Through the Rayleigh quotient (the ratio of intensity responses of a filter to different objects) we may generalize a great number of metrics used in optical pattern recognition. The Rayleigh quotient has been optimized in linear digital systems under the constraint of unit-energy filters. In optical pattern recognition at least two considerations violate the conditions under which the quotient has been digitally optimized: the noise background of the measurement invokes nonlinearity, and filters are constrained other than to unit energy. I show a solution that optimizes the ratio of biased measurements, subject to constraining filter values to arbitrary subsets of the complex plane. Previous solutions are discussed as special cases. A metric’s numerator and denominator may now both include the objects’ phase.
© 1998 Optical Society of America
Richard D. Juday, "Generalized Rayleigh quotient approach to filter optimization," J. Opt. Soc. Am. A 15, 777-790 (1998)