Unified Dynamic Dictionary and Projection Optimization With Full-Rank Representation for Hyperspectral Anomaly Detection

Hyperspectral anomaly detection (HAD) aims to classify each pixel in a hyperspectral image as either background or anomaly without requiring labeled data. Traditional reconstruction based methods model the background using a predefined static background dictionary and low-rank representation coefficients. However, when anomalies are present, the use of a static dictionary can lead to inaccurate background representation, which is easily disturbed by anomalous points. Moreover, existing methods typically focus on the low-rank and smooth characteristics of the background during reconstruction, overlooking deeper features of the background representation. This motivates us to reconsider how the background should be represented. To address these issues, we propose an innovative HAD method that integrates background dictionary learning into the anomaly decomposition process. By using projection operators to optimize the background dictionary, we overcome the limitations of traditional methods that rely on static dictionaries. In addition, we revisit the representation of the background and emphasize the importance of applying nonnegative full-rank constraint to the representation coefficients under the new background dictionary. These improvements result in a more accurate background representation, thereby enhancing anomaly detection performance. Experimental results on several hyperspectral datasets demonstrate that the proposed algorithm excels in anomaly detection tasks, offering new insights and approaches for HAD.