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

TL;DR

The paper tackles robust hyperspectral anomaly detection when images are corrupted by mixed noise, including sparse, stripe, and Gaussian components. It proposes a constrained convex formulation that simultaneously estimates background, anomalies, and three noise types, solved efficiently by a preconditioned primal-dual splitting method with operator-wise diagonal preconditioning. Key contributions include explicit noise modeling with hard constraints, dictionary-free background characterization via HTV/SSTV/HSSTV/Nuclear Norm, automatic stepsize selection, and a computationally efficient solver. Empirical results on six real HS datasets show competitive performance in clean data and markedly improved robustness under mixed-noise scenarios, highlighting practical impact for reliable HS anomaly detection without preprocessing.

Abstract

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 six 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.

Figures (9)

• Figure 1: Overview of the proposed method.
• Figure 2: Pseudocolor images and ground truths for each dataset.
• Figure 3: Resulting detection maps for Texas Coast, Gainesville, Los Angeles I, Los Angeles I I, and San Diego in Case 1 generated by all the detectors.
• Figure 4: Resulting detection maps for Pavia Centre in Case 1, 2, 3, 4, and 5 generated by all the detectors.
• Figure 5: 3D ROC curves of all the detectors for Pavia Centre in all cases.