5 May 2017 Invariance concepts in spectral analysis
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Abstract
Methods are developed for insuring robust discrimination performance in detection problems with epistemic unknowns. The problem is first solved for the class of problems exhibiting some symmetry, as expressed by invariances to some group of feature space transformations. The determination of whether a problem admits a uniformly most powerful invariant (UMPI) solution (and how to derive it) is solved with a new and simple procedure. This motivates an approach for solving problems where a symmetry is gracefully broken, which leads in turn to a general approach for producing robust detectors. This introduces a new category of detector, the UMPIC (UMPI constrained). Finally, principles of UMPIC construction are shown to apply to problems exhibiting no invariances.
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Alan Schaum, "Invariance concepts in spectral analysis", Proc. SPIE 10198, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXIII, 101980H (5 May 2017); doi: 10.1117/12.2260469; https://doi.org/10.1117/12.2260469
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