Image restoration is a classic ill-posed inverse problem that aims to recover high quality images from damaged images affected by various kinds of degradations. According to the types of degradation, it can be categorized into different subtasks such as image super-resolution, image denoising, JPEG image deblocking, etc.
The rise of deep learning has greatly facilitated the development of these subtasks. But these methods are often goal-specific, and we need to retrain the network when we deal with images different from training dataset. Furthermore, most methods usually aim to pursue high reconstruction accuracy in terms of PSNR or SSIM. However, image quality assessment from human opinion is relatively subjective, and low reconstruction distortion is not always consistent with high visual quality . In addition, in many practical applications (e.g., mobile), it is often difficult to obtain user's preference and the real degradation level of the corrupted images. All of these appeal to an interactive image restoration framework which can be applied to a wide variety of subtasks. However, to the best of our knowledge, currently there are few available networks which can satisfy both interactivity and generality requirements.
Some designs have been proposed to improve the flexibility of deep methods. Take image denoising for example, data augmentation is widely used to improve the generalization of a model. Training with the dataset which contains a series of noise levels, a single model can be applied to blind denoising task . However, this method still produces a fixed reconstruction result of the input, which does not necessarily guarantee satisfactory perceptual quality (as shown in Fig. 1). An alternative choice, zhang et al.  concatenated a tunable noise level map with degraded images as input to handle blind image denoising task. Though this scheme is also user-friendly, it can not be generalized to other tasks. In image super-resolution, 
added noise to the input in order to control the compromise between perceptual quality and distortion. However, this scheme is specific for image super-resolution and cannot guarantee smooth and continuous control. Recently, as a new alternative solution for low-level visual tasks, deep network interpolation has been proposed to realize continuous image transition, but it cannot ensure the optimality of the final results.
In this paper, we propose a novel framework to control the feature space for image restoration in a fine-grained way. To be more specific, we realize the interactive control of the reconstruction result by tuning the features of each unit block, called coupling module. Each coupling module consists of a main block and a tuning block. The parameters of two blocks are obtained under two endpoint optimization objectives. Taking image super-resolution as an example, the main block is optimized for low distortion while the tuning block is optimized for high perceptual quality. Besides, in order to ensure the quality of reconstruction results, we densely stack coupling modules and assign them different coupling coefficients. As a key to achieve fine feature control, our high-degree-of-freedom coupling coefficients are adaptively learned from a single control variable.
Our main contributions can be summarized as follows:
We propose a novel controllable end-to-end framework for interactive image restoration. This scheme makes it convenient to change perceptual quality smoothly in super-resolution task and process other blind tasks.
We propose a coupling module and an adaptive learning strategy of coupling coefficients to improve reconstruction performance.
Our CFSNet outperforms the state-of-the-art methods on super-resolution, compression artifacts reduction and image denoising in terms of flexibility and visual quality.
2 Related Work
Image Restoration. Deep learning methods have been widely used in image restoration. [15, 30, 29, 18, 41, 40, 35] continuously deepen, widen or lighten the network structure, aiming at improving the super-resolution accuracy as much as possible. While [13, 17, 26, 23]
paid more attention to the design of loss function in order to improve visual quality. Besides,[4, 33, 20] explored the perception-distortion trade-off. In , Dong et al. adopted ARCNN built with several stacked convolutional layers for JPEG image deblocking. Zhang et al.  proposed FFDNet to make image denoising more flexible and effective. Guo et al.  designed CBDNet to handle blind denoising of real images. Different from these task-specific methods, [37, 38, 20, 19] proposed some unified schemes that can be employed to different image restoration tasks. However, these fixed networks are not flexible enough to deal with volatile user needs and application requirements.
incorporated facial attribute vector into network to control facial appearance (e.g., gender, age, beard). In 
, deep feature interpolation was adopt to implement automatic high-resolution image transformation. also proposed a scheme that control adaptive instance normalization (AdaIN) in feature space to adjust high-level attributes. Shoshan et al.  inserted some tuning blocks in the main network to allow interactively modification of the network. However, all of these methods are designed for high-level vision tasks and can not be directly applied to image restoration. To apply controllable image transformation to low-level vision tasks, Wang et al.  performed interpolation in the parameter space, but this method can not guarantee the optimality of the outputs, which inspires us to further explore fine-grain control of image restoration.
