Optimal maximum correlation filter for arbitrarily constrained devices

Almost all coherent pattern recognition architectures are based on optical correlation of the input with a designed filter. However, the filter can be implemented via many different media, and each medium will impose different realizability constraints on the filter. That is, different media will have different regions of physical realizability. In the past, there has not been much work addressing the problem of designing an optimal filter given an arbitrary region of realizability. This paper presents the theory for just such an optimal filter design. A fast algorithm is presented to implement the theory. The algorithm is demonstrated with two examples.