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

Abstract

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 highdimensional 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.

Is there a best hyperspectral detection algorithm?

“…Although this approach may provide some additional insight to existing detection algorithms, the resulting algorithms cannot be easily applied to practical applications. A nice discussion of several extensions to classical detection algorithms is given in 31 and the provided references.…”

“…The quadratic detector is reduced to the linear matched filter (31) if Σ t = Σ b or if the observations are described by the additive signal model (39). The additive signal model assumes a fixed target with known shape and unknown amplitude.…”

Passive optoelectronics systems for standoff gas detection: results of tests

“…There are several ways to arrive at this expression [19]. One method is to maximize a signal-to-clutter ratio much like the one maximized for Fisher's discriminant.…”

“…Though there are many paths to consider, there are only a few that significantly contribute to the signal measured at the sensor in LWIR measurements. Only those important paths will be considered in this development, which is drawn mainly from the literature focusing on the detection problem, but also from some work done on artificial plume insertion [18,19,[21][22][23]. Firstly, a model will be developed for paths that arrive at a sensor which is pointed at the ground, but not viewing any gaseous plumes in the atmosphere.…”

“…An operation range of the interferometer is 3-5 m (MWIR version) or 8-12 m (LWIR) and tuning velocity is of about [10][11][12][13][14][15][16][17][18][19][20] ms. An interferometer module, containing a detector matrix, has been developed by the Physical Sciences, Inc. and it is known as AIRIS (Adaptive InfraRed Imaging Spectroradiometer) [2].…”