In order to improve the accuracy, resolution and computational efficiency of image salient object detection, a new salient object detection model is constructed by combining Schatten-$p$ norm and $l_{2,1}$-norm by using the relationship between image background space and image space. Compared with the traditional saliency object detection model based on the low-rank approximation of the nuclear norm, the new model considers the relationship between the image feature space and the background space, and the Schatten-$p$ norm can be better approximated by the low-rank function on numerical proportional than nuclear norm. For the matrix optimization problem of the new model, a fixed-point iterative algorithm is designed for solving the problem, and the feasibility is verified on the standard data sets of four salient object detection models, and the comparison experiments with four commonly used algorithms are also carried out. The experimental results verify that the algorithm has high computational efficiency and accuracy.