The linear matched filter has long served as a workhorse algorithm for illustrating the promise of multispectral target detection. However, an accurate description of a target's distribution usually requires expanding the dimensionality of its intrinsic signature subspace beyond what is appropriate for the matched filter. Structured backgrounds also deviate from the matched filter paradigm and are often modeled as clusters. However, spectral clusters usually show evidence of mixing, which corresponds to the presence of different materials within a single pixel. This makes a subspace background model an attractive alternative to clustering. In this paper we present a new method for generating detection algorithms based on joint target/background subspace modeling. We use it first to derive an existing class of GLF detectors, in the process illustrating the nature of the real problems that these solve. Then natural symmetries expected to be characteristic of otherwise unknown target and background distributions are used to generate new algorithms. Currently employed detectors are also interpreted using the new approach, resulting in recommendations for improvements to them.
Alan P. Schaum, Alan P. Schaum,
"Spectral subspace matched filtering", Proc. SPIE 4381, Algorithms for Multispectral, Hyperspectral, and Ultraspectral Imagery VII, (20 August 2001); doi: 10.1117/12.436996; https://doi.org/10.1117/12.436996