Optimal projection for multidimensional signal detection

The concept of projection, in which a set of samples is represented by a single sample, can be used to reduce the dimensionality of the data, thereby simplifying the detection process. A projection method that maximizes the probability of signal detection for a fixed probability of false alarm is derived. Samples containing signal plus noise and noise alone are assumed to be independently and identically distributed, but are otherwise arbitrary. Only one sample in the set of samples projected onto a single sample may contain the signal. It is shown that for high signal-to-noise ratios, the optimal projection algorithm can be approximated as the maximum-value projection scheme, and for low signal-to-noise ratios, it can be viewed as a summation projection algorithm. An example is presented of a computationally efficient 3-D line segment detector that uses maximum value projection. The algorithm is useful for optically detecting meteors, satellites, and other moving targets that move in a straight path across many frames of data