Optimal projection for multidimensional signal detection

The author derives the projection method which maximises the probability of signal detection for a fixed probability of false alarm. Samples containing signal plus noise and noise alone are assumed to have independent, identically distributed distributions, but are otherwise arbitrary. Only one sample in the set of samples projected onto a single sample may contain the signal. Performance of the optimal projection technique is compared with two simpler techniques-maximum value projection and summation projection.<>