Learning Double Subspace Representation for Joint Hyperspectral Anomaly Detection and Noise Removal

Efforts to enhance the detection accuracy of hyperspectral (HS) anomaly detection (AD) have been significant, but the impact of noise resulting from HS data acquisition and transmission has not been well studied. Furthermore, the separation of denoising and subsequent interpretation makes it challenging to evaluate and control the influence of noise on the detection results. To this end, we proposed a joint AD and noise removal (ADNR) paradigm called DSR-ADNR, which develops a double subspace representation method to obtain both denoised and detection results simultaneously. DSR-ADNR uses a low-dimensional orthogonal basis to represent HS images and extract distinctive features for AD. The feature matrix is represented by a dictionary-based low-rank subspace that captures the complex nature of the low-dimensional features. In each iteration, DSR-ADNR utilizes the nonlocal self-similarity of the feature matrix to remove noise and improve intermediate detection performance. Meanwhile, the progressive LR representation of the background and anomalies for the feature matrix upgrades the explicit LR expression of nonlocal self-similar patches for better denoising. The well-designed linearized alternating direction method of multipliers with an adaptive penalty (LADMAP) is utilized to solve the proposed DSR-ADNR. Extensive experiments on simulated and real-world datasets demonstrate the effectiveness of DSR-ADNR in the HS AD task under different noise cases.