3 Proposed Method
In this section, we first provide a global view of the proposed framework, called CFSNet and then, present the modeling process inspired by the image super-resolution problem. Instead of specializing for the specific super-resolution task, we finally generalize our CFSNet to multiple image restoration tasks, including super-resolution, denoising and deblocking. Moreover, we give the explicit model interpretation based on the manifold learning to show the intrinsic rationality of the proposed network. At the end of this section, we show the superiority and improvements of the proposed CFSNet through the detailed comparison with the current typical related methods.
3.1 Basic Network Architecture
As shown in Fig. 2, Our CFSNet consists of a main branch and a tuning branch. The main branch contains residual blocks  while the tuning branch contains tuning blocks with additional fully connected layers. Each main block and tuning block constitute a coupling module combining the features of the two separate branches effectively. We take the original degraded image and the scalar control variable as the input and output the restored image as the final result.
In the beginning, We first use a convolutional layer to extract the features from the degraded image ,
represents the feature extraction function andserves as the input of next stage. Here, together with the input image , we introduce a control variable at the same time to balance the different optimization goals. To be more specific, there are 3 shared fully connected layers to transform the input scalar into multi-channels vectors and 2 independent fully connected layers to learn the optimal coupling coefficient for each coupling module:
where both and denote the function of fully connected layers, is the coupling coefficient of the -th coupling module. Each coupling module entangles the output of the main block and the tuning block, which can be formulated as follows:
where represents the -th coupling operation, and denote the output features of -th main block and -th tuning block respectively, and are the -th main block function and -th tuning block function respectively. To address the image super-resolution task, we add an extra coupling module consisting of the upscaling block before the last convolutional layer, as shown in Fig. 2. Specifically, we utilize sub-pixel convolutional operation (convolution + pixel shuffle)  to upscale feature maps. Finally, we use a convolutional layer to get the reconstructed image,
where denotes convolution operation. The overall reconstruction process can be expressed as
where represents the function of our proposed CFSNet. , and represent the parameters of main branch, all tuning blocks and all fully connected layers respectively.
Since the two branches of our framework are based on different optimization objectives, in further detail, our training process can be divided into two steps:
Set the control variable as 0. Train the main branch with the loss function , where is the corresponding ground truth image.
Set the control variable as 1. Map the control variable to different coupling coefficients , fix parameters of the main branch and train the tuning branch with another loss function .
3.2 Coupling module
We now present the details of our coupling module. We mainly introduce our design from the perspective of image super-resolution. In order to balance the trade-off between perceptual quality and distortion, we usually realize it by modifying the penality parameter of the loss terms ,
where denotes distortion loss (e.g., MSE and MAE), contains GAN loss [33, 10] and perceptual loss , is the scalar. We usually pre-train the network with loss, then we fine-tune the network with combined loss to reach the different working point. That is to say, if we regard pre-trained results as reference point, then we can start from the reference point and gradually convert it to the result of another optimization goal in a coarse-to-fine manner.
However, it is not efficient to train a network for each working point. In order to address this issue, we convert the control scalar to the input and directly control the offset of the reference point in latent feature space. For this purpose, we implement a controllable coupling module to couple reference features and new features from together. We set the feature based on distortion optimization as the reference point which is denoted as . In the process of optimization based on perceptual quality, we keep the reference point unchanged and set as direction of change. In other words, in a middle layer, part of features are provided by reference information, and the other part are obtained from new exploration:
where , , and denotes the -th coefficient, is the number of channels.
