A spectral-spatial method based on low-rank and sparse matrix decomposition for hyperspectral anomaly detection

ABSTRACT

Recently, some methods based on low-rank and sparse matrix decomposition (LRASMD) have been developed to improve the performance of hyperspectral anomaly detection (AD). However, these methods mainly take advantage of the spectral information in hyperspectral imagery (HSI), and ignore the spatial information. This article proposes an LRASMD-based spectral-spatial (LS-SS) method for hyperspectral AD. First, the Go Decomposition (GoDec) algorithm is employed to solve the low-rank background component and the sparse anomaly component. Next, the sparse component is explored to calculate the spectral sparsity divergence index (SDI). Based on spectral SDI, the detection result in the spectral domain and the reliable background points, which are employed as training data to construct the background manifold by linear local tangent space alignment (LLTSA), can also be obtained. Then, based on the background manifold and the transformation matrix, the low-dimensional manifold of the whole data is computed by linear mapping. After that, the kernel collaborative representation detector (KCRD) is used in the low-dimensional manifold of the whole data for the spatial SDI. Finally, SS SDI is computed for the final detection result. The theoretical analysis and experimental results demonstrate that the proposed LS-SS can achieve better performance when compared with the comparison algorithms.

Acknowledgements

The authors would like to thank the handling editors and the reviewers for providing valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 61571145 and 61405041], the China Postdoctoral Science Foundation [grant number 2014M551221], and the Guiding Technology Project of Daqing [grant number zd-2016-055].