In this paper, a new total generalized variational (TGV) model for restoring images with Cauchy noise is proposed, which contains a non-convex fidelity term and a TGV regularization term. In order to obtain a strictly convex model, we add an appropriate proximal term to the non-convex fidelity term. We prove that the solution of the proposed model exists and is unique. Due to the convexity of the proposed model and in order to get a convergent algorithm, we employ an alternating minimization algorithm to solve the proposed model. Finally, we demonstrate the performance of our scheme by numerical examples. Numerical results demonstrate that the proposed algorithm significantly outperforms some previous methods for Cauchy noise removal.

The paper proposes improvements to YOLOv8n to enhance small target detection capabilities and introduces coordinate attention (CA) to the C2f module to improve focus on spatial information and local details. CA enhances spatial feature representation and small object recognition and replaces Path Aggregation Network with Bidirectional Feature Pyramid Network (BiFPN) in the neck to better fuse multi-scale features. BiFPN enables more effective fusion of features at different scales and adds a smaller detection head to improve perception of very small targets. The additional detection head utilizes more shallow feature information and incorporates Omni-dimensional Dynamic Convolution (ODConv) to adaptively adjust convolution kernels. ODConv allows flexible capture of critical information for various target patterns and sizes. Experimental results show the proposed improvements lead to better performance on small object detection tasks, with increases in metrics like average precision mean (mAP), precision, and recall. The combined enhancements aim to address common challenges in small target detection such as low contrast, large-scale differences, and the need for fine-grained feature capture. Compared to the original YOLOv8n algorithm, this algorithm improves the average accuracy on small targets by 3.2% for mAP@50, 4.4% for mAP@75, 3% for Precision rate, and 4% for Recall.