Randomized subspace-based robust principal component analysis for hyperspectral anomaly detection

Weiwei Sun; Gang Yang; Jialin Li; Dianfa Zhang

doi:10.1117/1.JRS.12.015015

2 March 2018 Randomized subspace-based robust principal component analysis for hyperspectral anomaly detection

Weiwei Sun, Gang Yang, Jialin Li, Dianfa Zhang

Author Affiliations +

Journal of Applied Remote Sensing, Vol. 12, Issue 1, 015015 (March 2018). https://doi.org/10.1117/1.JRS.12.015015

Abstract

A randomized subspace-based robust principal component analysis (RSRPCA) method for anomaly detection in hyperspectral imagery (HSI) is proposed. The RSRPCA combines advantages of randomized column subspace and robust principal component analysis (RPCA). It assumes that the background has low-rank properties, and the anomalies are sparse and do not lie in the column subspace of the background. First, RSRPCA implements random sampling to sketch the original HSI dataset from columns and to construct a randomized column subspace of the background. Structured random projections are also adopted to sketch the HSI dataset from rows. Sketching from columns and rows could greatly reduce the computational requirements of RSRPCA. Second, the RSRPCA adopts the columnwise RPCA (CWRPCA) to eliminate negative effects of sampled anomaly pixels and that purifies the previous randomized column subspace by removing sampled anomaly columns. The CWRPCA decomposes the submatrix of the HSI data into a low-rank matrix (i.e., background component), a noisy matrix (i.e., noise component), and a sparse anomaly matrix (i.e., anomaly component) with only a small proportion of nonzero columns. The algorithm of inexact augmented Lagrange multiplier is utilized to optimize the CWRPCA problem and estimate the sparse matrix. Nonzero columns of the sparse anomaly matrix point to sampled anomaly columns in the submatrix. Third, all the pixels are projected onto the complemental subspace of the purified randomized column subspace of the background and the anomaly pixels in the original HSI data are finally exactly located. Several experiments on three real hyperspectral images are carefully designed to investigate the detection performance of RSRPCA, and the results are compared with four state-of-the-art methods. Experimental results show that the proposed RSRPCA outperforms four comparison methods both in detection performance and in computational time.

Citation Download Citation

Weiwei Sun, Gang Yang, Jialin Li, and Dianfa Zhang "Randomized subspace-based robust principal component analysis for hyperspectral anomaly detection," Journal of Applied Remote Sensing 12(1), 015015 (2 March 2018). https://doi.org/10.1117/1.JRS.12.015015

Received: 3 November 2017; Accepted: 5 February 2018; Published: 2 March 2018

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