR) image by adding missing high-frequency information from a Low-Resolution (LR) image. Since the pioneer method by SRCNN 
, deep learning approaches[11, 12, 18, 46, 16, 36, 33] have exhibited impressive performance. However, most existing methods focus on a fixed degradation, , bicubic down-sampling or single Gaussian blurring. Those settings really limit their generalization ability. In addition to down-sampling, unknown blurring and noise may also be introduced during the acquisition of LR images. When the data distributions at test time mismatch the training distributions (referred to as distribution shift [26, 14]), those learning-based models will suffer severe performance drop .
In recent years, several non-blind and blind approaches for multiple degradations are proposed. The non-blind methods [27, 43, 44, 37] usually take the ground truth (GT) degradation maps as an additional input to establish the LR-HR mapping. Although the non-blind models have achieved satisfactory performance with the guidance of predefined information, the problem with unknown realistic degradation largely limits their usage in real-world applications. On the other hand, the blind methods [22, 29, 7, 3]
only considered the blur and down-sampling in the degradation mode. Then, the cascaded schemes with blind denoising, blur estimation and SR methods are organized to restore multi-degraded LR image[43, 19, 21]. However, each stage has a negative impact on each other, (, the denoiser will make the LR image more blurred and lead to kernel mismatch, increasing the difficulty of deblurring, seen in Fig. 4). Recently, there are some new attempts for blind SR. Several CycleGAN  based methods [4, 40, 21, 20] learn from unpaired LR-HR images, but they are more difficult to train. ZSSR  explores the zero-shot solution for the first time, where the CNN learns the mapping from the LR image and its downscaled versions (self-supervision). But it requires thousands of self-training iterations for each LR image. Recently, two optimization based meta-learning strategies, MZSR  and MLSR , have been proposed to accelerate the self-training steps from 1000 to 10. But they show worse results with large scale factor because the self-downsampled image cannot provide enough information.
Given the facts above, our work aims to the first attempts towards the following questions at the same time: (1) Can we propose a blind framework to effectively handle multiple degradations, especially when the accurate degradation estimation is very difficult? (2) Is it possible to overcome the distribution shift with an adaptive model, which can adapt its parameters to the unknown degraded LR images?
In this paper, we propose a conditional meta-network for blind SR with multiple degradations (CMDSR) to largely overcome the aforementioned two problems. For the first challenge, there is a prior knowledge which inspires us to handle it at task-level. As shown in Fig. 2, the LR images with different degradations obey different distributions. Although the accurate estimation of degradation is hard, images from the same task may contain the similar implicit feature to describe their common degradation patterns. Therefore, we group these LR images into different tasks and extract the degradation prior at task-level to describe the degradation patterns. For the second challenge, we use the distribution information extracted from a group of LR samples to make SR network adaptively adjust its parameters according to the distribution changes, such that our framework can handle distribution shifts.
Specifically, our CMDSR consists of two parts: the BaseNet and ConditionNet. As shown in Fig. 3, the shallow ConditionNet learn the feature representations of different tasks. Then, BaseNet multiplies its convolution weights with modulated conditional features in channel-wise. Finally, the adapted BaseNet restores the LR image. Inspired by recent contrastive learning [8, 9], we propose a task contrastive loss to decrease the distances of the conditional features from the same task and increase those from different tasks. Algorithm 1
presents the training stage, where BaseNet and ConditionNet are alternately optimized with different steps and loss functions. Algorithm2 presents the test stage, where the extracted degradation prior from ConditionNet adapts BaseNet to handle distribution shift.
Since the shallow ConditionNet only uses the small size of support patches (, ), the time and computation cost of conditional feature extraction will be very little compared with BaseNet reconstruction. Without designing new complicated SR network, the proposed framework simply use 10 res-blocks as BaseNet (called SRResNet-10) and achieves superior performance with blind methods. For complicated degradations, CMDSR even outperforms the non-blind models. It should be noted that our framework has no strict restrictions on the BaseNet structure. The ablation experiments in Table 5 proves CMDSR can be extended to other SISR models. To the best of our knowledge, the proposed CMDSR is the first meta-network framework for blind SISR with multiple degradations.
In summary, our overall contribution is three-fold: (1) We present a first blind meta-network framework to adaptively handle SISR with multiple degradations at task-level. (2) A task contrastive loss is proposed for task-level feature extraction. (3) Our method is blind, fast and flexible, hence, can be applied as a general framework.
