Feedback Band Group and Variation Low-Rank Sparse Model for Hyperspectral Image Anomaly Detection

For scenes with complex backgrounds and weak anomalies, how to effectively distinguish anomaly targets from the background is the key to perform hyperspectral image (HSI) anomaly detection (AD). Data decomposition-based methods have been widely studied due to their potential in separating background and anomaly components. However, due to its unclean background extraction and sensitivity to noise, it has an adverse effect on the detection of anomaly targets. In addition, a large amount of spectral data can lead to an increase in computation during data decomposition. To address this issue, we propose an AD method based on a feedback band group and variation low-rank (LR) sparse model (FBGVLRS-AD). First, we employ a uniform band selection (BS) strategy to partition spectral bands and perform data decomposition on the selected band group, to separate LR and sparse components. This decomposition on the band group can reduce computational time and mitigate the interference from spectral variability. Second, to preserve the integrity of abnormal target spectra during the background extraction process, the
${L}_{2,1}$
norm is employed for joint correlated total variation (TV) to extract the desired anomalous targets. Then, utilizing the detection information from the existing band groups, a feedback-driven iterative framework has been designed to consider the consistency and complementarity in AD across band groups. This framework facilitates the extraction of sparse components in the subsequent band groups and reinforces the anomalous elements. Iteratively addressing these subproblems on band groups helps prevent the loss of useful spectral information, maintaining sufficient anomaly information while reducing interference from redundant information and spectral variations. Finally, the proposed FBGVLR-AD is optimally solved by the augmented Lagrange multiplier (ALM) method. A comparison with state-of-the-art anomaly detectors on multiple data validates the competitiveness of the proposed method for AD tasks.