DPWSDNet: Dual PixelWavelet Domain Deep CNNs
for Soft Decoding of JPEGCompressed Images
Abstract
JPEG is one of the widely used lossy compression methods. JPEGcompressed images usually suffer from compression artifacts including blocking and blurring, especially at low bitrates. Soft decoding is an effective solution to improve the quality of compressed images without changing codec or introducing extra coding bits. Inspired by the excellent performance of the deep convolutional neural networks (CNNs) on both lowlevel and highlevel computer vision problems, we develop a dual pixelwavelet domain deep CNNsbased soft decoding network for JPEGcompressed images, namely DPWSDNet. The pixel domain deep network takes the four downsampled versions of the compressed image to form a 4channel input and outputs a pixel domain prediction, while the wavelet domain deep network uses the 1level discrete wavelet transformation (DWT) coefficients to form a 4channel input to produce a DWT domain prediction. The pixel domain and wavelet domain estimates are combined to generate the final soft decoded result. Experimental results demonstrate the superiority of the proposed DPWSDNet over several stateoftheart compression artifacts reduction algorithms.
1 Introduction
The number of devices with highresolution camera increases significantly over the last few years, with the introduction of smart phones and IoT (Internet of Things) devices. Limited by the transmission bandwidth and storage capacity, these images and videos are compressed. As shown in Fig. 1, compressed images usually suffer from compression artifacts due to the information loss in the lossy compression process, especially at low bitrates. In addition to poor perceptual quality, compression artifacts also reduce the accuracy of other processing steps such as object detection and classification. Therefore, it is necessary to improve the quality of compressed images. This paper focuses on the soft decoding of JPEG images due to the fact that the JPEG is one of the commonly used compression standards for still images.
In recent years, many works investigate the restoration of JPEG images, aiming to remove compression artifacts and enhance the perceptual quality and objective assessment scores. In literature, the restoration procedure is usually referred to as soft decoding [21, 22], deblocking [20, 33], or compression artifacts reduction [5, 10]. In this paper, we use these terms interchangeably. Inspired by the excellent performance of the deep convolutional neural networks (CNNs) on various computer vision problems, we propose a dual pixelwavelet domain deep CNNsbased soft decoding network for JPEGcompressed images, namely DPWSDNet. From Fig. 1 that illustrates a restored image by the proposed DPWSDNet, we can observe that most of the compression artifacts are removed and some missing textures are recovered. Overall, the main contribution of this work is a dualbranch deep CNN that can reduce compression artifacts in both the pixel domain and wavelet domain. More specifically, our contributions are two folds:

We develop an effective and efficient soft decoding method for JPEGcompressed images using dual pixelwavelet domain deep CNNs. The combination of the pixel domain and wavelet domain predictions leads to better soft decoding performance.

We reshape the compressed image and its 1level discrete wavelet transformation (DWT) coefficients into two tensors with smaller size, which are used as the inputs to the pixel and wavelet subnetworks, respectively. By performing soft decoding on two smaller tensors, the DPWSDNet achieves stateoftheart performance while maintaining efficiency.
The rest of this paper is organized as follows. We describe the related work in the next section. The proposed soft decoding algorithm is presented in Section 3. Experiments are shown in Section 4. Finally, Section 5 concludes this paper.
2 Related Work
Let and be the original uncompressed image and the corresponding JPEGcompressed version, respectively. Given the compressed image , the goal of soft decoding is to produce an estimate that is as close as possible to the original image . Existing methods for soft decoding of JPEGcompressed images can be roughly split into three categories: enhancementbased, restorationbased, and learningbased methods.
The enhancementbased methods usually remove compression artifacts via performing pixel domain or transform domain filtering. For instance, Foi et al. [7] proposed a shapeadaptive discrete cosine transformation (DCT)based image filtering, yielding excellent performance on deblocking and deringing of compressed images. Zhai et al. [31] proposed to reduce blocking artifacts via postfiltering in shifted windows of image blocks. In [30], the authors developed an efficient artifacts reduction algorithm through joint DCT domain and spatial domain processing. Yoo et al. [29] proposed an interblock correlationbased blocking artifacts reduction framework, in which the artifacts in flat regions and edge regions were removed using different strategies.
