Infrared dim small target detection is susceptible to interference from background clutter and edge structures, posing significant challenges to background suppression and target recognition. Therefore, we propose a structured regularization method named \(L_p\) -MCTV for infrared dim small target detection, which integrates the \(L_p\) -norm and minmax-concave total variation (MCTV) regularization to enhance detection performance. First, we decompose the input image into three main components: background, target, and noise, each corresponding to a specific image patch matrix. To effectively suppress the interference caused by complex backgrounds, we employ a partial sum minimization of singular values strategy to accurately estimate the background component. Meanwhile, we apply the \(L_p\) -norm regularization to extract the target signal, ensuring the integrity of the target information. Furthermore, we introduce the MCTV regularization to model the noise component, thereby enhancing the detection performance. Finally, the minimization problem associated with our detection model is tackled using the alternating direction method of multipliers. Experiments show that our method works well in different kinds of complex backgrounds. It can clearly improve the detection accuracy, achieving the highest SNRG values on four sequences, the best BSF performance on five sequences, and the highest AUC values of ROC curves on five sequences, outperforming compared methods.
