A Fast Recursive LRX Algorithm with Extended Morphology Profile for Hyperspectral Anomaly Detection

In this paper, a fast anomaly target detection method based on morphological profile and improved Reed-Xiaoli (RX) is proposed. First, an extended morphological profile (EMP) containing spatial information is extracted from the original hyperspectral images by means of mathematical morphological transformations. Moreover, a novel fast local RX (FLRX) algorithm is also proposed. This algorithm iteratively updates the inverse matrix of covariance using matrix inversion lemma, thereby reducing the computational complexity of the Mahalanobis distance and improving the algorithm's calculation speed. Finally, a combined EMP and FLRX detector, named the EMP-FLRX method is constructed; as this approach can effectively utilize the spectral information and spatial information of hyperspectral images, it greatly improves detection accuracy and reduces the running time. We compare the proposed method with some classical and recently proposed approaches on six real datasets. the area under the curve (AUC) value of EMP-FLRX on six datasets is 0.9978, 0.9822, 0.9780, 0.9492, 0.9999 and 0.9852 respectively, while the running time is 9.4070, 14.4330, 6.2478, 9.0242, 19.9820, and 1.9060 s respectively. Experimental results clearly demonstrate that the performance of our proposed method is quite competitive in terms of detection accuracy and running time.