Abstract

A generalization of the conventional synthetic discriminant function (SDF) solution in both spatial and frequency domains is provided. It is based on the concept of the generalized inverse. The results of this generalization are shown to specialize to previous work (namely, the minimum-output-variance SDF). A link is established between the quantities characterizing the spatial-domain SDF solutions and the frequency-domain ones through the pseudo-discrete Fourier-transform operation. Several properties of the various relevant matrices are presented to provide a general framework for characterizing SDF solutions. To help to illustrate the advantages of the generalized SDF solution method, two examples of SDF’s (a phase-only and a two-level SDF) are investigated.

© 1988 Optical Society of America

Minimum-variance synthetic discriminant functions

B. V. K. Vijaya Kumar
J. Opt. Soc. Am. A 3(10) 1579-1584 (1986)

Constraint phase optimization in minimum variance synthetic discriminant functions

B. V. K. Vijaya Kumar, Zouhir Bahri, and Abhijit Mahalanobis
Appl. Opt. 27(2) 409-413 (1988)

Selection of optimum output correlation values in synthetic discriminant function design

S. I. Sudharsanan, A. Mahalanobis, and M. K. Sundareshan
J. Opt. Soc. Am. A 7(4) 611-616 (1990)

Unified synthetic discriminant function computational formulation

David Casasent
Appl. Opt. 23(10) 1620-1627 (1984)

Theoretical framework for the design of purely real synthetic-discriminant-function-type correlation filters

Abhijit Mahalanobis and Sewoong Song
Appl. Opt. 31(35) 7450-7456 (1992)