Excellent performance, real time and strong robustness are three vital requirements for infrared small target detection. Unfortunately, many current state-of-the-art methods merely achieve one of the expectations when coping with highly complex scenes. In fact, a common problem is that real-time processing and great detection ability are difficult to coordinate. Therefore, to address this issue, a robust infrared patch-tensor model for detecting an infrared small target is proposed in this paper. On the basis of infrared patch-tensor (IPT) model, a novel nonconvex low-rank constraint named partial sum of tensor nuclear norm (PSTNN) joint weighted l1 norm was employed to efficiently suppress the background and preserve the target. Due to the deficiency of RIPT which would over-shrink the target with the possibility of disappearing, an improved local prior map simultaneously encoded with target-related and background-related information was introduced into the model. With the help of a reweighted scheme for enhancing the sparsity and high-efficiency version of tensor singular value decomposition (t-SVD), the total algorithm complexity and computation time can be reduced dramatically. Then, the decomposition of the target and background is transformed into a tensor robust principle component analysis problem (TRPCA), which can be efficiently solved by alternating direction method of multipliers (ADMM). A series of experiments substantiate the superiority of the proposed method beyond state-of-the-art baselines.

To improve the detection ability of infrared small targets in complex backgrounds, a novel method based on non-convex rank approximation minimization joint l2,1 norm (NRAM) was proposed. Due to the defects of the nuclear norm and l1 norm, the state-of-the-art infrared image-patch (IPI) model usually leaves background residuals in the target image. To fix this problem, a non-convex, tighter rank surrogate and weighted l1 norm are instead utilized, which can suppress the background better while preserving the target efficiently. Considering that many state-of-the-art methods are still unable to fully suppress sparse strong edges, the structured l2,1 norm was introduced to wipe out the strong residuals. Furthermore, with the help of exploiting the structured norm and tighter rank surrogate, the proposed model was more robust when facing various complex or blurry scenes. To solve this non-convex model, an efficient optimization algorithm based on alternating direction method of multipliers (ADMM) plus difference of convex (DC) programming was designed. Extensive experimental results illustrate that the proposed method not only shows superiority in background suppression and target enhancement, but also reduces the computational complexity compared with other baselines.

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