28 August 1995 Optimization algorithm to choose the region of support in a filter whose entries are zero or continuous phase
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Abstract
An algorithm to choose the region of support in a filter whose entries are either 0 or a continuous phase is presented. Such filters will be termed ZAP filters since their entries come from the set consisting of 0 and phases (complex numbers of modulus one). This paper is an immediate sequel to ideas presented previously. As in this previuos work, the algorithm involves a simple thresholding technique applied to the general spatial filter whose design is described. In the technique described the choice of threshold is made by the user in an ad hoc manner. Here the optimal threshold is chosen to be that threshold whose selection results are sometimes surprising. Examples of such are presented here. Having fixed those pixels which are 0 in the ZAP filter, one can then view the remaining phases as free parameters and design a good ZAP filter by optimizing the filter's signal-to-clutter ratio using the author's techniques. One can then optimally discretize this ZAP filter into one whose entries are 0 or one of the nth roots of unity. For example, ternary (o, +1, and -1) filters are of this form as are filters whose entries are 0 and the fifteenth roots of unity. These ideas form the basis for a sequence of computer codes which provide a completely automatic way to start with a training set of true and false targets of any size and automatically and without human intervention produce optimized filters for use in extent and future optical correlators.
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Robert R. Kallman, "Optimization algorithm to choose the region of support in a filter whose entries are zero or continuous phase", Proc. SPIE 2565, Optical Implementation of Information Processing, (28 August 1995); doi: 10.1117/12.217664; https://doi.org/10.1117/12.217664
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