Infrared Small Target Detection Using Spatiotemporal 4-D Tensor Train and Ring Unfolding

Infrared small target detection (ISTD) is vital for civil and military applications. However, existing methods often face challenges in coping with complex scenes, discriminating targets from similar objects, or leveraging temporal information effectively. To tackle these limitations, we offer an innovative approach that exploits the spatiotemporal structure of infrared images. A 4-D infrared tensor is initially constructed from a sequence of infrared images and decomposed into lower dimensional tensors using the tensor train (TT) and its extension—tensor ring (TR) techniques. The ISTD problem is then formulated as a sparse plus low-rank decomposition problem, where the sparse part is the target and the low-rank part is the background. We factorize the composed tensors into matrices via TT and TR unfolding approaches, which mitigates the imbalance between different modes containing spatial and temporal information. By constraining the balanced unfolded components with the weighted sum of nuclear norm, we solve the problem using the alternating direction multiplier method (ADMM). Furthermore, we validate models on several datasets and benchmark them with state-of-the-art techniques in detection accuracy and background suppression. Comparison results demonstrate the superiority of our approach over the existing methods. Moreover, the results of an ablation study with 3-D tensor structures show the effectiveness and feasibility of the dimension expansion to 4-D.