Generality of matched filtering and minimum Euclidean distance projection for optical pattern recognition

Matched filtering followed by a minimum Euclidean distance projection onto realizable filter values was previously shown to optimize the signal-to-noise ratio for single training images in optical correlation pattern recognition. The algorithm is now shown to solve the combination of(1) standard statistical pattern-recognition metrics with multiple training images, (2) additive input noise of known power spectral density and also additive detection noise that is irreducible by the filter, (3) the building of the filter on arbitrary subsets of the complex unit disk, and (4) the use of observable correlator outputs only. The criteria include the Fisher ratio, the Bayes error and Bayes cost, the Chernoff and Bhattacharyya bounds, the population entropy and expected information, versions of signal-to-noise ratio that use other than second power in their norm, and the area under the receiver operating characteristic curve. Different criteria are optimized by different complex scalar weights.