# Deep-Learning Steganalysis for Removing Document Images on the Basis of Geometric Median Pruning

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## Abstract

**:**

## 1. Introduction

## 2. Related Technologies

#### 2.1. Active Steganalysis

#### 2.2. Pruning Methods

## 3. Deep-Learning Steganography Removal Model

#### 3.1. DnCNN Model

#### 3.2. HGD Model

## 4. Methods

#### 4.1. Pruning Strategy for the Deep-Learning Steganography Removal Model

#### 4.2. Geometric Median Pruning

#### 4.3. Overall Iterative Pruning of Deep-Learning Steganography Removal Model Based on Geometric Median

Algorithm 1 Pruning the deep-learning steganography removal model via geometric median |

1: Prepare the pre-trained DnCNN and HGD models; |

2: Calculate geometric median on all filters ${\mathrm{F}}_{i,j}$ of a convolutional layer in the deep-learning steganography removal model, as in Formula (2), find the data center point f of filters in the convolutional layer; |

3: Filters ${F}_{i,{j}^{\prime}}$ that have redundant information are closed to the geometric median according to Formula (3). We prune these redundant filters to achieve the purpose of pruning, while maintaining the performance of the models; |

4: Prune a filter in a convolution layer, which will affect the kernel matrix and corresponding feature map channels in the next convolutional layer, As analyzed in 4.1. Therefore, it is necessary to remove the number of feature maps channels and corresponding weights involved in pruning. and to match the number of input and output channels of the relevant convolution layer; |

5: Retain the remaining kernel matrix after removing filters of one convolution layer of the deep-learning steganography removal model, complete a filter pruning operation based on geometric median. |

Algorithm 2 Iterative pruning process of the deep-learning steganography removal model |

1: Input: Prepare the pre-trained DnCNN and HGD models; |

2: Initialization: Set m pruning layers; set the maximum channels pruning rate r; set the channels iteration pruning rate p of the deep-learning steganography removal model. According to the maximum channels pruning rate and channels iterative pruning rate, set the number of iterative pruning channels of each convolutional layer, $\mathrm{C}=\left({c}_{1},{c}_{2},\cdots {c}_{n}\right),n=\frac{1}{p},0\le c\le \mathrm{channel}\times \mathrm{r}$; |

3: Conditions: Set the DIQA threshold while ensuring the image quality, that is, SSIM > 0.9 for the original image and purified image, SSIM > 0.9 for the stego image and purified image, PSNR > 26 for the original image and purified image, PSNR > 26 for the stego image and purified image; |

4: for i = 1:m do for j in C do Call Algorithm 1 to perform a geometric median pruning; Verify the network after each pruning. If the network after pruning meets the DIQA threshold and image-quality assessment, we should prune more channels for this convolutional layer. If the network after pruning does not meet the DIQA threshold and image-quality assessment, jump out of this layer loop, determine the final pruning result of the convolutional layer, save the pruning model and start pruning of the next convolutional layer; end end |

5: Output: The pruned models. |

#### 4.4. ABC Automatic Pruning of Deep-Learning Steganography Removal Model Based on Geometric Median

**Nectar sources**: Its value is composed of many factors, such as the amount of nectar, the distance from the hive and the difficulty of obtaining nectar. The fitness of nectar source is used to express the above factors;**Employed bees**: The number of employed bees and nectar sources is usually equal. Employed bees have memory function to store relevant information of a certain nectar source, including the distance, direction and abundance of nectar source and share this information with a certain probability to other bees;**Unemployed bees**: The responsibility of unemployed bees including onlooker bees and scout bees is to find the nectar source to be mined. Onlooker bees observe the swinging dance of the employed bees to obtain important nectar source information and choose the bees that they are satisfied with to follow. The number of onlooker bees and employed bees is equal. Scout bees that account for 5–20% of total bee colonies do not follow any other bees and randomly search for nectar sources around the hive.

