Block diagonal representations for covariance based anomalous change detectors
- Los Alamos National Laboratory
Change detection methods are of crucial importance in many remote sensing applications such as monitoring and surveillance, where the goal is to identify and separate changes of interest from pervasive changes inevitably present in images taken at different times and in different environmental and illumination conditions. Anomalous change detection (ACD) methods aim to identify rare, unusual, or anomalous changes among the changes of interest. Covariance-based ACD methods provide a powerful tool for detection of unusual changes in hyper-spectral images. In this paper we study the properties of the eigenvalue spectra of a family of ACD matrices in order to better understand the algebraic and numerical behavior of the covariance-based quadratic ACD methods. We propose to use singular vectors of covariance matrices of two hyper-spectral images in whitened coordinates for obtaining block-diagonal representations of the matrices of quadratic ACD methods. SVD transformation gives an equivalent representation of ACD matrices in compact block-diagonal form. In the paper we show that the eigenvalue spectrum of a block-diagonal ACD matrix can be identified analytically as a function of the singular value spectrum of the corresponding covariance matrix in whitened coordinates.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 979683
- Report Number(s):
- LA-UR-09-07941; LA-UR-09-7941; TRN: US201011%%380
- Country of Publication:
- United States
- Language:
- English
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