Theoretical framework for the design of purely real synthetic-discriminant-function-type correlation filters
A general algorithm for synthesizing purely real correlation filters in the frequency domain is developed by using the method of Lagrange multipliers. This method can be applied to filters that are derived by using linearly constrained quadratic minimization. The synthesis of purely real versions of minimum average correlation energy filters, minimum-variance synthetic discriminant functions, and other synthetic-discriminant-function-type filters is discussed to illustrate this approach. Their performance is found to be somewhat less than that of the original complex filters but still adequate for practical applications. The main advantage of this approach is that optimum purely real filters can be generated that are easy to implement in spatial light modulators without holograms and that yield the correlation output on the zero-order beam.