It is worth noting that different main blocks provide different reference information, so we should treat them differently. We expect to endow each coupling module a different coupling coefficient to make full use of reference information. Therefore, our control coefficients are learned from optimization process. To be more specific, we use some fully connected layers to map a single input control variable into different coupling coefficients (Eqn. 2). The proposed network will find the optimal coupling mode since our control coefficients are adaptive not fixed.
Thanks to the coupling module and linear mapping network, we can realize continuous and smooth transition by a single control variable . Moreover, if we can achieve a nice trade-off between perceptual quality and distortion in this way, then can we generalize this model to other restoration tasks? After the theoretical analysis and experimental tests, we find that this framework is applicable to a wide variety of image restoration tasks. Let's pick blind denoising for example, if we regard the reconstruction with known noise level as reference point, then we can represent other blind reconstruction point with reference point. In the next section, we will provide a more general theoretical explanation of our model.
3.3 Theoretical analysis
Set all natural images as the background space. The degradation process of a natural image can be regarded as continuous. So approximately, these degraded images are adjacent in a high-dimensional space. It is possible to approximate the reconstruction result of unknown degradation level with the result of known degradation level. Unfortunately, natural images lie on an approximate non-linear manifold . As a result, simple image interpolation tends to introduce some ghosting artifacts or other unexpected details to final results.
Instead of operating in pixel space, we naturally turn our attention to the feature space. Some literatures indicate that the data manifold can be flattened by neural network mapping and we can approximate the mapped manifold as a euclidean space[2, 5, 28]. Based on this hypothesis, as shown in Fig. 3, we denote and in latent space as two endpoints respectively, and we can represent unknown point as a affine combination of and :
where is the -th combination coefficient. This is exactly the representation of the controllable coupling module Eqn. 7. However, we should also note that this hypothesis is influenced by the depth and width of CNN. In other words, we do not know the degree of flattening that can be achieved of different channels and different layers. Therefore, the combination coefficients of different channels and different layers should be discrepant. Besides, we hope to find the optimal combination coefficients through the optimization process:
where represents the optimal solution. However, it is difficult to directly obtain the optimal , because the unknown working point cannot in general be computed tractably. So we solve Eqn. 9 in an implicit way. Specifically, we map the input control variable to different combination coefficients with some stacked fully connected layers, then, we can approximate the above process into optimizing the parameters of the linear mapping network:
where denotes mapping function of , is the approximated solution of the optimal . Fortunately, this network can be embedded into our framework. Therefore, we can optimize the parameters of the linear mapping network and the tuning blocks in one shot. This also explains why our network has dense coupling modes. Therefore, the entire optimization process (corresponding to Step 2) can be expressed as
Difference to Dynamic-Net Recently, Dynamic-Net  realized interactive control of continuous image conversion. In contrast, there are two main differences between Dynamic-Net and our CFSNet. First of all, Dynamic-Net is mainly applied to high-level vision tasks. It's difficult to achieve the desirable results when we use Dynamic-Net directly for image restoration tasks. In contrast, our proposed framework is carefully designed for image restoration. Secondly, the way Dynamic-Net used the tuning blocks can be expressed as
where is the latent representation of an intermediate point, denotes the function of tuning blocks and is the input control variable. Their is set exactly same for each channel. While in our CFSNet, our coupling modules are densely stacked, and the unknown point is the affine combination of two endpoints. Our combination coefficients are mapped from a single input control variable, in other words, our combination coefficients of different layers and different channels are learned adaptively through the training process. This is more user-friendly and we explain the reasonability of this design in Sec. 3.3.
