Salient Object Detection Based on Unified Convex Surrogate for Non-Convex Schatten- $p$ Norm

Nuclear norm and
$l_{1}$
norm are the common regularization in salient object detection. However, existing literatures show that these terms either 1) are very slow for large scale problems due to singular value decomposition (SVD) on full matrix in every iteration, or 2) over-penalize the large singular values. In this paper, we propose to use respectively the non-convex weighted Schatten-
$p$
quasi-norm and
${l_{p}}$
-norm
$(0 < p < 1)$
for characterizing background and salient object. By matrix factorization, the optimization process, associated with the alternating direction method of multiplier (ADMM), is based on a unified convex surrogate which is only required to handle some small size matrices. Simultaneously, the convergence of algorithm is analyzed and validated. Experimental results indicate the new method usually outperform the state-of-the-art methods.