Utilizing the Score of Data Distribution for Hyperspectral Anomaly Detection

TL;DR

ScoreAD integrates the manifold hypothesis with a score-based generative model to detect anomalies in hyperspectral images. By training on all spectra and using Gaussian perturbations per spectrum, ScoreAD estimates local score directions and aggregates them to quantify anomaly degree, exploiting the contrasting score-field behavior for on-manifold versus off-manifold points. The method delivers strong, consistent detection performance across HYDICE, Pavia, Hyperion, and Salinas datasets and demonstrates robustness to perturbation settings and neighborhood conditioning. This approach offers a principled, model-based HAD framework with potential applicability to other domains where normal data lie on a manifold but anomalies depart from it.

Abstract

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.

Figures (9)

• Figure 1: t-SNE visualization of Salinas dataset.
• Figure 2: Illustration of the differences between the score field around datapoint on the manifold and the score field around datapoint outside the manifold. The scores obtained from the perturbed datapoint of green datapoint (on manifold) are orthogonal to manifold and have diverse directions, while the scores around red datapoint have a consistent direction.
• Figure 3: Overall architecture of ScoreAD. The spectrum marked with red star represents the test spectrum, and the spectra around test spectrum are the contextual spectra within a dual-window neighborhood. The test spectrum is first perturbed via a Gaussian perturbation kernel to obtain a perturbed spectrum, which is then fed into the score-based generative model (SGM) along with its contextual spectra to estimate the score.
• Figure 4: The pseudo-color image, Ground Truth, and hyperspectral anomaly detection maps of the comparison methods on four hyperspectral datasets.
• Figure 5: Box-whisker plots of different methods on four datasets. Greater separability between the background and anomalies indicates better detection performance.

Theorems & Definitions (3)

• proof
• proof
• proof