Infrared small-target detection has attracted great interest in applications related to public safety, area monitoring, and various other fields. However, this task faces two challenges: 1) the diversity of background scenes leads to complexity of infrared content, and 2) the small size of targets results in limited available information. Most of methods mainly concentrate on modeling global features, overlooking the variations in local features due to complex scenes. To solve these problems, a single-frame infrared target detection method based on fast content-related modeling is proposed to combine global and local features of infrared images, describing the common features of varying scenes robustly and enhancing the distinction between targets and backgrounds. Specifically, we analyzed and integrated multidimensional global statistical characteristics to construct a weighted spatial sum of nuclear norm, achieving a comprehensive background modeling and mitigating complex background clutters. On the other hand, we incorporated local distribution priors generated by the target-constrained filter into the model to adaptively protect suspected target areas from suppression. Finally, we propose an efficient solving algorithm with stepwise reconstruction from seed images sampled from infrared images, enabling linear-time extraction of infrared small targets. Comparison experiments on SIRST, IRSTD-1k, NUDT-SIRST, and NUST-SIRST datasets indicate that the proposed method enhances detection accuracy and reduces detection time compared with state-of-the-art methods.