Abstract

The conventional synthetic discriminant functions (SDF’s) determine a filter matched to a linear combination of the available training images such that the resulting cross-correlation output is constant for all training images. We remove the constraint that the filter must be matched to a linear combination of training images and consider a general solution. This general solution is, however, still a linear combination of modified training images. We investigate the effects of noise in input training images and prove that the conventional SDF’s provide minimum output variance when the input noise is white. We provide the design equations for minimum-variance synthetic discriminant functions (MVSDF’s) when the input noise is colored. General expressions are also provided to characterize the loss of optimality when conventional SDF’s are used instead of optimal MVSDF’s.

© 1986 Optical Society of America

Full Article  |  PDF Article

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (30)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription