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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.
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P. Réfrégier (1994) studied this question.
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