Robust Nonnegative Matrix Factorization Based Background Reconstruction for Hyperspectral Image Anomaly Detection

In the anomaly detection of hyperspectral images (HSIs), aiming at the difficulty of distinguishing the abnormal target from the background and the low accuracy of background prediction, a new HSI anomaly detection approach based on robust nonnegative matrix factorization(NMF) background reconstruction is proposed. In this approach, a more robust new form objective function is introduced into the NMF process to improve the adaptability to noise and outliers, and a new background reconstruction objective function can be obtained. However, the new objective function is non-convex. The global optimal solution of one variable can be obtained when the other is fixed. Thus, we propose an efficient multiplicative updating algorithm with the theory of the iterative reweighted least squares. Finally, when iterative convergences, we can obtain the extracted endmembers and estimated abundances to reconstruct the background. Then, the reconstructed background image was subtracted from the origin image to obtain the residual image. Finally, the anomaly detection is achieved by using the local anomaly detector to traverse the residual image. Furthermore, the effectiveness of the HSI anomaly detection algorithm proposed based on robust NMF background reconstruction is illustrated in a series of real-world data experiments.