The process of infrared images via computer-based algorithms for better application is a frontier field integrating physical technology with computer science. One of the key techniques in infrared image processing is the detection of infrared targets. This technique is extensively applied in security and defense systems and search and tracking systems. However, due to their small size, dim light and lack of texture, the detection of infrared targets is a technical problem. One strategy to address this problem is to transform the detection work into a non-convex optimization problem of recovering a low-rank matrix (background) and a sparse matrix (target) from a patch-image matrix (original image) based on IPI (infrared patch-image) model. When targets are clear and recognizable, the APG (accelerated proximal gradient) algorithm works effectively to solve it. However, when targets become much dimmer and are screened by the intricate texture of background, the experimental detection results degrade dramatically. In order to solve this problem, a novel method via IRNN (iteratively reweighted nuclear norm) is proposed in this paper. Experimental results show that under different complicated backgrounds, targets with higher SCRG (signal-to-clutter ratio gain) values and BSF (background suppression factor) values can be acquired through IRNN algorithm compared with the APG algorithm, which means that our method performs better.