#### 4.4.1. Initialization of Nectar Sources

#### 4.4.2. Search Process of Employed Bees

#### 4.4.3. Search Process of Onlooker Bees

#### 4.4.4. Search Process of Scout Bees

Algorithm 3 ABC automatic pruning of deep-learning steganography removal model based on geometric median |

1: Input: Prepare the pre-trained DnCNN and HGD models. |

2: Initialization: Set t pruning rounds; initialization of nectar sources according to Formula (4); set n pruning layers; maximum channel pruning $\phi $ of each convolutional layer of the model; maximum of poor quality of nectar source is $limit$; the number of iteration search for poor quality of nectar source is $trail$. |

3: Conditions: Set the DIQA threshold while ensuring the image quality, that is, SSIM > 0.9 for the original image and purified image, SSIM > 0.9 for the stego image and purified image, PSNR > 26 for the original image and purified image, PSNR > 26 for the stego image and purified image, params and flops as small as possible. Use the above conditions as the nectar source fitness value ${f}_{{\mathrm{X}}_{i}}$. |

4: for i = 1:t do for j = 1:D do The employed bee searches for a new nectar source ${\mathrm{X}}_{i}^{\prime}$ around the nectar source ${\mathrm{X}}_{i}$ through formula (5), and calls algorithm 1 to obtain the combinations of each convolutional layer channels of the model, and calculates the fitness value ${f}_{{\mathrm{X}}_{i}^{\prime}}$; if ${f}_{{\mathrm{X}}_{i}}<{f}_{{\mathrm{X}}_{i}^{\prime}}$ then ${\mathrm{X}}_{i}={\mathrm{X}}_{i}^{\prime};$ ${f}_{{\mathrm{X}}_{i}}={f}_{{\mathrm{X}}_{i}^{\prime}};$ $trai{l}_{i}=0;$ else $trai{l}_{i}=trai{l}_{i}+1;$ end for j = 1:D do Calculate the probability of nectar being selected through formula (6); Generate a random number ${\mathsf{\theta}}_{i}\in \left[0,1\right]$; if ${\mathsf{\theta}}_{i}<={\mathrm{P}}_{{\mathrm{X}}_{i}}$ then The employed bee searches for a new nectar source ${\mathrm{X}}_{i}^{\prime}$ around the nectar source ${\mathrm{X}}_{i}$ through formula (5), and calls algorithm 1 to obtain the combinations of each convolutional layer channels of the model, and calculates the fitness value ${f}_{{\mathrm{X}}_{i}^{\prime}}$; if ${f}_{{\mathrm{X}}_{i}}<{f}_{{\mathrm{X}}_{i}^{\prime}}$ then ${\mathrm{X}}_{i}={\mathrm{X}}_{i}^{\prime};$ ${f}_{{\mathrm{X}}_{i}}={f}_{{\mathrm{X}}_{i}^{\prime}};$ $trai{l}_{i}=0;$ else $trai{l}_{i}=trai{l}_{i}+1;$ end for j = 1:n do if $trai{l}_{i}>limit$ thenperform formula (7); end end |

5: endend Output: The pruned models. |

#### 4.5. Analysis of Algorithm

## 5. Experiments

#### 5.1. Experimental Preparation and Environment

#### 5.2. Results of Pruning Experiments

#### 5.2.1. Sensitivity Analysis of the Individual Pruning

#### 5.2.2. Analysis of the Overall, Iterative Pruning

#### 5.2.3. Analysis of the Overall Iterative Pruning Threshold

#### 5.2.4. Analysis of the ABC Automatic Pruning

#### 5.2.5. Analysis of Pruning Rate Based on the Geometric Median Pruning

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Deep-learning steganography removal model called the feed-forward denoising convolutional neural network (DnCNN).

