Turbo-GoDec: Exploiting the Cluster Sparsity Prior for Hyperspectral Anomaly Detection

TL;DR

This work tackles hyperspectral anomaly detection by leveraging a cluster sparsity prior for anomalies. It extends the GoDec framework to include a CSP term, modeling the anomaly support with a grid-like Markov random field and performing inference via message passing on a factor graph to produce pixelwise anomaly probabilities. The method, Turbo-GoDec, outputs a low-rank background, a sparse anomaly component, and an anomaly-probability map, which are combined with RX to form the final detection map. Experiments on HYDICE Urban, Pavia, and Hyperion datasets show competitive detection performance and notably improved background suppression, illustrating the practical value of actively exploiting cluster sparsity in HAD; code is publicly available.

Abstract

As a key task in hyperspectral image processing, hyperspectral anomaly detection has garnered significant attention and undergone extensive research. Existing methods primarily relt on two prior assumption: low-rank background and sparse anomaly, along with additional spatial assumptions of the background. However, most methods only utilize the sparsity prior assumption for anomalies and rarely expand on this hypothesis. From observations of hyperspectral images, we find that anomalous pixels exhibit certain spatial distribution characteristics: they often manifest as small, clustered groups in space, which we refer to as cluster sparsity of anomalies. Then, we combined the cluster sparsity prior with the classical GoDec algorithm, incorporating the cluster sparsity prior into the S-step of GoDec. This resulted in a new hyperspectral anomaly detection method, which we called Turbo-GoDec. In this approach, we modeled the cluster sparsity prior of anomalies using a Markov random field and computed the marginal probabilities of anomalies through message passing on a factor graph. Locations with high anomalous probabilities were treated as the sparse component in the Turbo-GoDec. Experiments are conducted on three real hyperspectral image (HSI) datasets which demonstrate the superior performance of the proposed Turbo-GoDec method in detecting small-size anomalies comparing with the vanilla GoDec (LSMAD) and state-of-the-art anomaly detection methods. The code is available at https://github.com/jiahuisheng/Turbo-GoDec.

Figures (11)

• Figure 1: An example of the factor graph. The joint probability is factored as the product of three factor nodes.
• Figure 2: The overall framework of Turbo-GoDec. As shown in the figure, Turbo-GoDec has three inputs: the hyperspectral image $X$, the rank constraint $r$ for the low-rank component, and the sparsity constraint (cardinality) $k$ for the sparse component. The process of Turbo-GoDec can be viewed as alternating updates of the L-step and S-step. The L-step computes the low-rank component, while the S-step calculates the sparse component. Finally, after the iterations stop, Turbo-GoDec outputs the low-rank component $L$, the sparse component $S$, and the anomalous probability $J$ in the hyperspectral image.
• Figure 3: The factor graph used in Turbo-GoDec. This factor graph is equivalent to the factorization of the joint probability expressed in Eq. \ref{['eq:rewritte joint Posterior Probability']}.
• Figure 4: Markov Random Field and its factor graph.
• Figure 5: The pseudo-color image and Groundtruth of three hyperspectral datasets.