# Research on Improved YOLO11 for Detecting Small Targets in Sonar Images Based on Data Enhancement
## 4 Experiment Results and Analysis  
### Experimental Results  
In this experiment, the sonar image dataset was collected and organized from tests on Wuhan Mulan Lake, comprising two categories: bottom-resting and suspended targets. It has 544 training images and 120 validation and test images each. The experiment ran on Windows 11 with an NVIDIA RTX 2000 Ada Generation Laptop GPU (24 GB VRAM), using the torch2.0.0+cu118 deep learning framework and Python3.10. First, ADA-StyleGAN3 was used to generate 450 images for each target type. These images were used to pre-train the SFE-YOLO network for 100 epochs with an initial learning rate of 0.01 and SGD momentum of 0.937. After pre-training, the real dataset was fine-tuned for 150 epochs with the same parameters based on the pre-trained weights. The specific experimental environment and configuration are shown in Table 1.  
The model was evaluated using Precision, Recall, F1-score curves, average precision (AP), mean average precision (mAP), and parameter count. Precision quantifies the proportion of true-positive predictions among all predicted instances. After setting an IoU threshold, the predicted bounding boxes are matched with the ground-truth boxes. A prediction is considered a true positive (TP) if the predicted bounding box meets the IoU threshold and the predicted category is correct. If the model predicts an object not present in the ground truth or assigns the wrong category, the prediction is considered a false positive (FP). Conversely, if a ground-truth object is not detected by the model, it is categorized as a false negative (FN). The definition of precision is expressed as Equation (14). The recall quantifies the proportion of correctly identified positive instances relative to the total number of actual positive samples. A higher recall value indicates that the model successfully detects a larger fraction of positive-class samples, thereby demonstrating superior detection performance. The calculation method is formally defined in Equation (15). The F1 score is a critical metric in classification tasks, serving as a comprehensive evaluation of a model's precision and completeness in detecting all targets. It harmonizes precision (accuracy of positive predictions) and recall (ability to identify all relevant instances), with values bounded between 0 (worst) and 1 (optimal). The calculation method is formally defined in Equation (16). Average Precision (AP) evaluates the model's performance for individual categories, while mean Average Precision (mAP) assesses its overall effectiveness across all categories. The mAP is computed as the arithmetic mean of AP values over all categories. Their calculation methods are formally defined in Equations (17) and (18), respectively. Finally, FPS measures the detection speed of algorithms. The \begin{table}
\begin{tabular}{c c} \hline \hline
**Project** & **Parameter Values** \\ \hline CPU & AMD Ryzen 9 7945 HX \\ GPU & NVIDIA RTX 2000 Ada \\ Operating system & Windows 11 \\ Programming language & Python v3.10 \\ Deep learning framework & Pytorch v2.0.0 \\ CUDA & v11.8 \\ Image size & 640 \(\times\) 640 \\ Learning rate & 0.01 \\ Momentum & 0.937 \\ Weight decay & 0.0005 \\ Batch size & 32 \\ Epoch & 150 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Table of computer configurations for model training. larger the FPS value, the faster the model detection speed and the better the real-time performance. The calculation method is shown in Equation (19). \[P=\frac{TP}{TP+FP} \tag{14}\]  
\[R=\frac{TP}{TP+FN} \tag{15}\]  
\[F1=2\times\frac{P\times R}{P+R} \tag{16}\]  
\[AP=\int_{0}^{1}P(r)dr \tag{17}\]  
\[mAP=\frac{1}{C}\sum_{i=1}^{C}AP_{i} \tag{18}\]  
\[FPS=\frac{1000}{\text{Pre}+Infer+Post} \tag{19}\]  
The proposed SFE-YOLO model was evaluated on a self-collected dataset to assess its performance. After 150 training epochs, the model achieved convergence.