Towards Robust Hyperspectral Anomaly Detection: Decomposing Background, Anomaly, and Mixed Noise via Convex Optimization

We propose a novel hyperspectral (HS) anomaly detection method that is robust to various types of noise. Most of existing HS anomaly detection methods are designed for cases where a given HS image is noise-free or is contaminated only by small 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. Through comparison with existing methods, including state-of-the-art ones, we illustrate that the proposed method achieves a detection accuracy comparable to state-of-the-art methods in noise-free cases and is significantly more robust than these methods in noisy cases.