# LCAS-DetNet: A Ship Target Detection Network for Synthetic Aperture Radar Images
## 2 Methods
### Multi-Scale Cascade Feature Extractor  
The entire multi-scale cascade feature extractor consists of stacked MLCA blocks, as shown in Figure 4a. After passing through each MLCA block, the feature map of shape \((h,w,c)\) becomes \((\frac{h}{2},\frac{w}{2},2c)\). Through the cascading design, our feature extractor makes it possible for information to be passed and exchanged between different layers, combining features from different layers to produce richer and more complex feature representations, which enhances the network's representational and learning capabilities. In the SAR image ship detection task of this study, we obtain \(8\times\), \(16\times\), and \(32\times\) downsampled features from the multi-scale cascade feature extractor and pass them to the neck layer for feature fusion. **MLCA module**: It is the core of LCAS-DetNet, designed to handle the challenges posed by small targets and noise interference in the network. The MLCA module is a dual-branch structure, consisting of a local branch and a global branch, forming cross-attention, as shown in Figure 2. The feature of the input MLCA module is passed through layer normalization-convolution-GELU (NCG) to provide raw material for the two branches. NCG is a reusable module that ensures the learnability of the attention mechanism in feature maps using convolution, normalization, and GELU activation function, continuously updating the  
Figure 4: Different parts of the multi-scale cascade feature extractor. (**a**) The overall structure of the multi-scale cascade feature extractor. (**b**) The downsampling module. (**c**) The patch embedding module. Figure 3: Tensor shape changes in the global and local branches in Multi-Location Cross-Attention. relevance weights through backpropagation. Ensuring the nonlinear transformation of features while computing the relevance of different targets. Upon entering the branches, the feature map is serialized and undergo NCG to increase the dimensionality, serving as the input for the MLA block. After undergoing the transformation shown in Figure 4, the feature map generates attention maps for both global and local branches. The attention maps from both global and local branches are concatenated and then linearly integrated. Following the residual connection with the input, an output with attention is obtained. The network extracts multi-scale features and obtains multi-scale attention maps by vertically stacking MLCA blocks, enriching the network's receptive field. **Downsampling module**: It is an important part of the feature extractor and is designed to decrease the feature map size while retaining important information. It consists of four parts: Depthwise Separable Convolution (DWConv) [37], batch normalization [38], GELU activation function [39], and MaxPooling [40], as illustrated in Figure 4b. DWConv [37] is an advanced convolutional operation that integrates depthwise convolution with pointwise convolution; it significantly reduces the number of parameters while simultaneously enabling the extraction of both spatial and channel features. Batch normalization [38] adjusts the input values of the activation function to lie within a more responsive region, thereby increasing the gradient and mitigating the issue of gradient disappearance. The GELU [39] is a nonlinear activation function based on the Gaussian error, endowing the network with superior expressive and abstract capabilities. MaxPooling [40] reduces the spatial size of the feature map by half. **Patch embedding module**: It is a residual structure used for multi-scale localization of target ships. This module consists of an adaptive convolution, whose kernel size is the same as the patch size. It encodes the implicit local positions of the target ships in units of patches, as illustrated in Figure 4c. As the network deepens, the positional information from the upper layer is transmitted to the next layer through residual connections. Furthermore, in the network, the feature scale decreases layer by layer while the patch size remains unchanged.