Graph Laplacian regularization for fast infrared small target detection

Existing low-rank methods usually introduce manifold learning to achieve good detection performance in complex scenes. However, these methods suffer from high computational complexity because they construct graph on each pixel or each patch of infrared image. To solve this problem, our graph is constructed from each frame of infrared sequence, which helps reduce the number of vertices in the graph. Moreover, our graph Laplacian regularization can describe the low-rank information across each frame of infrared sequence images. Therefore, we use graph Laplacian regularization instead of nuclear norm to describe the low-rank properties, which avoids singular value decomposition computation and reduces computational complexity. Then, we use Minimax Concave penalty function instead of l1 norm to describe the sparsity of targets. Finally, the proposed method is solved by alternating direction multiplier method. Experimental results demonstrate that the proposed method outperforms state-of-the-art methods in terms of detection ability and detection efficiency. •Different from usual graphs that are constructed on each pixel or patch of infrared image, we propose to construct the graph with each frame of infrared sequence.•The proposed graph construction approach can reduce the number of vertices in the graph, thereby decreasing computational complexity.•Based on the above graph construction, we propose a fast graph Laplacian regularization (FGLR). The proposed FGLR can describe the low-rank information between infrared sequence images.•Compared with nuclear norm, the proposed FGLR avoids singular value decomposition computation and has a closed-form solution for background estimation. Therefore, the proposed FGLR is more efficient than nuclear norm.•We use Minimax Concave penalty function instead of l1 norm to describe the sparsity of targets.•The proposed method is solved by alternating direction multiplier method.