**Figure 2.**Deep-learning steganography removal model called the high-level representation guided denoiser (HGD).

**Figure 5.**Sensitivity analysis of each convolutional layer of the DnCNN model based on geometric median pruning. (

**a**) peak signal-to-noise ratio (PSNR) value between the original image and the purified image of each convolutional layer pruning 0–90%, (

**b**) structural similarity index measure (SSIM) value between the original image and the purified image of each convolutional layer pruning 0–90%, (

**c**) PSNR value between the stego image and the purified image of each convolutional layer pruning 0–90%, (

**d**) SSIM value between the stego image and the purified image of each convolutional layer pruning 0–90%, (

**e**) document image-quality assessment (DIQA).

**Figure 6.**Sensitivity analysis of each convolutional layer of the HGD model based on geometric median pruning. (

**a**) PSNR value between the original image and the purified image of each convolutional layer pruning 0–90%, (

**b**) SSIM value between the original image and the purified image of each convolutional layer pruning 0–90%, (

**c**) PSNR value between the stego image and the purified image of each convolutional layer pruning 0–90%, (

**d**) SSIM value between the stego image and the purified image of each convolutional layer pruning 0–90%, (

**e**) DIQA.

**Figure 7.**Renderings after the geometric median pruning in the DnCNN model when DIQA is equal to 0.2. First column of figure represents the cover image, the second column represents the stego image, the third column represents the purified image, the fourth column represents the document image secret message, and the fifth column represents the document image after removing.

**Figure 8.**Renderings after the geometric median pruning in the HGD model when DIQA is equal to 0.2. First column of figure represents the cover image, the second column represents the stego image, the third column represents the purified image, the fourth column represents the document image secret message, and the fifth column represents the document image after removing.

**Figure 9.**Renderings after the geometric median pruning in the HGD model under each DIQA threshold. (

**a**) Model renderings when DIQA < 0.4; (

**b**) model renderings when DIQA < 0.6.

Model | Orig_Remove_SSIM | Orig_Remove_PSNR | Stego_Remove_SSIM | Stego_Remove_PSNR | DIQA | Params (M) | Flops (G) |
---|---|---|---|---|---|---|---|

DnCNN | 0.961 | 29,323 | 0.966 | 33,696 | 0.068 | 0.558 | 36,591 |

HGD | 0.978 | 31,618 | 0.963 | 30,868 | 0.069 | 11,034 | 50,937 |

**Table 2.**The corresponding relationship between the foraging behavior of ABC and the channel pruning problem of the deep-learning steganography removal model.

Foraging Behavior of ABC | Channel Pruning Problem of the Deep-Learning Steganography Removal Model |
---|---|

Nectar sources | The combinations of each convolutional layer channels of model. |

Quality of nectar sources | The quality of combinations is achieved by calculating the combination fitness value, that is, sets the DIQA threshold, SSIM > 0.9, PSNR > 26 and params and flops of the model as small as possible. |

Optimal quality of nectar sources | The params and flops of the model are the smallest and the image quality and document image quality are guaranteed. |

Pick nectar | Search the pruning structure of the model. |

**Table 3.**Geometric median pruning of each convolutional layer in the DnCNN model when the document image-quality assessment (DIQA) valve is equal to 0.2.

Prune | Orig_Remove_SSIM | Orig_Remove_PSNR | Stego_Remove_SSIM | Stego_Remove_PSNR | DIQA | Params (M) | Flops (G) |
---|---|---|---|---|---|---|---|

oralModel | 0.961 | 29,323 | 0.966 | 33,696 | 0.068 | 0.558 | 36,591 |

conv1_rm_44channels (70%) | 0.961 | 29,323 | 0.966 | 33,695 | 0.068 | 0.532 | 34,852 |

conv2_rm_38channels (60%) | 0.961 | 29,323 | 0.966 | 33,695 | 0.068 | 0.503 | 32,965 |

conv3_rm_50channels (80%) | 0.961 | 29,323 | 0.966 | 33,695 | 0.068 | 0.462 | 30,304 |

conv4_rm_50channels (80%) | 0.961 | 29,323 | 0.966 | 33,695 | 0.068 | 0.427 | 27,997 |

conv5_rm_38channels (60%) | 0.961 | 29,323 | 0.966 | 33,695 | 0.068 | 0.400 | 26,244 |

conv6_rm_50channels (80%) | 0.961 | 29,323 | 0.966 | 33,695 | 0.068 | 0.360 | 23,583 |