2 Related Work
Blind Single-Image Super-Resolution. Compared with typical SISR models [5, 11, 18, 46] tailored to specific single downsampler, blind SISR is a more challenging task, which assumes that the blur kernels are unavailable at test time. Previous methods usually combine the well-designed kernel-estimation and typical SISR methods. Michaeli et al.  mined the internal patch recurrence to estimate the blur kernel. Bell et al.  proposed KernelGAN to learn the blur kernel distribution. In order to relieve the mismatch between the estimated kernel and the real kernel, IKC 
iteratively trained the estimation and correction networks. Although the accuracy of estimated kernel is largely improved, it remains very challenging for severe degradation. By using ideas from zero-shot and self-supervised learning, ZSSR efficiently exploited the internal recurrence of information inside an image. But this image-specific model requires self-training for each LR image, which is time-comsuming and cannot be applied to deep structure.
Multiple Degradations. Relatively less attention has been paid to SISR with multiple degradations despite it is important for real applications. Based on the perspective from maximum a posteriori (MAP) framework, existing non-blind methods, , SRMD  and UDVD , concatenated LR image, predefined blur kernel and noise maps as the input. Thus, SR result closely depends on both LR image and degradation pattern. The blind schemes [43, 21] are usually the sequential combinations of denoising , blur estimation  and SR models . CBSR  adapted a cascaded architecture, which can be jointly end-to-end learned from training data. All those methods will degrade for distribution shifts. Recently, the unpaired SISR methods [4, 21] conducted the domain transfer between the clean and real degraded domains. But it remains very challenging to train a stable model for various shifts.
Meta-Learning. Meta-learning, commonly known as learn how to learn, refers to the process of improving a learning algorithm over multiple learning episodes. As [17, 39] point, diverse meta-learning methods can be categorized into three groups: (1) Metric based methods [35, 30, 32] perform non-parametric learning in the metric space, which are far largely restricted to the popular. (2) Optimization based methods [2, 6, 17, 45] use gradient descent to solve the optimization problem of meata-learner. A most famous example is MAML , which learns the transferable initial parameters, such that few gradient updates lead to performance improvement. Recently,  proposed Adaptive Risk Minimization to handle group distribution shift for image classification. (3) Network based methods [28, 23, 24] use network to learn across task knowledges and rapidly updates its parameters to new task.
There are few explorations of meta-learning for SISR. Recently, two gradient based meta-learning models [31, 25] have been proposed. MZSR  and MLSR  both employed the typical MAML framework  to accelerate the self-supervised training. Nevertheless, for large scale factors, the size of self-downsampled LR son image becomes too small to provide enough information. Our proposed framework directly extract distribution prior at task-level and adapt the parameters of SR network, which avoids their shortcomings.
3 Proposed Method
3.1 CMDSR Setting
Our work focuses on blind SISR with multiple degradations, including blur, noise and down-sampling, which will simultaneously happen in a real-world case . The degradation process is formulated as:
where , , k, , and n denote LR, HR image, blur kernel, convolution, decimation with scaling factor of . and Gaussian noise. In this paper, we use the configuration in Eq. (1). to synthesize LR images for training.
The key goal of our work is to develop a framework that can adapt and generalize in the face of degradation shift using only a small number of examples. To accomplish this, we need to find the representation which can describe degradation prior of the LR image and guide the model to adapt to this degradation pattern. As explained in Section 1, there is a fact that LR images from the same task are degraded with the same pattern, which inspires us to view this problem at task-level, not the single image. Therefore, we present a new thought to mine the implicit task-level semantics with different tasks. This extracted feature can be further used as a context prior to adapt the parameters of SR model.
In our framework, we provide two settings to access training data: (1) The training data should be grouped into different tasks. We consider the multi-degradation distribution over meta-training tasks . For task , it consists of LR-HR pairs, where LR images are synthesized from HR images with th degradation configuration. (2) ConditionNet extracts task-level feature from n LR patches (named support set) belonging to the same task, and BaseNet restores the single LR input . With those settings, our framework can treat the training data at task-level.
3.2 Networks of CMDSR
Our framework consists of ConditionNet and BaseNet, which are shown in Fig. 3. It should be noted that our framework has no strict restrictions on the BaseNet structure. In this paper, the backbone of BaseNet is simply designed as SRResNet-10, which consists of 10 res-blocks.
