Beyond the adaptive matched filter: nonlinear detectors for weak signals in high-dimensional clutter

For known signals that are linearly superimposed on gaussian backgrounds, the linear adaptive matched filter (AMF) is well-known to be the optimal detector. The AMF has furthermore proved to be remarkably effective in a broad range of circumstances where it is not optimal, and for which the optimal detector is not linear. In these cases, nonlinear detectors are theoretically superior, but direct estimation of nonlinear detectors in high-dimensional spaces often leads to flagrant overfitting and poor out-of-sample performance. Despite this difficulty in the general case, we will describe several situations in which nonlinearity can be effectively combined with the AMF to detect weak signals. This allows improvement over AMF performance while avoiding the full force of dimensionality's curse.

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