Enhancing Hyperspectral Anomaly Detection by Difference-of-Convex Sparse Anomaly Modeling

Abstract

We propose a hyperspectral (HS) anomaly detection method using a novel characterization of anomalies. Among HS anomaly detection approaches, decomposition-based methods, which simultaneously estimate a background part and an anomaly part from an HS image, have attracted much attention. In these methods, various approaches have been proposed for mathematical modeling of the background part, but the anomaly part is mostly modeled by an ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -norm or an ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</inf> -norm. However, these norms have limited ability to promote the exact sparsity of the anomaly part, leading to detection failure. In this paper, we introduce a difference-of-convex (DC) approach to HS anomaly detection. First, we design a DC function that properly models the sparsity of the anomaly part. Next, we formulate a constrained DC optimization problem that decomposes a given HS image into the two parts and noise. Then, we develop an efficient solver for the problem based on the proximal linearized DC algorithm (PLDC) and the preconditioned primal-dual splitting method (P-PDS). Finally, we demonstrate the effectiveness of our method compared to state-of-the-art methods through experiments on several HS anomaly detection datasets.