Sparse Matrix Transform for Hyperspectral Image Processing

A variety of problems in remote sensing require that a covariance matrix be accurately estimated, often from a limited number of data samples. We investigate the utility of several variants of a recently introduced covariance estimator-the sparse matrix transform (SMT), a shrinkage-enhanced SMT, and a graph-constrained SMT-in the context of several of these problems. In addition to two more generic measures of quality based on likelihood and the Frobenius norm, we specifically consider weak signal detection, dimension reduction, anomaly detection, and anomalous change detection. The estimators are applied to several hyperspectral data sets, including some randomly rotated data, to elucidate the kinds of problems and the kinds of data for which SMT is well or poorly suited. The SMT is based on the product of
K
pairwise coordinate (Givens) rotations, and we also introduce and compare two novel approaches for estimating the most effective choice for
K
.