Many realistic detection problems cannot be solved with simple statistical tests for known alternative probability models. Uncontrollable environmental conditions, imperfect sensors, and other uncertainties transform simple detection problems with likelihood ratio solutions into composite hypothesis (CH) testing problems. Recently many multi- and hyperspectral sensing CH problems have been addressed with a new approach. Clairvoyant fusion (CF) integrates the optimal detectors (“clairvoyants”) associated with every unspecified value of the parameters appearing in a detection model. For problems with discrete parameter values, logical rules emerge for combining the decisions of the associated clairvoyants. For many problems with continuous parameters, analytic methods of CF have been found that produce closed-form solutions–or approximations for intractable problems. Here the principals of CF are reviewed and mathematical insights are described that have proven useful in the derivation of solutions. It is also shown how a second-stage fusion procedure can be used to create theoretically superior detection algorithms for ALL discrete parameter problems.
Alan Schaum, "Clairvoyant fusion: a new methodology for designing robust detection algorithms," Proc. SPIE 10004, Image and Signal Processing for Remote Sensing XXII, 100040C (Presented at SPIE Remote Sensing: September 26, 2016; Published: 18 October 2016); https://doi.org/10.1117/12.2240092.
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