conv7_rm_50channels (80%) | 0.961 | 29,323 | 0.966 | 33,695 | 0.068 | 0.325 | 21,276 |

conv8_rm_50channels (80%) | 0.961 | 29,323 | 0.966 | 33,695 | 0.068 | 0.289 | 18,969 |

conv9_rm_44channels (70%) | 0.961 | 29,323 | 0.966 | 33,695 | 0.068 | 0.258 | 16,939 |

conv10_rm_31channels (50%) | 0.961 | 29,323 | 0.966 | 33,695 | 0.068 | 0.235 | 15,399 |

conv11_rm_31channels (50%) | 0.961 | 29,323 | 0.966 | 33,695 | 0.068 | 0.208 | 13,622 |

conv12_rm_38channels (60%) | 0.956 | 28,811 | 0.962 | 33,018 | 0.083 | 0.175 | 11,443 |

conv13_rm_38channels (60%) | 0.954 | 28,560 | 0.959 | 32,554 | 0.091 | 0.144 | 9420 |

conv14_rm_31channels (50%) | 0.954 | 28,548 | 0.957 | 32,497 | 0.092 | 0.119 | 7771 |

conv15_rm_31channels (50%) | 0.954 | 28,548 | 0.957 | 32,497 | 0.092 | 0.091 | 5993 |

conv16_rm_57channels (90%) | 0.954 | 28,548 | 0.957 | 32,497 | 0.092 | 0.073 | 4775 |

**Table 4.**Geometric median pruning of each convolutional layer in the HGD model when the DIQA valve is equal to 0.2.

Prune | Orig_Remove_SSIM | Orig_Remove_PSNR | Stego_Remove_SSIM | Stego_Remove_PSNR | DIQA | Params (M) | Flops (G) |
---|---|---|---|---|---|---|---|

oralModel | 0.978 | 31,618 | 0.963 | 30,868 | 0.069 | 11,034 | 50,937 |

conv1_rm_38channels (60%) | 0.978 | 31,618 | 0.963 | 30,868 | 0.069 | 11,011 | 49,430 |

conv2_rm_19channels (30%) | 0.963 | 29,368 | 0.966 | 31,257 | 0.090 | 10,974 | 48,060 |

conv3_rm_89channels (70%) | 0.963 | 29,368 | 0.966 | 31,257 | 0.090 | 10,835 | 45,787 |

conv4_rm_89channels (70%) | 0.963 | 29,368 | 0.966 | 31,257 | 0.090 | 10,701 | 43,593 |

conv5_rm_102channels (80%) | 0.958 | 28,823 | 0.978 | 35,270 | 0.159 | 10,312 | 40,115 |

conv6_rm_127channels (50%) | 0.958 | 28,823 | 0.978 | 35,270 | 0.159 | 9990 | 38,794 |

conv7_rm_178channels (70%) | 0.952 | 28,457 | 0.988 | 34,200 | 0.145 | 9373 | 36,266 |

conv8_rm_204channels (80%) | 0.952 | 28,457 | 0.988 | 34,200 | 0.145 | 8289 | 33,271 |

conv9_rm_230channels (90%) | 0.952 | 28,654 | 0.987 | 34,693 | 0.175 | 7651 | 32,618 |

conv10_rm_230channels (90%) | 0.952 | 28,495 | 0.988 | 35,965 | 0.132 | 7067 | 32,020 |

conv11_rm_230channels (90%) | 0.949 | 27,910 | 0.988 | 35,346 | 0.172 | 5953 | 31,286 |

conv12_rm_230channels (90%) | 0.943 | 26,070 | 0.988 | 30,255 | 0.128 | 5369 | 31,136 |

conv13_rm_230channels (90%) | 0.950 | 28,292 | 0.991 | 37,972 | 0.144 | 4784 | 30,987 |

conv14_rm_230channels (90%) | 0.950 | 28,076 | 0.987 | 36,073 | 0.184 | 4200 | 30,427 |

conv15_rm_230channels (90%) | 0.951 | 28,334 | 0.987 | 36,249 | 0.137 | 3562 | 29,774 |

