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

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.

Utilizing the Score of Data Distribution for Hyperspectral Anomaly Detection

Hyperspectral images (HSIs) are a type of image that contains abundant spectral information. As a type of real-world data, the high-dimensional spectra in hyperspectral images are actually determined by only a few factors, such as chemical composition and illumination. Thus, spectra in hyperspectral images are highly likely to satisfy the manifold hypothesis. Based on the hyperspectral manifold hypothesis, we propose a novel hyperspectral anomaly detection method (named ScoreAD) that leverages the time-dependent gradient field of the data distribution (i.e., the score), as learned by a score-based generative model (SGM). Our method first trains the SGM on the entire set of spectra from the hyperspectral image. At test time, each spectrum is passed through a perturbation kernel, and the resulting perturbed spectrum is fed into the trained SGM to obtain the estimated score. The manifold hypothesis of HSIs posits that background spectra reside on one or more low-dimensional manifolds. Conversely, anomalous spectra, owing to their unique spectral signatures, are considered outliers that do not conform to the background manifold. Based on this fundamental discrepancy in their manifold distributions, we leverage a generative SGM to achieve hyperspectral anomaly detection. Experiments on the four hyperspectral datasets demonstrate the effectiveness of the proposed method. The code is available at https://github.com/jiahuisheng/ScoreAD.