Abstract: The traditional low-rank sparse decomposition model can not be applied directly to a single image for target detection. And it ignores the spatial structure of the target pixels leading to the detection accuracy is not high. Aiming at these two problems, a small target detection algorithm in a single foggy image based on low-rank and structured sparse is proposed. Firstly, the original fog image is preprocessed to obtain the fog patch image composed of local sub-images, and the problem of small target detection is transformed into low-rank and sparse decomposition problem. Then, considering the spatial structure of the target pixels, the structured sparsity-inducing norm is introduced into matrix decomposition of the fog patch image to constrain the target. Finally, the patch images which are obtained by matrix decomposition are post-processed to obtain the background image and the target image. The experimental results on single foggy images show that the proposed algorithm ensures the integrity of the small target detection and improves the detection accuracy.

Key words: small target detection, low-rank, structured sparse, inducing norm

摘要： 针对传统的低秩稀疏分解模型不能直接应用到单幅图像进行目标检测，且忽略了目标像素的空间结构性导致检测精度不高等问题，提出一种基于低秩和结构化稀疏的单幅大雾图像小目标检测算法。首先，对原始大雾图像进行预处理得到由局部子图像构成的大雾补片图像，将小目标检测问题转化为低秩和稀疏分解问题。然后，考虑到目标像素间的空间结构关系，在对大雾补片图像进行矩阵分解时，引入结构化稀疏诱导范数对目标进行约束。最后，将矩阵分解得到的补片图像进行后处理得到背景图像和目标图像。通过对单幅大雾图像实验仿真表明，所提算法确保了小目标检测的完整性并且提高了检测精度。

关键词: 小目标检测, 低秩, 结构化稀疏, 诱导范数