conv16_rm_230channels (90%) | 0.949 | 28,031 | 0.990 | 36,867 | 0.155 | 2978 | 29,176 |

conv17_rm_102channels (40%) | 0.949 | 28,041 | 0.990 | 36,803 | 0.154 | 2719 | 28,184 |

conv18_rm_153channels (60%) | 0.949 | 28,041 | 0.990 | 36,803 | 0.154 | 2082 | 25,577 |

conv19_rm_178channels (70%) | 0.949 | 28,041 | 0.990 | 36,803 | 0.154 | 1507 | 23,220 |

conv20_rm_153channels (60%) | 0.949 | 28,041 | 0.990 | 36,803 | 0.154 | 1223 | 19,863 |

conv21_rm_89channels (70%) | 0.949 | 28,041 | 0.990 | 36,803 | 0.154 | 1017 | 16,488 |

conv22_rm_102channels (80%) | 0.949 | 28,041 | 0.990 | 36,803 | 0.154 | 0.863 | 13,973 |

conv23_rm_102channels (80%) | 0.949 | 28,041 | 0.990 | 36,803 | 0.154 | 0.781 | 9654 |

conv24_rm_38channels (60%) | 0.948 | 27,994 | 0.990 | 36,519 | 0.160 | 0.734 | 6623 |

conv25_rm_57channels (90%) | 0.948 | 27,994 | 0.990 | 36,519 | 0.160 | 0.721 | 5731 |

Model | Orig_Remove_SSIM | Orig_Remove_PSNR | Stego_Remove_SSIM | Stego_Remove_PSNR | DIQA | Params (M) | Flops (G) |
---|---|---|---|---|---|---|---|

oralModel | 0.961 | 29,323 | 0.966 | 33,696 | 0.068 | 0.558 | 36,591 |

DIQA < 0.2 | 0.954 | 28,548 | 0.957 | 32,497 | 0.092 | 0.073 | 4775 |

DIQA < 0.4 | 0.954 | 28,548 | 0.957 | 32,497 | 0.092 | 0.073 | 4775 |

DIQA < 0.6 | 0.954 | 28,548 | 0.957 | 32,497 | 0.092 | 0.073 | 4775 |

Model | Orig_Remove_SSIM | Orig_Remove_PSNR | Stego_Remove_SSIM | Stego_Remove_PSNR | DIQA | Params (M) | Flops (G) |
---|---|---|---|---|---|---|---|

oralModel | 0.978 | 31,618 | 0.963 | 30,868 | 0.069 | 11,034 | 50,937 |

DIQA < 0.2 | 0.948 | 27,994 | 0.990 | 36,519 | 0.160 | 0.721 | 5731 |

DIQA < 0.4 | 0.953 | 27,925 | 0.981 | 33,609 | 0.321 | 0.603 | 4349 |

DIQA < 0.6 | 0.946 | 27,296 | 0.990 | 33,878 | 0.275 | 0.758 | 5642 |

**Table 7.**Optimal nectar source of ABC automatic pruning under the condition of DIQA threshold and maximum channel pruning φ of the convolutional layer of DnCNN model.

Threshold | $\mathsf{\phi}$ | Nectar Source |
---|---|---|

DIQA < 0.2 | 9 | [7, 6, 7, 8, 5, 8, 7, 8, 7, 5, 4, 4, 4, 4, 4, 3] |

6 | [4, 6, 6, 5, 5, 5, 5, 4, 6, 5, 5, 5, 5, 4, 5, 4] | |

DIQA < 0.4 | 9 | [7, 6, 8, 8, 6, 8, 7, 7, 7, 3, 5, 6, 3, 5, 5, 2] |

6 | [6, 6, 6, 6, 6, 4, 6, 5, 4, 5, 5, 6, 4, 4, 5, 2] | |

DIQA < 0.6 | 9 | [7, 6, 7, 7, 5, 6, 3, 8, 5, 4, 3, 6, 6, 4, 4, 3] |

6 | [3, 5, 5, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 4, 5, 4] |

**Table 8.**Optimal nectar source of ABC automatic pruning under the condition of DIQA threshold and maximum channel pruning φ of the convolutional layer of HGD model.

