Infrared small target and background separation via column-wise weighted robust principal component analysis

• WIPI model incorporates structural prior into the target-background separation.
• Weight is adaptive for each column in patch-image according to its patch structure.
• The adaptive weight for each column is designed based on the steering kernel.
• To solve the CWPRCA problem, an algorithm is developed based on ADM.

When facing extremely complex infrared background, due to the defect of l1l1 norm based sparsity measure, the state-of-the-art infrared patch-image (IPI) model would be in a dilemma where either the dim targets are over-shrinked in the separation or the strong cloud edges remains in the target image. In order to suppress the strong edges while preserving the dim targets, a weighted infrared patch-image (WIPI) model is proposed, incorporating structural prior information into the process of infrared small target and background separation. Instead of adopting a global weight, we allocate adaptive weight to each column of the target patch-image according to its patch structure. Then the proposed WIPI model is converted to a column-wise weighted robust principal component analysis (CWRPCA) problem. In addition, a target unlikelihood coefficient is designed based on the steering kernel, serving as the adaptive weight for each column. Finally, in order to solve the CWPRCA problem, a solution algorithm is developed based on Alternating Direction Method (ADM). Detailed experiment results demonstrate that the proposed method has a significant improvement over the other nine classical or state-of-the-art methods in terms of subjective visual quality, quantitative evaluation indexes and convergence rate.