4DST-BTMD: An Infrared Small Target Detection Method Based on 4-D Data-Sphered Space

Infrared (IR) small target detection is a crucial aspect in both military and civilian fields. Due to the poor quality and complex scenarios, the existing technologies lack superior real-time and overall detection performance. Tensor analysis has shown superiority, but there are three key issues. The first pertains to appropriate tensor-structured data, the second concerns a more comprehensive tensor decomposition architecture, and the third is to achieve more satisfactory real-time performance. This article proposes an IR small target detection method named 4-D spatial-temporal tensor decomposition with block term decomposition-based norm and multidirectional derivative-based priors (4DST-BTMD). It converts the target detection task into a low-rank and sparse decomposition (LRSD) optimization problem of decomposing background, target, and noise tensors from 4-D spatial-temporal domain. First, we construct a 4-D spatial-temporal tensor, followed by projecting it into a constructed data-sphered space, which lays the data foundation for decomposition. Then, based on the 4-D sphered tensor, a low-rank surrogate named block term decomposition-based norm (BTDN) for background estimation is proposed, which fully integrates global information across different dimensions. Meanwhile, more effective salient 4-D prior tensors based on multidirectional derivatives are designed to effectively guide the model to focus on significant areas. Finally, an efficient ADMM-based solving framework is designed for the LRSD model. Furthermore, with seven state-of-the-art competitive methods, extensive experiments and analysis illustrate that the proposed 4DST-BTMD not only demonstrates the superiority in background suppressibility (BS) and target detectability (TD) but also has satisfactory real-time detection performance.