A Tensor Decomposition-Based Anomaly Detection Algorithm for Hyperspectral Image

Anomalies usually refer to targets with a spot of pixels (even subpixels) that stand out from their neighboring background clutter pixels in hyperspectral imagery (HSI). Compared to backgrounds, anomalies have two main characteristics. One is the spectral anomaly, i.e., their spectral signatures are different from those associated to their surrounding backgrounds; another is the spatial anomaly, i.e., anomalies occur as few pixels (even subpixels) embedded in the local homogeneous backgrounds. However, most of the existing anomaly detection algorithms for HSI only employed the spectral anomaly. If the two characteristics are exploited in a detection method simultaneously, better performance may be achieved. The third-order (two modes for space and one mode for spectra) tensor representation of HSI has been proved to be an effective tool to describe the spatial and spectral information equivalently; therefore, tensor representation is convenient for exhibiting the two characteristics of anomalies simultaneously. In this paper, a new anomaly detection method based on tensor decomposition is proposed and divided into three steps. Three factor matrices and a core tensor are first estimated from the third-order tensor that is constructed from the HSI data cube by using the Tucker decomposition, and their major and minor principal components (PCs) are more likely to correspond to the spectral signatures of the backgrounds and the anomalies, respectively. In the second step, a reconstruction-error-based method is presented to find the first largest PCs along each mode to eliminate the spectral signatures of the backgrounds as much as possible, and thus, the remaining data may be modeled as the spectral signatures of the anomalies with a Gaussian noise. Finally, a CFAR test is implemented to detect the anomalies from the remaining data. Experiments with simulated, synthetic, and real HSI data sets reveal that the proposed method outperforms those spectral-anomaly-based methods with better detection probability and less false alarm rate.

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