Difference to Deep Network Interpolation Deep Network Interpolation (DNI) is another choice to control the compromise between perceptual quality and distortion [33, 32]. DNI also can be applied to many low-level vision tasks . However, this method needs to train two networks with the same architecture but different loss and will generate a third network to control. In contrast, our framework can achieve a better interactive control with a unified end-to-end network. On the other hand, our framework make better use of reference information using coupling module. DNI performs interpolation in the parameter space to generate continuous transition effects, and interpolation coefficients are kept same in the whole parameter space. However, this simple strategy can not guarantee the optimality of the outputs. While in our CFSNet, we performs the interpolation in the feature space and the continuous transition of the reconstruction effect is consistent with the variation of the control variable . We can produce a better approximation of the unknown working point. See Sec. 4.3 for more experimental comparisons.
In this section, we first demonstrate implementation details of our framework. Then we validate the control mechanism of our CFSNet. Finally, we apply our CFSNet to three classic tasks: image super-resolution, image denoising, JPEG image deblocking. All experiments validate the effectiveness of our model. Due to space limitations, more examples and analyses are provided in the appendix.
4.1 Implement Details
For image super-resolution task, our framework contains 30 main blocks and 30 tuning blocks (i.e., ). As for the other two tasks, the main branch parameters of our CFSNet are kept similar to that of the compared method  (i.e., ) for a fair comparison. Furthermore, we first generate a 512-dimensional vector with values of all 1. Then we multiply it by the control variable to produce a control input. All convolutional layers have 64 filters and the kernel size of each convolutional layer is . We use the method in  to perform weight initialization. For both training stage of all tasks, we use the ADAM optimizer  by setting , , and
with the initial learning rate 1e-4. We adopt 128 as the minibatch size in image denoising task and set it as 16 in other three tasks. We use PyTorch to implement our network and perform all experiments on GTX 1080Ti GPU.
For image denoising and JPEG image deblocking, we follow the settings as in  and  respectively. The training loss function in Step 1 and Step 2 remains unchanged: . In particular, for image denoising, we input the degraded images of noise level 25 when we train the main branch in Step 1 and we input the degraded images of noise level 50 when we train the tuning branch in Step 2. Training images are cut into
patches with a stride of 10. And the learning rate is reduced by 10 times every 50000 steps. For JPEG deblocking, we set quality factor as 10 in the first training stage and change it to 40 in the second training stage. Besides, we chooseas patch size and the learning rate is divided by 10 every 100000 steps. For image super-resolution, we first train the main branch with objective MAE loss, then we train the tuning branch with objective , where denotes mean absolute error (MAE), represents wgan-gp loss  and is a variant of perceptual loss . We set HR patch size as and we multiply the learning rate by 0.6 every 400000 steps.
4.2 Ablation Study
Fig. 4 presents the ablation study on the effects of adaptive learning coupling coefficients strategy. We directly set the coupling coefficients of different channels and different layers as a same in CFSNet-SA. That is, compared to CFSNet, CFSNet-SA removes the linear mapping network of control variable . Besides, we keep the training process of CFSNet-SA consistent with CFSNet. We can find that, no matter in denoising task or in deblocking task, the best restored result of CFSNet is better than that of CFSNet-SA for unknown degradation level. In particular, the curve of CFSNet is concave-shaped, which means that there is a bijective relationship between the reconstruction effect and the control variable. In contrast, there is no obvious change law in the curve of CFSNet-SA. The reason is that adaptive coupling coefficients help to produce better intermediate features. This merit provides more friendly interaction control. What's more, JPEG deblocking task is more robust to control variable than image denosing task, we speculate that this is because JPEG images of different degradation levels are closer in the latent space.
4.3 Image Super-resolution
For image super-resolution, we adopt a widely used DIV2K training dataset  that contains 800 images. We down-sample the high resolution image using MATLAB bicubic kernel with a scaling factor of 4. Following [24, 33], we evaluate our models on PIRM test dataset provided in the PIRM-SR Challenge . We use the perception index (PI) to measure perceptual quality and use RMSE to measure distortion. Similar to the PIRM-SR challenge, we choose EDSR , CX  and EnhanceNet  as baseline methods. Furthermore, we also compare our CFSNet with another popular trade-off method, deep network interpolation [32, 33]. We directly use source code from ESRGAN  to produce SR results with different perceptual quality, namely ESRGAN-I.