First, ConditionNet, denoted , extracts the conditional feature , which describes the degradation pattern of the input support set . It is formulated as:
where is the parameters of ConditionNet and
denotes the size of support size at each step. In order to extract task-level feature, we design a shallow ConditionNet with 2 average pooling layers and 4 convolution layers followed with ReLU and keep the input sample size unchanged during training and test time. The internal channels of convolution layers are, 64, 64, 128, 128.
Then, BaseNet, denoted as , adapts its original parameters to with the conditional feature . Specifically, we adapt the parameters of 20 conv-layers of internal 10 res-blocks. We use 20 full-connected layers to generate adaptive coefficients with as input. The FC modulation layers change the number of channels to match convolution weights and also adjusts for each conv-layer. Then, the modulated features multiply with the weight of convolution in channel-wise:
where and are the original and adapted weights, is the modulated variable corresponding to the th channel of th conv-layer. Finally, the adapted BaseNet restores the input LR image to the SR image . The whole process of BaseNet is formulated as:
3.3 Species of Loss Functions
Owing to the fact that ConditionNet and BaseNet serve different purposes, they have different sensitivity to learning rate and loss functions. Hence, we optimize them alternately with different learning rates and optimization objectives. ConditionNet is trained after every steps of BaseNet training. The details of loss functions are listed as follows.
Task Contrastive Loss. As the prior knowledge explains before, our ConditionNet should output the conditional features, which are similar to those from the same degradation and dissimilar to others from different degradations. Instead of matching an input to a fixed target, recent works of contrastive learning [8, 9] measure the similarities of sample pairs in a representation space. Inspired by them, we propose a task contrastive loss, which decreases the inner-task distance and increases the cross-task distance between different conditional features.
For the inner-task loss, we sample two support sets from the same task, each containing LR patches, represented as . And ConditionNet ; extracts features , from , . The inner-task loss are calculated as:
For the cross-task loss, we resample LR images from another task, denoted as support set , which show different degradation distribution from . Also, ConditionNet ; extracts conditional features , from , . Then, the cross-task loss can be calculated as
Finally, we use the Logarithm and Exponential transformations to combine and . Those transformations can smoothly optimize ConditionNet to increase the inner-task distance and decrease the cross-task distance. When is small and is large, the combined will be close to . The task contrastive loss is formulated as:
Combined Loss. As shown in Table 4, if we only train ConditionNet by the task contrastive loss in an unsupervised way, the output feature may not be entirely beneficial for the generalization of SISR. In order to make a balance between task-level feature extraction and SR reconstruction, we combine the reconstruction loss in Eq. (5) and task contrastive loss in Eq. (8) with coefficient to constraint ConditionNet, which is formulated as:
3.4 CMDSR Algorithm
CMDSR training procedure is shown in Algorithm 1. ConditionNet and BaseNet are alternately trained until they converge. In line 4, tasks are randomly sampled from degradation distribution for each step. In Line 3-9, BaseNet is adapted and supervised with HR-LR pairs. In Line 10-18, for every steps, ConditionNet is optimized with the combined unsupervised of Line 16 and supervised of line 7.
CMDSR test stage is shown in Algorithm 2. For test support set , we can randomly sample patches from other LR images, which have the same degradation pattern with , or from itself. For convenience, we choose the self-patches to get the support set at test time. With the conditional feature extracted from support set, BaseNet performs fast adaptation to test distribution at one step and produces the restored SR image.
4.1 Experimental Setting
As introduced before, the input of CMDSR consists of two parts: the support set for ConditionNet and the LR image for BaseNet. During training, the sizes of support sets and LR images are separately and . At test time, the input of ConditionNet is and LR input is the full image. For training configurations, we set the task size as and the size of support set is 20. The patch size is . The update step is , which means ConditionNet is joined for training after BaseNet has been trained for 9 steps. The loss coefficient of Eq. (9) is The initial learning rates of BaseNet and ConditionNet are and , respectively. The ADAM optimizer  is applied.