Compression artifacts reduction is formulated as an illposed inverse problem for the restorationbased soft decoding methods, where the prior knowledge about highquality images, compression algorithms, and compression parameters is used to assist the restoration process [2, 4, 13, 20, 21, 22, 23, 24, 25, 32, 33, 36, 37, 38]. For instance, in [25], the original image and compression distortion were modeled as a highorder Markov random field and spatially correlated Gaussian noise, respectively. Nonlocal selfsimilarity property was widely used in deblocking algorithms. In general, the lowrank [20, 24, 33, 36] and group sparse representation [32, 38] were applied to model this property. In [2, 21, 22, 23, 32, 38], sparsity was utilized as an image prior to regularize the restored image. The graph model was used in the deblocking methods proposed in [13] and [21]. In some works [21, 22, 33, 36, 38], the quantization constraint on DCT coefficients was applied to restrain the resultant image. In particular, Dar et al. [4] designed a sequential denoisingbased soft decoding algorithm, where the existing stateoftheart denoising method was used to construct a regularization. On the whole, most of the restorationbased soft decoding methods are timeconsuming to some extent due to the complex optimization process.
Recently, excellent results were obtained by deep learningbased approaches [1, 3, 5, 8, 9, 10, 19, 27, 34]. Dong et al. [5] developed a shallow CNN for compression artifacts reduction on the basis of the network for superresolution [6]. The authors of [5] found that it is hard to train a network beyond four layers in lowlevel vision tasks. To address this issue, Kim et al. [17] introduced the residual learning technique and designed a very deep network of twenty layers for single image superresolution. In [34], Zhang et al. presented a very deep network via incorporating the residual learning and batch normalization for a series of general image denoising problems, including denoising, superresolution, and deblocking. Li et al. [19] combined the skip connection and residual learning to ease the network training process. Cavigelli et al. [1] developed a deep compression artifacts reduction network with a multiscale loss function. In [3], Chen and Pock proposed a trainable nonlinear reaction diffusion model for efficient image restoration. Inspired by the success of the dual DCTpixel domain sparse coding [22], the authors of [9] and [27] designed dualdomain networks for the deblocking of JPEG images. More recently, some works aim to improve the perceptual quality of compressed images [8, 10]. Overall, deep learningbased approaches show obvious superiority over conventional soft decoding methods in terms of both the restoration performance and running time ^{1}^{1}1 In general, the deep learningbased image restoration approaches are timeconsuming in model training phase but efficient in testing phase. In this paper, the running time refers to the time cost in testing phase only..
Inspired by the success of the wavelet domain networks for superresolution [11, 14], we present a dual pixelwavelet domain deep CNN for the soft decoding of JPEGcompressed images in this paper. The proposed DPWSDNet is different from previous deep learningbased soft decoding algorithms in the following aspects: 1) The DPWSDNet consists of two parallel branches that perform restoration in the pixel domain and wavelet domain, respectively. 2) The DPWSDNet takes two tensors as the network inputs rather than the original compressed image and DWT coefficients. Experiments show that the DPWSDNet achieves competitive restoration performance and execution speed on JPEGcompressed images. Moreover, the extensions of the proposed DPWSDNet to other compression standards are straightforward.
3 Proposed DPWSDNet
As outlined in Fig. 2, the proposed DPWSDNet composes of two parallel branches: the pixel domain soft decoding branch and the wavelet domain soft decoding branch. The network in the pixel domain branch (namely PSDNet) removes compression artifacts in pixel domain directly, while the network in the wavelet domain branch (namely WSDNet) performs restoration in wavelet domain. The pixel domain and wavelet domain estimates are combined to generate the final soft decoded result. Note that we do not directly use the original compressed image and its DWT subbands as the inputs of the two subnetworks. In the following sections, more details about the DPWSDNet are presented. For convenience, we assume that the input is a grayscaled image of size where are both even.
3.1 The Pixel Domain Branch
In the pixel domain branch (shown in the bottom half of Fig. 2), first the compressed image is downsampled to generate four downsampled subimages of size . Since we have to recover an image that has the same size with the input, a reversible downsampling strategy is used in this process as [35]. Fig. 3 illustrates the reversible downsampling process. Given , the pixels located at , , , and (, ) are respectively sampled to form four different subimages, which are concatenated to constitute a tensor of size . Then, the tensor is fed into the pixel domain deep CNN. At least two benefits can be achieved by using a smaller tensor as the input of a deep CNN. First, a smaller input means lower computational complexity. In addition, working on the downsampled images can enlarge the receptive field, which is beneficial to restoration process.
For convenience, we name the pixel domain deep CNN PSDNet. The input and output of the PSDNet are tensors. The layer PSDNet consists of two kinds of blocks. The first blocks are “CONV+BN+ReLU”, and the last block only includes a convolutional layer. Note that the abbreviation “CONV” represents a convolutional layer, “BN” denotes the batch normalization [15], and “ReLU” represents the rectified linear unit [18]. The kernel number of each convolutional layer is set to except the last layer that outputs a channel residual image. The kernel size of each convolutional layers is set to . In each layer, the zero padding strategy is adopted to keep all feature maps having the same size. Since the input and output of the PSDNet are very similar, we adopt the residual learning [12] for stable and fast training. Hence, the training loss function of the PSDNet is defined as
(1) 
where the represents all parameters in PSDNet, is the predicted residual component, and denotes compressedclean tensor pairs in the pixel domain.
