Sparse matrix decomposition and low rank based techniques for anomaly detection in hyperspectral images

Hyperspectral imagery is a popular remote sensing technology to distinguish materials on the ground surface. The reflected and emitted radiation detected by a high number of narrow, contiguous, and continuous spectral bands are collected by imaging spectrometers. They are, then, analyzed, and evaluated by this technology. Hyperspectral image processing techniques have been applied in many application fields with different aims, such as in military for target detection, in agriculture to classify crops, in nourishment to determination of freshness of food, in medicine detecting diseased areas. In this study, a sparse and low-rank matrix decomposition-based anomaly detection method for hyperspectral data is proposed. High dimensional data is decomposed into low-rank and sparse matrices representing background and anomalies, respectively. The problem of the decomposition process is defined from the dictionary learning point of view. Therefore, the way of obtaining these matrices differs from previous studies. It aims to find a correct partition of the data and separate anomaly pixels from the background. After decomposition, Mahalanobis Distance is applied to the sparse part of the data in order to get anomaly locations. Experimental results suggest that anomaly detection performance of the proposed method surpasses those of the state-of-the-art methods.