# ISAR Imaging Analysis of Complex Aerial Targets Based on Deep Learning
## 3 CapsNet Assists ISAR Imaging
### A Radar ISAR Imaging System Based on CapsNet  
In 2011, [PERSON] put forward the concept of a capsule [16]. Distinct from the traditional scalar neurons, the capsule network constitutes a vector composed of numerous neurons. The vector length of the capsule neuron model indicates the probability of the existence of the target passed by the upper network, and its direction represents the actual state of the entity, namely, \"Instance parameters\", as depicted in Figure 2[17]. The dynamic routing algorithm (squash) solves the problem by the output value \(i\) of the capsule. The updated formula is as follows:  
\[c_{ij}=\frac{\exp(b_{ij})}{\sum_{k}\exp(b_{ik})} \tag{6}\]  
\[b_{ij}=b_{ij}+U_{i}\cdot V_{j} \tag{7}\]  
where \(c_{ij}\) is the dynamic routing coupling coefficient, and \(k\) is the number of initial similarity weights \(b_{ij}\). The capsule output \(S_{j}\) is obtained from the lower-level capsule inputs \(U_{i}\) and \(c_{ij}\):  
\[S_{j}=\sum_{i}c_{ij}U_{i} \tag{8}\]  
where \(U_{i}\) is derived from \(U_{i}=W_{ij}u_{i}\), \(W_{ij}\) is the weight of the capsule network. Figure 1: The spatial relationship between radar and target imaging. The output \(V_{j}\) should be expressed as a probability. Thus, the output value should be controlled for (0, 1], and can be obtained using nonlinear compression:  
\[V_{j}=\frac{\left|\left|S_{j}\right|\right|^{2}}{1+\left|\left|S_{j}\right| \right|^{2}}\times\frac{S_{j}}{\left|\left|S_{j}\right|\right|} \tag{9}\]  
The image is initially input into the convolutional layer, where a basic capsule layer is generated through the convolution operation. Subsequently, the data from the basic capsule layer are transmitted to the image via the dynamic routing algorithm (squash). The capsule layer then transfers the data from the image capsule layer to the feature capsule layer. Finally, a fully connected layer is employed to reorganize and model the data from the feature capsule layer. The structure of the CapsNet is illustrated in Figure 3.  
The contraction path comprises two convolutional layers: AKconv and GSconv. A max-pooling operation with a stride of 2 is employed to down-sample the feature map. Consequently, the number of feature channels is doubled, while the size of each layer's features is halved. The expansion path consists of up-sampling layers and convolutional layers, where the convolutional layers halve the number of feature channels and double the size of the features. Figure 3: Schematic diagram of the CapsNetv2 structure. Figure 2: Capsule neuron model. AKconv  
AKconv, or Alterable Kernel Convolution, is a convolution operation employed in convolutional neural networks, with the aim of addressing the inherent deficiencies in traditional convolutions. AKconv enables the arbitrary setting of convolution kernel parameters, and its size and shape can be freely adjusted in accordance with specific application requirements, thereby more accurately adapting to the target features of different scales. It introduces an innovative algorithm for determining the initial sampling positions for convolution kernels of various sizes, enhancing the adaptability of the network in handling targets of different sizes. It also adopts dynamic offset technology to adjust the sampling positions, achieving more accurate feature capture. GSconv  
GSconv (Grouped Spatial Convolution) is a convolution operation in convolutional neural networks that aims to tackle the inherent deficiencies of traditional convolutions. GSconv allows for the arbitrary setting of convolution kernel parameters and can freely adjust its size and shape in accordance with specific application requirements to adapt more accurately to the target features of different scales. It introduces an innovative algorithm for determining the initial sampling positions of convolution kernels of various sizes, enhancing the adaptability of the network in handling targets of different sizes.