Phase extraction pattern recognition is a special case of nonlinear matched filtering. The phase extraction procedure is executed on the input function's Fourier transform as well as on the filter function's Fourier transform, both of which are manipulated for correlation purposes. This novel process is examined theoretically, by computer simulations and laboratory experiments. The implementation of a coherent electro-optical phase extraction pattern recognition system demonstrates the advantages of this new approach.

Image restoration from degraded observations and from properties that the image is supposed to satisfy has been approached by the method of projections onto convex constraint sets. Previous attempts have incorporated only partially the knowledge that we possess about the image to be restored because of difficulties in the implementation of some of the projections. In the parallel-projection algorithm presented here the a priori knowledge can be fully exploited. Moreover, the algorithm operates well even if the constraints are nonconvex and/or if the constraints have an empty intersection, without a limitation on the (finite) number of constraint sets.

Multiple-object input to the recently introduced phase-extraction correlator may cause difficulties owing to interference effects. Similar effects have been observed previously in the nonlinear joint transform correlator. It is shown theoretically and by computer simulations that these effects are seldom observable in practice, and even then they can be substantially reduced by employing a proper space-variant threshold. The implementation of this scheme by a hybrid electro-optical architecture is also explained briefly and demonstrated. The results presented permit manipulation of information (spectral phase) that was previously believed to be contaminated beyond recovery.

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Mutually orthogonal pattern distortions are handled by an adaptive optical recognition system. A double-channel system is presented that implements pattern recognition with rotation, scale, and shift invariance. The recognition process is based on a two-stage operation: An object-independent determination of one distortion parameter (the scale, in the example presented here) is performed, and then the recognition is completed by a shift- and rotation-invariant optical correlator that is adapted to the measured parameter. Thus, complete invariance to three distortion parameters is achieved by the combination of two channels. The overall process is performed efficiently and can be executed in real time.