Multi-band anomaly detection using signal subspace processing

In the past, many researchers have approached the "Hyperspectral-imagery-anomaly-detection" problem from the point of view of classical detection theory. This perspective has resulted in the development of algorithms like RX (Reed-Xiaoli) and the application of processing techniques like PCA (Principal Component Analysis) and ICA (Independent Component Analysis) - algorithms and techniques that are based primarily on statistical and probabilistic considerations. In this paper we describe a new anomaly detection paradigm based on an adaptive filtering strategy known as "signal subspace processing". The signal-subspace-processing (SSP) techniques on which our algorithm is based have yielded solutions to a wide range of problems in the past (e.g. sensor calibration, target detection, and change detection). These earlier applications, however, utilized SSP to relate reference and test signals that were collected at different times. For our current application, we formulate an approach that relates signals from one spatial region in a hyperspectral image to those from a nearby spatial region in the same image. The motivation and development of the technique are described in detail throughout the course of the paper. We begin by developing the signal subspace processing anomaly detector (SSPAD) and proceed to illustrate how it arises naturally from the adaptive filtering formulation. We then compare the algorithm with existing anomaly-detection schemes, noting similarities and differences. Finally, we apply both the SSPAD and various existing anomaly detectors to a hyperspectral data set and compare the results via receiver operating characteristic (ROC) curves.