Fig. 6 and Fig. 1 show the visual comparison between our results and the baselines. We can observe that CFSNet can achieve a mild transition from low distortion results to high perceptual quality results without unpleasant artifacts. In addition, it can be found that our CFSNet outperforms the baselines on edges and shapes. Due to different user preferences, it is necessary to allow users to freely adjust the reconstruction results.
We also provide quantitative comparisons on PIRM test dataset. Fig. 5 shows the perception-distortion plane. As we can see, CFSNet improve the baseline (EnhanceNet) in both perceptual quality and reconstruction accuracy. The blue curve shows that our perception-distortion function is steeper than ESRGAN-I (orange curve). Meanwhile, CFSNet performs better than ESRGAN-I in most regions, although our network is lighter than ESRGAN. This means that our result is closer to the theoretical bound of perception-distortion.
4.4 Image Denoising
In image denoising experiments, we follow  to use 400 images from the Berkeley Segmentation Dataset (BSD)  as the training set. We test our model on BSD68  using the mean PSNR as the quantitative metric. Both training set and test set are converted to gray images. We generate the degraded images by adding Gaussian noise of different levels (e.g., 15, 25, 30, 40, and 50) to clean images.
We provide visual comparison in Fig. 7 and Fig. 1. As we can see, users can easily control to balance noise reduction and detail preservation. It is worth noting that, our highest PSNR results () have similar visual quality with other methods, but it does not necessarily mean the best visual effects, for example, the sky patch of ‘test017” enjoys a smoother result when . Users can personalize each picture and choose their favorite results by controlling at test-time.
In addition to perceptual comparisons, we also provide objective quantitative comparisons. We change from 0 to 1 with an interval of 0.1 for preset noise range (). Then we choose the final result according to the highest PSNR. We compare our CFSNet with several state-of-the-art denoising methods: BM3D , TNRD , DnCNN , IRCNN , FFDNet . More interestingly, as shown in Tab. 1, our CFSNet is comparable with FFDNet on the endpoint ( and
), but our CFSNet still achieves the best performance on the noise level 30 which is not contained in the training set. Moreover, our CFSNet can even deal with unseen outlier (). This further verifies that we can obtain a good approximation of the unknown working point.
4.5 JPEG Image Dblocking
We also apply our framework to reduce image compression artifacts. As in [8, 37, 20], we adopt LIVE1  as the test dataset and use the BSDS500 dataset  as base training set. For a fair comparison, we perform training and evaluating both on the luminance component of the YCbCr color space. We use the MATLAB JPEG encoder to generate JPEG deblocking input with four JPEG quality settings q = 10, 20, 30, 40.
We select the deblocking result in the same way as the image denosing task. We select SA-DCT , ARCNN , TNRD  and DnCNN  for comparisons. Tab. 2 shows the JPEG deblocking results on LIVE1. Our CFSNet achieves the best PSNR results on all compression quality factors. Especially, our CFSNet does not degrade too much and still achieves 0.12 dB and 0.18 dB improvements over DnCNN-3 on quality 20 and 30 respectively, although JPEG images of quality 20 and 30 never appear in training process. Fig. 8 shows visual results of different methods on LIVE1. Too small produces too smooth results, while too large leads to incomplete artifacts elimination. Compared to ARCNN  and DnCNN , our CFSNet can make a better compromise between artifacts removal and details preservation.
In this paper, we introduce a well-designed framework which performs coupling in latent space. The reconstruction results can be finely controlled using a single input variable. Besides that, it is capable of producing high quality images on image super-resolution, image blind denoising and image blind deblocking, and it outperforms the existing state-of-the-art methods in terms of flexibility and visual quality. This suggests that, the proposed framework is solid and effective for image restoration. Future works will focus on the expansion to multiple degraded tasks.
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