Finally, the four feature maps in the output of PSDNet are assembled according to the inverse process of the downsampling procedure to form the pixel domain estimate.
3.2 The Wavelet Domain Branch
The framework of the wavelet domain branch is similar to the pixel domain branch. Given a compressed image , we first conduct the 1level 2dimensional discrete wavelet transformation (2DDWT) and obtain its four wavelet subbands coefficients. The size of each subband is . Similarly, the four wavelet subbands are concatenated to constitute a tensor of size , which is used as the input of the wavelet domain deep CNN, namely WSDNet. By concatenating four wavelet subbands, the information in different subbands can be fused while keeping the consistency among them. Moreover, the computational cost can be reduced.
The architecture of the WSDNet is set to be the same as the PSDNet, including the network depth, number of kernels, and kernel size. Therefore, we do not introduce the WSDNet in details to avoid redundancy. The main difference between the two subnetworks is that the WSDNet predicts wavelet coefficients residual while the PSDNet predicts pixel intensity residual. Correspondingly, the training loss function of the WSDNet is defined as
(2) 
where the represents all parameters in WSDNet, is the predicted residual component, and denotes compressedclean tensor pairs in the wavelet domain.
The four feature maps in the output of WSDNet are the wavelet subbands of the soft decoded image. Therefore, the 2dimensional inverse discrete wavelet transformation (2DIDWT) is performed on these coefficients to produce the wavelet domain estimate.
3.3 The Combination of the DualBranch
As mentioned above, the pixel domain and wavelet domain branches both produce a soft decoded version of the input image. Since the two predictions are generated in different spaces, they have their respective characteristics. Hence, combining them should improve the restoration performance further. There are many ways to fuse the two intermediate results. For example, we can design a network with a 2channel input and a 1channel output to combine them. Considering the computational complexity, the two estimates derived from the dualdomain are simply equally weighted to generate the final output in this work.
4 Experiments
In this section, we first introduce some implementation details, followed by experimental results.
4.1 Implementation Details
Training Data: The publicly available imageset BSDS500 ^{2}^{2}2Available: https://www2.eecs.berkeley.edu/Research/Projects/CS/
vision/grouping/resources.html is used to train the DPWSDNet. We adopt the data augmentation (rotation and downsampling) to generate more training images. For the PSDNet, we extract training sample pairs from original images and the corresponding compressed images. Correspondingly, the 2DDWT coefficients of the original images and compressed images are used to generate training sample pairs for the WSDNet. We generate training sample pairs for each subnetwork, and the size of each sample is set to .
Training Parameters: We use the Caffe package [16] to implement the proposed network, and the depths of PSDNet and WSDNet are set to (). The stochastic gradient descent algorithm is adopted to optimize our networks. The batch size, weight decay, momentum are set to , , and , respectively. The initial learning rate is set to , and it decreases by a factor of every epochs. The maximum number of iterations is set to for both the pixel domain and wavelet domain subnetworks.
