Moving Object Detection in Satellite Videos via Spatial–Temporal Tensor Model and Weighted Schatten p-Norm Minimization

Abstract

Low-rank matrix decomposition approaches have achieved significant progress in small and dim object detection in satellite videos. However, it is still challenging to achieve robust performance and fast processing under complex and highly heterogeneous backgrounds since satellite video data can neither adequately fit the foreground structure nor the background model in the existing matrix decomposition models. In this letter, we propose a novel object detection method based on a spatial–temporal tensor data structure. First, we construct a tensor data structure to exploit the inner spatial and temporal correlation within a satellite video. Second, we extend the decomposition formulation with bounded noise to achieve robust performance under complex backgrounds. This formulation integrates low-rank background, structured sparse foreground, and their noises into a tensor decomposition problem. For background separation, a weighted Schatten <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -norm is incorporated to provide adaptive threshold to obtain the singular value of the background tensor. Finally, the proposed model is solved using the alternative direction method of multipliers (ADMM) scheme. Experimental results on various real scenes demonstrate the superiority of the proposed method against the compared approaches.