The application of a regularization technique to filter synthesis in pattern recognition with synthetic discriminant function filters is presented. The proposed technique uses the stabilizing functional approach for two-dimensional ill-posed problems. Filter synthesis is thus formulated as the minimization of some relevant criteria with specified correlation values for some training input images and limited maximum value of a stabilizing functional. The choice of a particular stabilizing functional to be minimized is related to a priori knowledge regarding the pattern-recognition problem. The analogy between the regularization methods and optimal trade-off filters is also presented and is illustrated with numerical experiments.
© 1994 Optical Society of America
Original Manuscript: May 21, 1993
Revised Manuscript: September 28, 1993
Manuscript Accepted: October 6, 1993
Published: April 1, 1994
Ph. Réfrégier, "Application of the stabilizing functional approach to pattern-recognition filters," J. Opt. Soc. Am. A 11, 1243-1252 (1994)