# Image Forensics Using Non-Reducing Convolutional Neural Network for Consecutive Dual Operators
## 3 Framework of the Proposed CNN  
The CNN has proved its worthiness in many applications such as image classification, fake face detection, image forgery detection, etc. In this paper, a robust deep architecture is proposed to detect single and dual operators in the processed images. The proposed architecture is effective on both compressed and non-compressed images. The proposed CNN architecture can suppress the need for any preprocessing layer as used in some previous techniques [20,26]. In the previous techniques, exclusive preprocessing is required according to the operator, which is not feasible in a practical situation and restricted the network performance for particular operators. When two operations are applied simultaneously, the artifacts of the first operator can be diminished by the second operator. In Figure 4, some pairs of operators are considered to check the behavior of operations on the BOSSbase [30] image database. The normal distribution of image entropy is reflected in the plots. There is an overlap in some places for five possible cases of two operators, where the overlapping makes the problem challenging. The proposed architecture can resist the problem of operator sequence in a better way. The CNN contains multiple layers and filters to classify the input into their respective classes. The CNN parameters like weight and biases are updated as the network learns. The image input layer is followed by seven blocks and four layers in the proposed CNN. The block diagram of the proposed CNN is shown in Figure 5.  
Figure 4: Normal distribution of entropy after applying operator on the image set. Each block in the network has two convolutional layers, followed by the batch normalization (BN) layer and the ReLU layer. No padding is used in any layer of the proposed CNN to retain the maximum statistical information. The first convolution layer performs 1x1 point-wise convolution. The second convolution layer performs 3 \(\times\) 3 depth-wise convolution. In steganalysis [31], 1 \(\times\) 1 point-wise convolution improves the results when applied with a depth-wise convolution. The training parameters of the proposed seven CNN blocks are 113,728. However, training parameters become 175,680 while considering a 3 \(\times\) 3 size filter instead of a 1 \(\times\) 1 size filter in the first convolutional layer in each block. The computational complexity can reduce by using a 1 \(\times\) 1 filter and a 3 \(\times\) 3 filter, consecutively. The performance improvement is also noticed in experiments as shown in Figure 6. The detection accuracy using Conv 1 \(\times\) 1 is 92.47% and 91.37% for Conv 3 \(\times\) 3 in the first layer of each block for two operator sequences, where \(\alpha\) = GAU_1.0 & \(\beta\) = MF5 with JPEG compression Q1 = 85 & Q2 = 75. The training time using Conv 1 \(\times\) 1 is only one-third in comparison to Conv 3 \(\times\) 3 training time and also has an improvement in the detection accuracy. Therefore, there are two considerable benefits of following the bottleneck approach. Figure 5: Block diagram of proposed CNN. Figure 6: Analysis of Conv 1 \(\times\) 1 vs. Conv 3 \(\times\) 3. The abstract diagram of the bottleneck approach and internal detail of blocks can be observed in Figure 7. The first and second convolution layer contains 64 filters of size \(1\times 1\) and \(3\times 3\) in blocks 1 and 5. Equal numbers of filters are considered as filter size \(1\times 1\) in \(3\times 3\) convolutional layers for every particular block. Convolutional layers are utilized 32 filters in block 2, block 4, and block 6. Convolutional layers are utilized 16 filters in block 3 and block 7. The stride of one is considered in each convolution layer. The batch normalization (BN) layer is used to increase the training pace and decrease the sensitivity to network initialization. The BN layer can diminish the inner covariant shift [32]. The learning parameters are updated according to the mean and variance of a mini-batch.