The existing infrared target detection algorithm in compressive domain achieves obtain good performance with low required data storage, but have its own shortcomings. One shortcoming is the difficulty to estimate background parameters, which are sensitive to noise and complex background, the other is the high false dismissal probability when targets are close to their neighbors. Considering those shortcomings, an infrared small target detection algorithm in compressive domain based on self- adaptive parameter configuration and noise statistics is proposed. The original infrared image is projected on a sensing matrix to obtain the measurement vector. The sparse target matrix and the low-rank background matrix can be recovered and separated simultaneously from the measurements based on low- rank and sparse matrix decomposition in compressive domain with adaptive parameter. The infrared small target detection is realized by threshold segmentation of statistical model of noise. Results indicate that the proposed method outperforms the previous method in both subjective and objective qualities under complex infrared background with less data storage, and solves the false dismissal probability problem when targets are close to their neighbors.