Robust Hyperspectral Anomaly Detection with Simultaneous Mixed Noise Removal via Constrained Convex Optimization

Hyperspectral (HS) anomaly detection is the task of identifying pixels with spectral signatures that differ significantly from surrounding pixels. Most existing anomaly detection methods do not take into account the effect of noise in HS images, or if they do, it is only Gaussian noise. In practice, however, it is inevitable that non-Gaussian noise is superimposed on HS images due to sensor failure and/or calibration errors, resulting in considerable degradation of the detection performance of these methods. In this paper, we propose a method to achieve robust anomaly detection even when HS images contain various types of noise. Specifically, we newly formulate a constrained convex optimization problem that decomposes a given HS image into a background part, an anomaly part, and three types of noise. We also develop an efficient solver for the problem based on a preconditioned version of a primal-dual splitting algorithm, which can automatically determine the appropriate stepsizes. Experiments on HS datasets show that the proposed method 1) achieves state-of-the-art detection performance both in noise-free and noisy cases and 2) is much more robust against noise than existing methods.