IMNN-LWEC: A Novel Infrared Small Target Detection Based on Spatial–Temporal Tensor Model

Despite that many state-of-the-art methods have been proposed for infrared (IR) small target detection, target detectability (TD) and background suppressibility (BS) cannot be significantly improved simultaneously, especially in complex situations. This article proposes a novel IR small target detection method named improved multimode nuclear norm joint local weighted entropy contrast (IMNN-LWEC), which represents the IR target detection task as an optimization problem for tensor decomposition of three components in the spatial–temporal domain, including background tensor, target tensor, and sparse structure tensor. First, to utilize the spatial and temporal information in an IR sequence effectively, we transform the original IR sequence into a nonoverlapping spatial–temporal patch tensor. Second, a nonconvex approximation of tensor rank called improved multimode weighted tensor nuclear norm (IMWTNN) is proposed to estimate background tensor rank, which is of benefit to separate the background component more completely from the original image. Third, based on the structure tensor theory, we introduce a new sparse prior map called LWEC via a designed image entropy operator and a new prior information filter, which can further preserve the target and suppress the background simultaneously. Besides, a novel tubewise sparse regularization term is designed to identify linear sparse structures. The Frobenius norm is used to characterize noise. Finally, to solve the proposed model, an efficient optimization scheme utilizing the alternating direction method of multipliers (ADMM) is designed to retrieve the small targets. Comprehensive experiments on five datasets witness the superior TD and BS performance of the proposed method compared with nine state-of-the-art detection methods.