Anomaly Detection and Reconstruction From Random Projections

• Published in: IEEE transactions on image processing Vol. 21; no. 1; pp. 184 - 195
• Main Authors: Fowler, J. E., Qian Du
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2012; Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Anomaly detection; Applied sciences; Clutter; compressed sensing (CS); Computer Simulation; Detectors; Exact sciences and technology; hyperspectral data; Hyperspectral imaging; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Image reconstruction; Information, signal and communications theory; Models, Statistical; Pattern Recognition, Automated - methods; Pixel; principal component analysis (PCA); Reproducibility of Results; Sampling, quantization; Sensitivity and Specificity; Signal and communications theory; Signal processing; Signal Processing, Computer-Assisted; Signal to noise ratio; Subtraction Technique; Telecommunications and information theory; Hyperspectral imaging sensor; Dimension reduction; hyperspectral data; compressed sensing (CS); Simulation; Hyperspectral imagery; principal component analysis (PCA); Compressed sensing; Anomaly detection
• ISSN: 1057-7149; 1941-0042; 1941-0042
• DOI: 10.1109/TIP.2011.2159730

Compressed-sensing methodology typically employs random projections simultaneously with signal acquisition to accomplish dimensionality reduction within a sensor device. The effect of such random projections on the preservation of anomalous data is investigated. The popular RX anomaly detector is derived for the case in which global anomalies are to be identified directly in the random-projection domain, and it is determined via both random simulation, as well as empirical observation that strongly anomalous vectors are likely to be identifiable by the projection-domain RX detector even in low-dimensional projections. Finally, a reconstruction procedure for hyperspectral imagery is developed wherein projection-domain anomaly detection is employed to partition the data set, permitting anomaly and normal pixel classes to be separately reconstructed in order to improve the representation of the anomaly pixels.