# RETRACTED: Image Super-Resolution Algorithm Based on Dual-Channel Convolutional Neural Networks

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^{2}

^{3}

^{4}

^{5}

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

#### 2.1. The SCRNN Model

#### 2.2. Image Super-Resolution Algorithm Based on Dual-Channel Convolutional Neural Networks

## 3. Dual-Channel Convolutional Neural Networks

#### 3.1. The Improved Ideas

#### 3.2. The Network Structure of DCCNN

#### 3.3. Residual Blocks and Long-Term and Short-Term Memory Block

**X**and

_{l}**X**represent the input and output vectors of residual blocks, respectively. The function F(X) denotes residual mapping. The residual block in this paper contained only the convolutional layer and the ReLU layer. The modified linear unit (ReLU) has unilateral suppression and sparsity. In most cases, the ReLU gradient is a constant term, avoiding the problem of gradient disappearance to a certain extent. The relevant mathematical expression can be expressed by Equation (2):

_{l}_{+1}**x**is the input signal of the ith layer, and a

_{i}_{i}is the coefficient of the negative part. In Equation (3), the parameter a

_{i}is set to zero, but the negative part of PReLU can be learned. Finally, the output of the activation function can be expressed by Equation (4):

_{l}is the final output feature graph and B

_{l}is the offset of the lth layer.

**B**) were used to synthesize the long-term and short-term memory block for the up-sampling feature space at the beginning of reconstruction. The design of the long-term and short-term memory block was inspired by He et al. [31], who proposed a very deep persistent MemNet. The construction of our long-term and short-term memory blocks is presented in Figure 4.

_{1}, B_{2}, B_{3}**x**of the up-sampling phase as input; the residual block B

_{i}can be expressed by Equation (5):

**B**,

_{1}**B**, and

_{2}**B**, respectively represent the output of the corresponding residual block. When i = 1,

_{3}**B**=

_{i}_{−1}**x**. F represents the residual mapping, and

**w**represents the weight vector of the residual block to learn. Since each residual block consists of two volume layers and ReLU activation functions, Equation (5) can be further expressed as Equation (6):

_{i}**w**

**and**

^{1}**w**

**are the two weight vectors of the volume layer, respectively. In the interest of simplicity, the bias is omitted in the above equations.**

^{2}**B**represents the final output and passes to the next layer.

_{out}#### 3.4. Loss Function and Evaluation Standard

_{i}, b

_{i}}. For a group of real high-resolution images X

_{j}and a group of super-resolution images, F

^{j}(Y; Θ), is reconstructed by the network. This paper uses MSE as the cost function:

_{d}(Θ) and L

_{s}(Θ) are the loss costs of the deep channel and shallow channel respectively. The network uses the Adam optimization method and back-propagation algorithm [38] to minimize MSE in order to adjust the network parameters, and the update process of the network weights is as in Equation (10):

_{k}represents the updating value of the last weight, l represents the number of layers of the network, and k represents the number of iterations from the network; η is the learning rate,

**W**represents the weight of the kth iteration in level l, $\frac{\partial L}{\partial {W}_{k}^{l}}$ represents the corresponding weight of the cost function and derivation of the derivative. The weights are randomly initialized according to a Gaussian distribution with mean value of zero and variance of 0.001. The model can automatically adjust the learning rate in the range of training, making the learning of the parameters more stable.

^{l}_{k}^{n}− 1)

^{2}is the signal maximum square, and n is the number of bits per sampling value.

_{X}and μ

_{Y}are represented by X and Y, respectively, while σ

_{X}and σ

_{Y}represent the variances of the super-resolution image and of the original high-resolution image, respectively, and σ

_{XY}represents the covariance of the super-resolution image and the original high-resolution image. C

_{1}, C

_{2}, C

_{3}are constant terms. In order to avoid a zero in the denominator, the usual practice is to take C

_{1}= (K

_{1}× L)

^{2}, C

_{2}= (K

_{2}× L)

^{2}, C

_{3}= C

_{2}/2 and, generally, K

_{1}= 0.01, K

_{2}= 0.03, L = 255.

## 4. Experimental Results and Analysis

#### 4.1. Parameter Settings

_{i}, the experimental environment was Keras, and Python 3.5 and OpenCV 3.0 were applied to carry out the simulation experiments. The results of the network training were compared with those of existing methods in terms of three aspects: subjective visual effect, objective evaluation index, and efficiency comparison.

#### 4.2. Experimental Results and Comparative Analysis

#### 4.3. Efficiency Comparison

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The processing procedure of Super Resolution using Convolutional Neural Networks (SRCNN) construction.

**Figure 3.**The processing construction with improved residual blocks described in the paper. (

**a**) Original Residual Blocks; (

**b**) Improved Residual Blocks in the Paper.

**Table 1.**Average Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) at different reconstruction scales on Set5 and Set14 datasets.

Dataset | Reconstruction Multiple | Bicubic [5] | A+ [11] | SRCNN [18] | EEDS [20] | Proposed DCCNN |
---|---|---|---|---|---|---|

PSNR/SSIM | PSNR/SSIM | PSNR/SSIM | PSNR/SSIM | PSNR/SSIM | ||

Set5 | ×2 | 33.64/0.9296 | 36.55/0.9543 | 36.67/0.9541 | 37.30/0.9578 | 37.43/0.9603 |

×3 | 30.38/0.8681 | 32.57/0.9089 | 32.76/0.9091 | 33.46/0.9190 | 33.59/0.9204 | |

×4 | 28.41/0.8106 | 30.29/0.8602 | 30.49/0.8627 | 31.15/0.8782 | 31.32/0.8842 | |

Set14 | ×2 | 30.23/0.8687 | 32.29/0.9058 | 32.43/0.9062 | 32.82/0.9104 | 32.95/0.9115 |

×3 | 27.54/0.7743 | 29.14/0.8187 | 29.29/0.8208 | 29.61/0.8283 | 29.70/0.8307 | |

×4 | 26.01/0.7028 | 27.31/0.7492 | 27.48/0.7502 | 27.81/0.7625 | 28.13/0.7696 |

Method | Feature Extraction/ms | Up-Sampling/ms | Reconstruction/ms | Shallow Channel/ms |
---|---|---|---|---|

EEDS | 38,015 | 4112 | 154,834 | 7265 |

DCCNN | 19,151 | 24,895 | 70,500 | 5231 |

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## Share and Cite

**MDPI and ACS Style**

Chen, Y.; Wang, J.; Chen, X.; Sangaiah, A.K.; Yang, K.; Cao, Z.
RETRACTED: Image Super-Resolution Algorithm Based on Dual-Channel Convolutional Neural Networks. *Appl. Sci.* **2019**, *9*, 2316.
https://doi.org/10.3390/app9112316

**AMA Style**

Chen Y, Wang J, Chen X, Sangaiah AK, Yang K, Cao Z.
RETRACTED: Image Super-Resolution Algorithm Based on Dual-Channel Convolutional Neural Networks. *Applied Sciences*. 2019; 9(11):2316.
https://doi.org/10.3390/app9112316

**Chicago/Turabian Style**

Chen, Yuantao, Jin Wang, Xi Chen, Arun Kumar Sangaiah, Kai Yang, and Zhouhong Cao.
2019. "RETRACTED: Image Super-Resolution Algorithm Based on Dual-Channel Convolutional Neural Networks" *Applied Sciences* 9, no. 11: 2316.
https://doi.org/10.3390/app9112316