Dimensionality Reduction for Signal Detection

A new approach to the problem of dimensionality reduction is proposed. The specific application is to the detection of signals in noise, although it should be applicable to other signal processing problems of current interest. Using a minimum mean square error estimator of the likelihood ratio one can determine a low dimensional statistic, not necessarily linear in the data, that performs well for detection, i.e., with minimal loss of information. If a sufficient statistic does exist for the problem then the proposed approach yields the well known result that one should use the likelihood ratio of the sufficient statistic for detection. Other interesting relationships are explored and some specific examples are given.