QF  10  20  30  40  
Classic5  JPEG  27.82/0.7595/25.21  30.12/0.8344/27.50  31.48/0.8666/28.94  32.43/0.8849/29.92 
CONCOLOR [33]  29.24/0.7963/29.14  31.38/0.8541/31.18  32.70/0.8809/32.50  33.60/0.8961/33.36  
D2SD [22]  29.21/0.7960/28.87  31.47/0.8551/31.15  32.79/0.8813/32.40  33.66/0.8962/33.20  
ARCNN [5]  29.05/0.7929/28.78  31.16/0.8517/30.60  32.52/0.8806/32.00  33.33/0.8953/32.81  
TNRD [3]  29.28/0.7992/29.04  31.47/0.8576/31.05  32.78/0.8837/32.24    
DnCNN3 [34]  29.40/0.8026/29.13  31.63/0.8610/31.19  32.90/0.8860/32.36  33.77/0.9003/33.20  
DPWSDNet  29.74/0.8124/29.37  31.95/0.8663/31.42  33.22/0.8903/32.51  34.07/0.9039/33.24  
LIVE1  JPEG  27.77/0.7730/25.34  30.08/0.8512/27.57  31.41/0.8852/28.93  32.36/0.9041/29.96 
CONCOLOR [33]  28.87/0.8018/28.76  31.08/0.8681/30.90  32.42/0.8985/32.16  33.39/0.9157/33.07  
D2SD [22]  28.83/0.8023/28.54  31.08/0.8690/30.80  32.41/0.8987/32.10  33.37/0.9156/33.06  
ARCNN [5]  29.04/0.8076/28.77  31.31/0.8733/30.79  32.73/0.9043/32.22  33.63/0.9198/33.14  
TNRD [3]  29.14/0.8111/28.88  31.46/0.8769/31.04  32.84/0.9059/32.28    
DnCNN3 [34]  29.19/0.8123/28.91  31.59/0.8802/31.08  32.99/0.9090/32.35  33.96/0.9247/33.29  
DPWSDNet  29.53/0.8210/29.13  31.90/0.8854/31.27  33.31/0.9130/32.52  34.30/0.9282/33.44 
4.2 Soft Decoding Performance Evaluation
The DPWSDNet is compared with five stateoftheart soft decoding algorithms for JPEGcompressed images, including two restorationbased approaches (i.e., CONCOLOR [33] and D2SD [22]) and three deep learningbased algorithms (i.e., ARCNN [5], TNRD [3], and DnCNN3 [34]). Referring to [34], two benchmark imagesets Classic and LIVE are used as test datasets. For the color images in the LIVE dataset, only the luminance components are processed. The MATLAB JPEG encoder is used to generate JPEGcompressed images at different quality factors (QFs). We compare the performance of these algorithms in the cases of QF = , , , and . For the DPWSDNet, a dedicated model is trained for each QF. For the five competitors, we use the original codes and models provided by the authors.
Table 1 reports the objective assessment scores achieved by all tested algorithms, including the PSNR, SSIM [26], and PSNRB [28] ^{3}^{3}3 For the TNRD [3], the results at QF = are not presented as the corresponding model is not available.. Note that the PSNRB is a specifically developed assessment metric for blocky and deblocked images. It can be observed from Table 1 that the DPWSDNet consistently outperforms the five competitors with considerable improvements. The only exception is the PSNRB value on Classic in the case of QF = , where the CONCOLOR [33] is superior to the DPWSDNet. Overall, the DnCNN3 [34] and TNRD [3] generate the secondbest and the thirdbest results, respectively. The CONCOLOR [33], D2SD [22], and ARCNN [5] achieve comparable performance overall. On average, the proposed DPWSDNet achieves about () dB PSNR gains, () SSIM gains, and () dB PSNRB gains over the secondbest approach DnCNN3 [34]. The gains over the two restorationbased soft decoding algorithms and ARCNN [5] are more significant. The improvements over stateoftheart deblocking approaches demonstrate the effectiveness of the proposed DPWSDNet.
One important aim of soft decoding algorithms is to recover images with high visual quality as JPEGcompressed images at high compression ratios usually suffer from severe artifacts. Therefore, some soft decoded images produced by different methods at QF = are shown in Fig. 4, Fig. 5, and Fig. 6 in order to compare visual quality. It can be observed that most of the compression artifacts in JPEG images are removed by performing soft decoding on them. However, some soft decoded images are oversmoothed to some extent, or still suffer from visible artifacts. By contrast, the DPWSDNet shows superiority in reducing artifacts and restoring details. The restored images using DPWSDNet are more perceptually appealing, which can be seen from the highlighted regions. The results in this section verify that the DPWSDNet not only achieves higher objective evaluation scores, but also produces better visual quality.
QF  10  20  30  40  
Classic5  PSDNet  29.69/0.8116/29.33  31.89/0.8657/31.39  33.18/0.8899/32.49  34.04/0.9036/33.22 
WSDNet  29.70/0.8117/29.33  31.91/0.8660/31.37  33.18/0.8900/32.48  34.03/0.9036/33.21  
DPWSDNet  29.74/0.8124/29.37  31.95/0.8663/31.42  33.22/0.8903/32.51  34.07/0.9039/33.24  
LIVE1  PSDNet  29.49/0.8203/29.10  31.86/0.8849/31.25  33.27/0.9126/32.49  34.26/0.9278/33.41 
WSDNet  29.51/0.8205/29.11  31.87/0.8850/31.25  33.28/0.9127/32.50  34.26/0.9279/33.42  
DPWSDNet  29.53/0.8210/29.13  31.90/0.8854/31.27  33.31/0.9130/32.52  34.30/0.9282/33.44  
4.3 Discussion on DualDomain Soft Decoding
In DPWSDNet, two parallel branches are used to restore the compressed image in the pixel domain and wavelet domain, respectively. It is meaningful to study the ability of the two branches and discuss the effectiveness of the dualdomain combination. Table 2 presents the objective assessment scores of the DPWSDNet and its two variants, i.e., the PSDNet and WSDNet. Here the PSDNet represents that only the pixel domain branch is used to restore the compressed image, while the WSDNet represents that only the wavelet domain branch is used.
