  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.