|15||BI-structured SR model||RCAN ||24.83||23.64||23.33|
|Blind multi-degraded SR model||ZSSR ||25.40||24.30||24.05|
|Blind denoising/deblurring + Blind SR model||DnCNN +KernelGAN +ZSSR ||27.02||25.46||25.34|
|DnCNN  + IKC ||28.16||26.11||25.68|
|Blind denoising+ Gt blur kernel maps+ Non-blind SR model||DnCNN  + SRMDNF ||28.31||26.19||25.79|
|Gt Degradation maps+ Non-blind SR model||SRMD ||28.79||26.48||25.95|
|15||BI-structured SR model||RCAN ||23.24||22.42||22.48|
|Blind multi-degraded SR model||ZSSR ||24.91||23.74||23.57|
|Blind denoising/deblurring + Blind SR model||DnCNN +KernelGAN +ZSSR ||26.08||24.66||24.65|
|DnCNN  + IKC ||26.84||25.09||25.02|
|Blind denoising+ Gt blur kernel maps+ Non-blind SR model||DnCNN  + SRMDNF ||23.85||21.04||21.79|
|Gt Degradation maps+ Non-blind SR model||SRMD ||26.82||25.12||24.86|
We use the LR-HR pairs of DIV2K  for meta-training. Following previous works [43, 37], the degraded LR images of different tasks are synthesized based on Eq. (1). Specifically, we only use isotropic Gaussian blur kernels. The blur kernel widths are in range [0.2, ] for scale factor
. We sample the kernel width by a stride of 0.1. For noise, we set the Additive White Gaussian Noise (AWGN) with the noise levelsin range [0, 75]. Due to the page limit, we present results of SR tasks. All the experiments were conducted on NVIDIA Tesla-V100 GPUs.
|50||BI-structured SR model||RCAN ||16.10||15.79||15.75|
|Blind multi-degraded SR model||ZSSR ||17.89||17.46||17.79|
|Blind denoising/deblurring + Blind SR model||DnCNN +KernelGAN +ZSSR ||22.32||21.69||22.34|
|DnCNN  + IKC ||22.18||21.63||22.23|
|Blind denoising+ Gt blur kernel maps+ Non-blind SR model||DnCNN  + SRMDNF ||21.63||21.18||21.99|
|Gt degradation maps+ Non-blind SR model||SRMD ||22.43||21.83||22.43|
4.2 Experiments on Synthetic Images
To demonstrate the effectiveness and generalization of our framework, we evaluate the proposed CMDSR from the perspectives of matched degradation and shift degradation. Following [43, 37], we use the Simple and Middle testsets, which are in range of meta-training data. Since our framework is trained with isotropic Gaussian blur kernel, we add the Severe testset with anisotropic Gaussian blur kernel to validate whether CMDSR can handle degradation shift. Precisely, three testsets are synthesized as: (1) Simple: isotropic Gaussian blur kernel with kernel width followed by BI downsampler () and AWGN with noise level 15. (2) Middle: isotropic Gaussian blur kernel with kernel width followed by BI downsampler () and AWGN with noise level 15. (3) Severe: anisotropic Gaussian blur kernel with kernel width , , angle followed by BI downsampler () and AWGN with noise level 50.
We systematically compare the proposed framework with non-blind and blind methods. For non-blind methods, two latest models SRMD  and UDVD  are used, which use the accurate blur kernel and noise maps as the additional inputs. For blind methods, the SOAT BI structured SR model, RCAN  is first compared. Because the blind SR method for multiple degradations has not been studied sufficiently, except ZSSR  (5000 steps) and IRCNN , we follow [43, 3, 21] to add cascaded schemes, which combine SR models with blind denoising and deblurring methods: DnCNN + KernelGAN + ZSSR (5000 steps), DnCNN  + IKC . Moreover, in order to evaluate the mutual negative influence between cascaded stages, we add a baseline by combining blind denoiser and non-blind SR model, DnCNN  + SRMDNF .
Matched Degradation. Table 1 shows PSNR values on Simple and Middle
degradations, where degradation patterns match the range of training data. Due to the unawareness of multiple degradations, the BI structured model RCAN produces worse PSNR. When kernel width and noise level are increasing, the cascaded blind methods suffer the mutual negative influence between different stages, because the denoiser will make the LR image more blurred and lead to kernel mismatch, increasing the difficulty of deblurring. The severe PSNR drops in Table 1 and the over-sharp results of DnCNN  + SRMDNF  in Fig. 4 can prove this phenomenon. Our CMDSR achieves better PSNR than all blind schemes for Simple degradation, but a little lower than non-blind methods, SRMD  and UDVD , because they take the accurate blur kernel and noise maps as the additional inputs. However, it is noted that when degradation is more complicated, the generalization of our adaptive framework becomes prominent. Our CMDSR achieves the best performance for Middle degradation, even better than non-blind methods. As shown in Fig. 4, CMDSR produces sharper and clearer SR results. These results demonstrate that CMDSR is an effective blind framework to handle multiple degradations.
