Sparse and collaborative representation-based anomaly detection
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ORIGINAL PAPER
Sparse and collaborative representation-based anomaly detection Maryam Imani1 Received: 8 February 2019 / Revised: 29 April 2020 / Accepted: 8 May 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract A sparse and collaborative representation-based detector (SCRD) is proposed in this work. It uses the benefits of both sparse and collaborative representation for anomalous target detection. Anomalies compose the minority of image scene. So, sparse representation that involves a low number of dictionary’s atoms is an appropriate approach for estimating of targets. In contrast, the background pixels compose the majority of image scene. So, collaborative representation, which utilizes all atoms of dictionary, is a desired representation to model the background data. The used dictionary in sparse representation is constituted from the anomalous pixels, while the used dictionary in collaborative representation is constituted from the background ones. The proposed SCRD method has high probability of detection and low computations in comparison with several state-of-the-art anomaly detectors. The superior performance of SCRD is shown on both synthetic and real hyperspectral images. Keywords Sparse representation · Collaborative representation · Dictionary · Hyperspectral image · Anomaly detection
1 Introduction Hyperspectral images are rich sources of spectral information about the Earth’s surface [1, 2]. Hyperspectral sensor by acquiring hundreds of spectral channels provides a hypercube image with high spectral resolution. So, discrimination among different materials is possible even with similar spectral characteristics. Therefore, hyperspectral images have been successfully used in many classification and target detection problems [3–9]. Both of these applications can be implemented supervised or unsupervised. The unsupervised target detection is known as anomaly detection [10–12]. Due to no requirement to prior knowledge about the spectral characteristics of targets, anomaly detection is a very interesting and attractive topic in researches of remote sensing. Anomaly detection has been widely used in border surveillance, mine detection, search missions and so other applications [13, 14]. The RX algorithm is known as a benchmark anomaly detector, which has been widely implemented for multispectral and hyperspectral images [15]. This detector is based on calculation of Mahalanobis distance of each pixel from
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Maryam Imani [email protected] Image Processing and Information Analysis Lab, Faculty of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran
the background clutter. The global RX globally calculates the mean vector and covariance matrix, while the local RX locally estimates the background statistics. The RX detector has some disadvantages. First, the background statistics may be contaminated by anomalous pixels. Anomalous targets degrade stability of the calculated Mahalanobis distance, and so, the performance of RX is unstable. Second, R
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