## 3 Proposed Method
### Batch Normalization Acceleration Layer  
The multi-objective classification network of remote sensing images designed in this paper is depth, which can fully learn the features of the image. However, as the network depth increases, the network convergence becomes more and more difficult, and the training speed becomes worse. Therefore, we design a batch normalization (BN) layer in the full convolution neural network. In this way, the input of each layer satisfies the same distribution, and can accelerate the convergence of the network. As the network deepens, the distribution of the activation input values gradually shifts, which causes the network to converge slowly. Through the batch normalization method, the distribution of the input values is transformed into a normal distribution, which the variance is 0, and the mean is 1. It avoids the gradient disappearance and the gradient dispersion problem. The normalized formula is:  
\[\hat{x}^{(k)}=\frac{x^{(k)}-E[x^{(k)}]}{\sqrt{Var[x^{(k)}]}}, \tag{1}\]  
Figure 4: Max-pooling indices and deconvolution up-sampling.  
where \(x\) represents the input vector of the network, \(E[x^{(k)}]\) represents the mean of the input, and \(Var[x^{(k)}]\) represents variance.  
The normalization operation can enhance the flow of backpropagation information and accelerate the convergence of the network. However, such a transformation can also lead to poor expression of the network, which is fatal for networks that need to learn complex features. In order to solve this problem, two adjustment parameters need to be added to each neuron. The inverse transformation of the transformed activation is used to restore the normalized data to a certain extent. The average value \(\mu_{B}\) and the variance \(\sigma_{B}{}^{2}\) are obtained for the batch as follows:  
\[\mu_{B}\leftarrow\frac{1}{m}{\sum_{i=1}^{m}x_{i}}, \tag{2}\]  
\[\sigma_{B}^{2}\leftarrow\frac{1}{m}{\sum_{i=1}^{m}{(x_{i}-\mu_{B})^{2}}}. \tag{3}\]  
Batch normalization:  
\[\hat{x}_{i}\leftarrow\frac{x_{i}-\mu_{B}}{\sqrt{\sigma_{B}^{2}+}}. \tag{4}\]  
Perform scale and translation transformations:  
\[y_{i}\leftarrow\gamma\hat{x}_{i}+\beta\equiv BN_{\gamma,\beta(x_{i})}, \tag{5}\]  
where \(x\) represents a mini-batch input value, and \(B\) represents the parameters that need to be learned. Then the normalization of the network input during the training process can be completed. After the trained model is obtained, the batch normalization of the test process is to obtain the mean and variance for the entire data set, which is different from the current batch used in the training process. During the training process, it is necessary to record the mean and variance of each batch and perform unbiased estimation as the basis for batch normalization in the testing process.  
The network convergence process can be significantly accelerated, followed by the batch normalization. The training time can be reduced. The network can use a large learning rate, and the classification performance of the network is improved to some extent. If the input scales of the layers in the network differ greatly, then the training of the network should be performed using a lower learning rate according to the barrel theory. After introducing the batch normalization layer, data can be normalized to the same scale, which allows for a larger learning rate. This makes the network less sensitive to the learning rate, and makes network parameters optimization easier. This method is convenient to obtain a better remote sensing image classification network.