Tensor Spectral k-Support Norm Minimization for Detecting Infrared Dim and Small Target Against Urban Backgrounds

In the low-altitude urban background with heavy interference, especially in the face of corner interference with higher intensity than the target, infrared (IR) dim and small target is extremely lack of prior information (i.e., size, shape, and contrast information). In such case, the existing detection methods usually suffer from high false alarm or even failure. To deal with this situation, we develop a novel spatial–temporal tensor model with tensor spectral
$k$
-support norm minimization (STTM-TSNM) for detecting IR dim and small target. First, the spatial–temporal information of the original image sequence can be preserved completely by constructing the holistic STTM. Then, according to the spatial–temporal related prior knowledge of the target and background, the target detection task is customized as an optimization problem of low-rank and sparse (LRS) tensor recovery. To better preserve the internal structure and capture more global information, the tensor spectral
$k$
-support norm minimization is introduced as the regularization term of the constraint background. Finally, draw support from the framework of alternating direction method of multipliers (ADMM) algorithm, the precise separation of target and background is achieved. In addition, to promote the prosperity of sequential detection methods, we released to the scientific community a small IR target dataset containing six image sequences with urban background. The experimental results on six real IR sequences demonstrate that our method outputs the most outstanding detection performance compared with the latest sequential detection methods.