Sparse linear filters for detection and classification in hyperspectral imagery

Abstract

We investigate the use of convex optimization to identify sparse linear filters in hyperspectral imagery. A linear filter is sparse if a large fraction of its coefficients are zero. A sparse linear filter can be advantageous because it only needs to access a subset of the available spectral channels, and it can be applied to high-dimensional data more cheaply than a standard linear detector. Finding good sparse filters is nontrivial because there is a combinatorially large number of discrete possibilities from which to choose the optimal subset of nonzero coefficients. But, by converting the optimality criterion into a convex loss function, and by employing an L1 penalty, one can obtain sparse solutions that are globally optimal. We investigate the performance of these sparse filters as a function of their sparsity, and compare the convex optimization approach with more traditional alternatives for feature selection. The methodology is applied both to the adaptive matched filter for weak signal detection, and to the Fisher linear discriminant for terrain categorization.