Total least squares for anomalous change detection

Abstract

A family of subtraction-based anomalous change detection algorithms is derived from a total least squares (TLSQ) framework. This provides an alternative to the well-known chronochrome algorithm, which is derived from ordinary least squares. In both cases, the most anomalous changes are identified with the pixels that exhibit the largest residuals with respect to the regression of the two images against each other. The family of TLSQbased anomalous change detectors is shown to be equivalent to the subspace RX formulation for straight anomaly detection, but applied to the stacked space. However, this family is not invariant to linear coordinate transforms. On the other hand, whitened TLSQ is coordinate invariant, and special cases of it are equivalent to canonical correlation analysis and optimized covariance equalization. What whitened TLSQ offers is a generalization of these algorithms with the potential for better performance.

Block-diagonal representations for covariance-based Anomalous change detectors

“…Motivated by the ordinary least squares interpretation of the Chronochrome, we recently derived an anomalous change detector using Total Least Squares [5]. We showed that Whitened Total Least Squares (WTLSQ) is equivalent to Optimized Covariance Equalization [6], as well as to the Canonical Correlation Analysis-based Multivariate Alteration Detection [7].…”

“…A number of ACD algorithms can be expressed as quadratic functions of the data, where the coefficients are based on the covariances and cross-covariances of two images [2] being compared. Among these methods are the RX [3], Chronochrome [4], Whitened Total Least Squares (WTLSQ) [5], Covariance Equalization [6], Multivariate Alteration Detection [7], Hyperbolic [8] and Subpixel Hyperbolic [9] methods. The eigenvalue spectrum of coefficient matrices can provide valuable insights into the algebraic and numerical properties of the covariance-based quadratic ACD methods.…”

Efficient Kernel Cook's Distance for Remote Sensing Anomalous Change Detection

“…Although there were related studies before, first focused study of ACD was proposed by Theiler and Perkins using a machine learning approach [9] with many other subsequent studies of Theiler and his colleagues [10]- [17]. In the literature, ACD was tackled using distribution-based [9], [12], distance-based [13], classifier-based [11], and reconstructionbased [18] approaches. Note that ACD is also closely related to anomaly detection [16] and novelty detection [19], where all employ similar approaches.…”

Spatio-spectral anomalous change detection in hyperspectral imagery

“…Instead of a linear regression, one might perform a nonlinear fit, for instance using a neural network [11]: e = y−L(x). Instead of minimizing simple least squares, one can minimize total least squares [12], which leads to a family of algorithms that are mathematically similar to "multivariate alteration detection" [13] and "covariance equalization" [14].…”