Geometric matched filter for hyperspectral partial unmixing

In this paper, a new geometric matched filter is presented by combining the standard matched filtering with concepts of convex geometry. The purpose of the method is partial unmixing of a hyperspectral image, where an estimate is given for the relative contribution of each pixel to a specific target spectrum. In standard matched filtering, the filter is designed based on the background statistics of the entire image, which works fine when the target is contained in a limited number of pixels, but fails when the target is abundantly present throughout the whole image. The presented method calculates the filter based on the statistics of pixels that do not contain the target spectrum. These background pixels are identified based on the simplex formed by the target and other relevant endmembers of the dataset. In the experiments, the presented method is shown to outperform standard matched filtering for partial unmixing.