It can be observed from Table 2 that both the PSDNet and WSDNet generate excellent restoration performance, which proves the ability of the presented network. Moreover, the gains of the DPWSDNet over the PSDNet and WSDNet verify the effectiveness of the dualdomain soft decoding. Furthermore, it is believed that the fusion of the two branches could be more effective with a more complex combination method.
QF  10  20  30  40  
Classic5  DnCNN3 [34]  29.40/0.8026/29.13  31.63/0.8610/31.19  32.90/0.8860/32.36  33.77/0.9003/33.20 
DPWSDNet  29.74/0.8124/29.37  31.95/0.8663/31.42  33.22/0.8903/32.51  34.07/0.9039/33.24  
BDPWSDNet  29.69/0.8104/29.34  31.92/0.8660/31.39  33.18/0.8900/32.44  34.01/0.9035/33.19  
LIVE1  DnCNN3 [34]  29.19/0.8123/28.91  31.59/0.8802/31.08  32.99/0.9090/32.35  33.96/0.9247/33.29 
DPWSDNet  29.53/0.8210/29.13  31.90/0.8854/31.27  33.31/0.9130/32.52  34.30/0.9282/33.44  
BDPWSDNet  29.48/0.8193/29.10  31.87/0.8849/31.26  33.27/0.9127/32.46  34.24/0.9278/33.38 
4.4 Discussion on Blind Soft Decoding
In above experiments, we use a dedicated model for each compression QF. To test the capacity of the DPWSDNet further, we train a universal model for compressed images at different QFs. We refer to the universal model as the blind DPWSDNet (BDPWSDNet), which is trained using the samples compressed at different QFs ^{4}^{4}4 Note that the same training dataset and the same number of training samples are used to train the universal model and the dedicated model.. In Section 4.2, DPWSDNet and DnCNN3 [34] perform the best and the secondbest on the whole, respectively. Therefore, we compare the BDPWSDNet with them in Table 3.
As expected, the BDPWSDNet is slightly inferior to DPWSDNet. However, in most cases, it still outperforms DnCNN3 [34] with obvious gains. Compared with DPWSDNet, BDPWSDNet is more flexible and practical. Given QF, DPWSDNet can be used to obtain better restoration performance, while BDPWSDNet can produce competitive results when the QF is unknown. Hence, one can select a proper model according to the practical application.
4.5 Empirical Study on Training Convergence and Running Time
In Fig. 7, we show the PSNR values of DPWSDNet with different training iterations. The trends are similar for different QFs, so only the curves at QF = are presented. It can be seen that the training converges after about 200,000 iterations. In our experiments, the maximum number of iterations is set to 300,000. The training of a single model takes about hours on a GeForce GTX Ti GPU.
Running time is an important factor for a soft decoding algorithm. We run different deblocking methods on the same desktop computer with an Inter Core i CPU GHz, 32GB RAM, and Matlab environment. Fig. 8 presents the execution time of different approaches on three representative image sizes in Classic and LIVE ^{5}^{5}5 In this experiment, the running time of the TNRD [3] is evaluated with the multithreaded computation implementation.. It can be seen that the proposed PSDNet and WSDNet are the most efficient approaches. The DPWSDNet costs about time compared with the PSDNet and WSDNet, but it is still less timeconsuming than other compared algorithms. Moreover, the execution speed of the DPWSDNet can be greatly accelerated with a GPU.
5 Conclusion and Future Work
A dual pixelwavelet domain deep networkbased soft decoding framework is developed for JPEGcompressed images, namely DPWSDNet. In DPWSDNet, the compressed image is restored in both pixel and wavelet spaces using deep CNNs. In addition, we use 4channel tensors as the inputs of our networks rather than the 2dimensional images, which makes the DPWSDNet efficient and effective. Experimental results on benchmark datasets demonstrate the effectiveness and efficiency of our soft decoding algorithm. Future work includes the extensions of the proposed DPWSDNet to other image compression standards as well as other image restoration problems.
6 Acknowledgment
This work was supported in part by the National Natural Science Foundation of China under Grant 61471248, in part by the Fundamental Research Funds for the Central Universities under Grant 2012017yjsy159, and in part by the China Scholarship Council under Grant 201706240037. The authors thank Cheolhong An and Wenshu Zhan for helpful discussions.
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