Adaptive detection of signals with linear feature mappings and representations

In a previous paper, Reed (1993) developed a new test function for detecting a 2-D signal with limited prior information about the signal waveform and the statistical properties of clutter. This was accomplished by substituting a maximum likelihood estimate (MLE) of the unknown clutter covariance matrix and the MLE's of the amplitudes of the selected signal-feature components into a maximum invariant ratio test. However, performance analyses of this detector were not obtained. In this paper, the test statistic in Reed's previous paper is extended to the complex domain for application to synthetic aperture radar (SAR) imagery. The performance of the detector is studied analytically. Closed-form expressions for the performance of the detector, under both hypotheses H/sub 0/ and H/sub 1/ are obtained. The theoretical results show that the detectability of the test is strongly effected by the feature mapping and selection techniques used to represent a signal. Here the effectiveness of a feature representation is evaluated in terms of the number of features needed to represent a signal and the separability of those features from the clutter background. The dependence of the detection probability on the effectiveness of the features is quantitatively shown by a set of performance curves. The resulting analyses indicate that the detector has the property of a constant false alarm rate (CFAR). To make the results of the detection performance analysis more applicable to real problems, the loss due to a "mismatched feature" representation is also studied analytically.