Joint Background–Anomaly–Noise Decomposition for Robust Hyperspectral Anomaly Detection via Constrained Convex Optimization

We propose a novel hyperspectral (HS) anomaly detection method that is robust to various types of noise. Most existing HS anomaly detection methods are designed without explicit consideration of noise or are based on the assumption of Gaussian noise. However, in real-world situations, observed HS images are often degraded by various types of noise, such as sparse noise and stripe noise, due to sensor failure or calibration errors, significantly affecting the detection performance. To address this problem, this article establishes a robust HS anomaly detection method with a mechanism that can properly remove mixed noise while separating background and anomaly parts. Specifically, we newly formulate a constrained convex optimization problem to decompose background and anomaly parts, and three types of noise from a given HS image. Then, we develop an efficient algorithm based on a preconditioned variant of a primal dual splitting method to solve this problem. Experimental results using seven real HS datasets demonstrate that the proposed method achieves detection accuracy comparable to state-of-the art methods on original images and exhibits significantly higher robustness in scenarios where various types of mixed noise are added.