Threshold | $\mathsf{\phi}$ | Nectar Source |
---|---|---|

DIQA < 0.2 | 9 | [5, 2, 3, 4, 7, 4, 9, 5, 9, 8, 7, 2, 5, 4, 4, 5, 3, 5, 7, 5, 7, 8, 6, 6, 1] |

6 | [2, 2, 6, 5, 6, 6, 6, 5, 6, 6, 6, 6, 6, 3, 3, 6, 3, 2, 6, 3, 6, 6, 3, 5, 2] | |

DIQA < 0.4 | 9 | [6, 2, 9, 3, 9, 4, 7, 4, 9, 5, 9, 7, 2, 2, 9, 7, 3, 8, 3, 3, 5, 8, 4, 5, 4] |

6 | [4, 2, 6, 6, 5, 3, 5, 6, 6, 6, 6, 6, 5, 6, 6, 6, 3, 6, 6, 6, 6, 1, 5, 4, 4] | |

DIQA < 0.6 | 9 | [3, 3, 7, 7, 6, 5, 9, 9, 9, 4, 3, 9, 4, 7, 9, 8, 3, 4, 4, 6, 3, 7, 5, 7, 2] |

6 | [3, 4, 6, 4, 6, 6, 6, 4, 2, 4, 5, 4, 6, 2, 4, 6, 3, 6, 4, 4, 6, 4, 3, 6, 2] |

**Table 9.**Analysis of ABC pruning under the conditions of DIQA threshold and maximum channel pruning φ of the convolutional layer of the DnCNN model.

Threshold | $\mathsf{\phi}$ | Orig_Remove_SSIM | Orig_Remove_PSNR | Stego_Remove_SSIM | Stego_Remove_PSNR | DIQA | Params (M) | Flops (G) |
---|---|---|---|---|---|---|---|---|

oralModel $\mathsf{\phi}=9$ | 0.961 | 29,323 | 0.966 | 33,696 | 0.068 | 0.558 | 36,591 | |

DIQA < 0.2 | 9 | 0.944 | 27,499 | 0.956 | 31,491 | 0.061 | 0.116 | 7626 |

6 | 0.960 | 29,291 | 0.965 | 33,586 | 0.066 | 0.136 | 8900 | |

DIQA < 0.4 | 9 | 0.955 | 28,797 | 0.960 | 32,940 | 0.084 | 0.104 | 6807 |

6 | 0.956 | 28,788 | 0.962 | 32,930 | 0.077 | 0.141 | 9264 | |

DIQA < 0.6 | 9 | 0.938 | 26,901 | 0.950 | 30,541 | 0.131 | 0.131 | 8565 |

6 | 0.954 | 28,560 | 0.959 | 32,556 | 0.091 | 0.133 | 8709 |

**Table 10.**Analysis of ABC pruning under the conditions of DIQA threshold and maximum channel pruning φ of the convolutional layer of the HGD model.

Threshold | $\mathsf{\phi}$ | Orig_Remove_SSIM | Orig_Remove_PSNR | Stego_Remove_SSIM | Stego_Remove_PSNR | DIQA | Params (M) | Flops (G) |
---|---|---|---|---|---|---|---|---|

oralModel $\mathsf{\phi}=9$ | 0.978 | 31,618 | 0.963 | 30,868 | 0.069 | 11,034 | 50,937 | |

DIQA < 0.2 | 9 | 0.944 | 28,458 | 0.942 | 30,541 | 0.061 | 2261 | 10,723 |

6 | 0.957 | 28,420 | 0.995 | 35,815 | 0.105 | 2993 | 15,843 | |

DIQA < 0.4 | 9 | 0.955 | 27,726 | 0.985 | 34,092 | 0.385 | 1832 | 10,529 |

6 | 0.978 | 31,617 | 0.964 | 30,886 | 0.071 | 2312 | 13,967 | |

DIQA < 0.6 | 9 | 0.949 | 28,044 | 0.985 | 34,651 | 0.398 | 1556 | 10,451 |

6 | 0.953 | 28,291 | 0.993 | 38,681 | 0.582 | 3329 | 14,303 |

**Table 11.**Analysis of pruning rate under the conditions of DIQA threshold and maximum channel pruning φ of the convolutional layer of the DnCNN model based on geometric median.

