## 4 Network Model Pruning with L1 Norm Criterion  
Improved SSD with deconvolution can improve the ability of small objects detection. However, there is a sharp increase of the network model size and calculation load. The network model size can be decreased with weight parameters pruning. In this paper, the SSD network is pruned with the L1 norm criterion of the convolution kernels. The pruned network weights are used as initial parameters for fine tuning. Through this, the model size and calculation load of the improved SSD network can be greatly reduced without an obvious loss of accuracy. The convolution operation can be expressed as Equation (4):  
\[g(i,j)= \sum_{k,l}f(i+k,j+l)h(k,l) \tag{4}\]  
where \(g(i,j)\) is the value of each pixel in the output feature map; \(f(i+k,j+l)\) is each pixel value in the input feature map; and \(h(k,l)\) is the convolution kernel value. When the convolution kernel slides over the whole image, the image convolution is essentially the sum of the product of the convolution kernel and the corresponding pixels of the coverage area. In this paper, \(L_{1}(F_{j})\) is the L1 norm of each convolution kernel \(F_{j}\). It is considered that the convolution kernels with a smaller L1 norm have less influence on the network model and belong to redundant convolution kernels. The convolution kernels with a smaller L1 norm are pruned after sorting all L1 norms of each convolution kernel. The pruned  
Figure 5: Improved SSD network. FF2, FF1, Conv7, Conv8_2, Conv9_2, Conv10_2 and Conv11_2 are used to extract the default boxes. By deconvolution and feature fusion, the detection ability of the SSD network for small objects is improved. network is retrained to ensure its accuracy. The L1 norm of the convolution kernel can be defined as Formula (5):  
\[L_{1}(F_{j})=\sum_{i=1}^{n_{k}}\left(\sum_{s\in S}\left|F_{j}\right|\right) \tag{5}\]  
where \(F_{j}\) denotes the \(j\)th convolution kernel, \(s\) is the size of the convolution kernel, \(n_{k}\) denotes the dimension of the convolution kernels, and \(L_{1}(F_{j})\) is the L1 norm of \(F_{j}\). The process of pruning using the L1 norm criterion is shown in Figure 6. The original network is shown in Figure 6a. The input feature map H\({}_{0}\) with M\({}_{0}\) channels is convoluted with the M\({}_{1}\) convolution kernels to generate the feature map H\({}_{1}\) with M\({}_{1}\) channels. The feature map H\({}_{1}\) with M\({}_{1}\) channels is convoluted with the M\({}_{2}\) convolution kernels to generate the feature map H\({}_{2}\) with M\({}_{2}\) channels. The pruning process of the network structure is shown in Figure 6b. In the first convolution level, the m\({}_{1}\) convolution kernels are removed from M\({}_{1}\) by the L1 norm criterion. The input feature map H\({}_{0}\) with M\({}_{0}\) channels is convoluted with the (M\({}_{1}\)-m\({}_{1}\)) convolution kernels to generate the feature map H\({}_{1}\)' with (M\({}_{1}\)-m\({}_{1}\)) channels. In the second convolution level, the m\({}_{2}\) convolution kernels are removed from the M\({}_{2}\) kernels. The feature map H\({}_{1}\)' with (M\({}_{1}\)-m\({}_{1}\)) channels is convoluted with the (M\({}_{2}\)-m\({}_{2}\)) convolution kernels to generate the feature map H\({}_{2}\)' with (M\({}_{2}\)-m\({}_{2}\)) channels. The procedure of the improved SSD network pruning is as follows:  
1. For each layer, the L1 norm of each convolution kernel is sorted from small to large. The convolution kernels with a smaller L1 norm are pruned. After pruning, the channels of the feature map will be reduced. Therefore, the convolution kernels of the next level should also be pruned. 2. The pruned network weight is used as an initial parameter for fine-tuning. During the fine-tuning phase, the pre-VGG network structure is firstly frozen. The convolution layers after VGG are fine-tuned until their accuracy is stable. Then, the pre-VGG network is fine-tuned. This method can reduce the loss of network accuracy as much as possible. 3.