A Geometric Matched Filter for Hyperspectral Target Detection and Partial Unmixing

In this letter, a new geometric matched filter (MF) is proposed by combining the standard MF with concepts of convex geometry. The purpose of the method is twofold: for subpixel target detection and for partial unmixing of a hyperspectral image. In standard matched filtering, the filter is designed based on the background statistics of the entire image, which works fine for rare targets but fails when the target is frequently present throughout the whole image. In the presented method, the background is restricted to pixels that have a zero contribution to the target spectrum. These background pixels are identified based on the simplex formed by the target and other relevant endmembers of the data set. Experiments are conducted for the specific case of targets which are frequently present in an image. The presented method is shown to outperform standard matched filtering and orthogonal subspace projection for target detection, and for the estimation of the target abundances.