A Model-Driven Deep Mixture Network for Robust Hyperspectral Anomaly Detection

Hyperspectral anomaly detection (HAD) aims to identify samples with unknown atypical spectra from the background. Deep learning (DL)-based methods, particularly autoencoders (AEs), have proven effective in uncovering the underlying profiles for HAD. However, in real-world applications of hyperspectral images (HSIs), complex background land covers and anomaly corruptions are common, leading to two issues: 1) a low-dimensional manifold characterized by DL-based HAD methods can only reveal a few underlying variation factors of the background distribution and cannot capture the complex structures behind land covers of all categories and 2) DL-based HAD methods trained on anomaly-contaminated HSIs tend to overfit specific anomalies, resulting in poor background characterization. To tackle these issues, this study presents a novel and robust framework for HAD called model-driven deep mixture network (MDMN) that combines the strengths of model-driven and data-driven approaches while emphasizing interpretability. By assuming that the background, consisting of various land-covers, arises from a mixture of low-dimensional manifolds, the MDMN incorporates a novel deep mixture module to comprehensively characterize the background. This module uses a low-dimensional manifold learned by an AE to represent a specific category of background land covers. To mitigate the impact of anomaly corruptions, the MDMN incorporates a convex relaxation of a sparse constraint, which helps prevent overfitting anomalies. Extensive experimental results demonstrate that the proposed MDMN offers more satisfactory and robust detection performance.