Model | Threshold | $\mathsf{\phi}$ | Channels | Pruned | Params (M) | Pruned | Flops (G) | Pruned |
---|---|---|---|---|---|---|---|---|

oralModel | 9 | 1030 | 0% | 0.558 | 0% | 36,591 | 0% | |

overall iterative pruning | DIQA < 0.2 | 9 | 359 | 65.14% | 0.073 | 86.92% | 4775 | 86.95% |

DIQA < 0.4 | 9 | 359 | 65.14% | 0.073 | 86.92% | 4775 | 86.95% | |

DIQA < 0.6 | 9 | 359 | 65.14% | 0.073 | 86.92% | 4775 | 86.95% | |

ABC pruning | DIQA < 0.2 | 9 | 455 | 55.83% | 0.116 | 79.21% | 7626 | 79.16% |

6 | 515 | 50.00% | 0.136 | 75.63% | 8900 | 75.68% | ||

DIQA < 0.4 | 9 | 441 | 57.18% | 0.104 | 81.36% | 6807 | 81.40% | |

6 | 524 | 49.13% | 0.141 | 74.73% | 9264 | 74.68% | ||

DIQA < 0.6 | 9 | 499 | 51.55% | 0.131 | 76.52% | 8565 | 76.59% | |

6 | 511 | 50.39% | 0.133 | 76.16% | 8709 | 76.20% |

**Table 12.**Analysis of pruning rate under the conditions of DIQA threshold and maximum channel pruning φ of the convolutional layer of the HGD model based on geometric median.

Model | Threshold | $\mathsf{\phi}$ | Channels | Pruned | Params (M) | Pruned | Flops (G) | Pruned |
---|---|---|---|---|---|---|---|---|

oralModel | 9 | 4870 | 0% | 11,034 | 0% | 50,937 | 0% | |

overall iterative pruning | DIQA < 0.2 | 9 | 1210 | 75.15% | 0.721 | 93.47% | 5731 | 88.75% |

DIQA < 0.4 | 9 | 1134 | 76.71% | 0.603 | 94.54% | 4349 | 91.46% | |

DIQA < 0.6 | 9 | 1263 | 74.07% | 0.758 | 93.13% | 5642 | 88.92% | |

ABC pruning | DIQA < 0.2 | 9 | 2242 | 53.96% | 2261 | 79.51% | 10,723 | 78.95% |

6 | 2536 | 47.93% | 2993 | 72.87% | 15,843 | 68.90% | ||

DIQA < 0.4 | 9 | 2185 | 55.13% | 1832 | 83.40% | 10,529 | 79.33% | |

6 | 2324 | 52.28% | 2312 | 79.05% | 13,967 | 72.58% | ||

DIQA < 0.6 | 9 | 1906 | 60.86% | 1556 | 85.90% | 10,451 | 79.48% | |

6 | 2725 | 44.05% | 3329 | 69.83% | 14,303 | 71.92% |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhong, S.; Weng, W.; Chen, K.; Lai, J.
Deep-Learning Steganalysis for Removing Document Images on the Basis of Geometric Median Pruning. *Symmetry* **2020**, *12*, 1426.
https://doi.org/10.3390/sym12091426

**AMA Style**

Zhong S, Weng W, Chen K, Lai J.
Deep-Learning Steganalysis for Removing Document Images on the Basis of Geometric Median Pruning. *Symmetry*. 2020; 12(9):1426.
https://doi.org/10.3390/sym12091426

**Chicago/Turabian Style**

Zhong, Shangping, Wude Weng, Kaizhi Chen, and Jianhua Lai.
2020. "Deep-Learning Steganalysis for Removing Document Images on the Basis of Geometric Median Pruning" *Symmetry* 12, no. 9: 1426.
https://doi.org/10.3390/sym12091426