Variable factorization model based on numerical optimization for hyperspectral anomaly detection

The objective of this article is to develop an anomaly detector as an analytical expression for detecting anomalous objects in remote sensing using hyperspectral imaging. Conventional anomaly detectors based on the subspace model have a parameter which is the dimension of the clutter subspace. The range of possible values for this parameter is typically large, resulting in a large number of images of detector output to be analyzed. An anomaly detector with a different parameter is proposed. The pixel of known random variables from a data cube is modeled as a linear transformation of a set of unknown random variables from the clutter subspace plus an error of unknown random variables in which the transformation matrix of constants is also unknown. The dimension of the clutter subspace for each spectral component of the pixel can vary, hence some elements in the transformation matrix are constrained to be zeros. The anomaly detector is the Mahalanobis distance of the resulting residual. The experimental results which are obtained by implementing the anomaly detector as a global anomaly detector in unsupervised mode with background statistics computed from hyperspectral data cubes with wavelengths in the visible and near-infrared range show that the parameter in the anomaly detector has a significantly reduced number of possible values in comparison with conventional anomaly detectors.