Anomaly detection is now a significantly important part of hyperspectral image analysis to detect targets in an unsupervised manner. Traditional hyperspectral anomaly detectors fail to consider spatial information, which is vital in hyperspectral anomaly detection. Moreover, they usually take the raw data without feature extraction as input, limiting the detection performance. We propose a new anomaly detector based on the fractional Fourier transform (FrFT) and a modified patch-image model called the hyperspectral patch-image (HPI) model to tackle these two problems. By combining them, the proposed anomaly detector is named fractional hyperspectral patch-image (FrHPI) detector. Under the assumption that the target patch-image is a sparse matrix while the background patch-image is a low-rank matrix, we first formulate a matrix by sliding a rectangle window on the first three principal components (PCs) of HSI. The matrix can be decomposed into three parts representing the background, targets, and noise with the well-known low-rank and sparse matrix decomposition (LRaSMD). Then, distinctive features are extracted via FrFT, a transformation which is desirable for noise removal. Background atoms are selected to construct the covariance matrix. Finally, anomalies are picked up with Mahalanobis distance. Extensive experiments are conducted to verify the proposed FrHPI detector's superiority in hyperspectral anomaly detection compared with other state-of-the-art detectors.
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