Shifted Degradation. Table 2 shows PSNR values on Severe degradation, where the degradation levels are higher and the blur kernel doesn’t appear in training data. The qualitative comparisons are shown in Fig. 1 and Fig. 5. Our CMDSR significantly outperforms all the blind and non-blind methods, because the parameters of BaseNet are not fixed but adaptive for a new degradation at test time. It should be emphasized that non-blind SRMD  is trained with both isotropic and anisotropic Gaussian blur kernel, but our blind CMDSR achieves better qualitative and quantitative results, only trained with isotropic blur kernel. These results further demonstrate the generalization of our framework to handle distribution shifts.
4.3 Experiments on Real Images
We further extend the experiments to real images. The most representative blind and non-blind methods, DnCNN  + IKC  and SRMD  are compared with our framework. Since there are no GT degradation patterns for real images, SRMD  is searched by manual grid as in . The qualitative results of real images ”frog”  and ”flower”  are shown in Fig. 6. The blind scheme produces over-sharp results and non-blind SRMD  fails to recover sharp edges. Our CMDSR produces best results with less artifacts, sharper edges, and even brighter color.
4.4 Ablation Experiments
In this section, we use training data and settings in Section 4.1 to conduct all the ablation studies.
|SRResNet-10 w/o ConditionNet||1.04M||26.09|
|SRResNet-16 w/o ConditionNet||1.48M||26.62|
|SRResNet-10 w/ ConditionNet||1.46M||27.10|
BaseNet w/ and w/o ConditionNet. We first evaluate the performance of BaseNet w/ and w/o ConditionNet to show the importance of conditional feature. Although ConditionNet is not directly used for SISR, it involves more parameters. For a fair comparison, we add SRResNet-16, the number of parameters of which nearly equals to the completed CMDSR. Then, SRResNet-16 is trained with the same synthetic data as ours. As shown in Table 3, PSNR result of CMDSR is much better, which proves the significance of conditional meta-network.
Visualizations between Conditional Features. To prove ConditionNet can efficiently extract task-level features, we should compare the conditional features between inner-tasks and cross-tasks. Using DIV2K validation set, we randomly sample 8 different tasks and sample 400 support sets for each task. We choose the conditional features modulated by the first modulation layer and show the t-SNE  visualizations in Fig. 7. Due to the page limit, we also list the values of 64 channels for each feature in Supplementary. It’s clear that the modulated features of inner-tasks are similar and those from cross-tasks are significantly different, which is consistent with the prior knowledge in Fig. 2.
Combination of Loss Functions. We compare results of CMDSR, where ConditionNet is separately trained with task contrastive loss , reconstruction loss and combined loss. As shown in Table 4, if ConditionNet is trained with , CMDSR gets collapsed to produce results even worse than single BaseNet. Only using unsupervised is acceptable, but using the combined loss achieves best results, because it makes a balance between task-level feature extraction and the generalization of SISR.
|VDSR  w/o ConditionNet||0.67M||26.49|
|VDSR  w/ ConditionNet||26.97|
|IDN  w/o ConditionNet||0.80M||26.53|
|IDN  w/ ConditionNet||27.03|
|EDSR  w/o ConditionNet||43M||26.81|
|EDSR  w/ ConditionNet||27.51|
Can CMDSR Extend to Other SISR Structure? As mentioned before, our CMDSR is a flexible and general framework, which has no strict restrictions on the BaseNet structure. Therefore, we replace SRResNet-10 with other three SISR models, VDSR, EDSR and IDN . Moreover, we still use the same training data in Section 4.1 to train those models without ConditionNet. As listed in Table 5, all those joint models get significant improvement and EDSR  achieves the best results with largest parameters. We believe our framework can be extended to more complicated structures in the future.
In this paper, we investigated the blind SISR problem with multiple degradations. Inspired by meta-learning, we design a framework that learns how to adapt to changes in input distribution. Specifically, we use a ConditionNet to extract task-level features with batches of LR patches and BaseNet rapidly adapts its parameters according to the conditional features. Extensive experiments reveal that our framework can handle distribution shift by only one-step adaptation. For complicated cases, it even outperforms non-blind methods. When we extend the structure of BaseNet to other SISR models, our framework is also applicable. In future work, we will extend our general framework to more CNN models and more low-level vision tasks.
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